Structure analysis LRFD steel design

sikSaKNnaeRKOgbgÁúMGMBIEdk LRFD STEEL DESIGN

GñkniBn§³ WIILIAM T. SEGUI bkERbeday³ etg qay

viTüasßanCatiBhubec©keTskm<úCa mhaviTüal½ysMNg;sIuvil

qñaM 2010

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

matika i T.Chhay

matika Contents

I. esckþIepþIm (Introduction)

1>1> karsikSaKNnaeRKOgbgÁúM (Structural Design) ..............................................................1

1>2> bnÞúk (Loads)...............................................................................................................4

1>3> Building Codes .......................................................................................................... 5

1>4> Design Specifications ..................................................................................................5

1>5> eRKOgbgÁúMGMBIEdk (Structural Steel) ...............................................................................6 1>6> rUbragmuxkat;bTdæan (standard Cross-sectional Shapes) ............................................11

II. eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁÁúMEdk (Concepts in Structural Steel Design)

2>1> TsSnviC¢akñúgkarsikSaKNnamuxkat; (Design Philosophies) ...................................... 20

2>2> American Institute of Steel Construction Specification ......................................... 22 2>3> emKuNersIusþg; nigemKuNbnÞúkEdleRbIR)as;enAkñúg AISC Specification

(Load and Resistance Factors Used in the AISC Specification) ............................. 23

2>4> mUldæanRbU)ab‘ÍlIetrbs; Load and Resistance Factors (Probabilistic Basis of Load and Resistance Factors) ............................................. 25

2>5> Manual of Steel Construction ................................................................................. 30

III. eRKOgbgÁúMrgkarTaj (Tension Members)

3>1> esckþIepþIm (Introduction) ......................................................................................... 30

3>2> ersIusþg;KNna (Design strength) ............................................................................. 31

3>3> RkLaépÞmuxkat;suT§RbsiT§PaB (Effective net area) .................................................... 36

3>4> karteRmobtamEbbqøas ; (Staggered fasteners) ......................................................... 43

3>5> Block shear ............................................................................................................. 50

3>6> karKNnaGgát;rgkarTaj (Design of tension members) .......................................... 52

3>7> EdksrésEdlmaneFμj nigExSkab (Threaded rods and Cables) ................................ 59

mhaviTüal½ysMNg;sIuvil NPIC

T.Chhay ii Contents

3>8> Ggát;rgkarTajenAkñúgdMbUl (Tension members in roof trusses) ............................... 61

3>9> Ggát;EdltPa¢b;edayknøas; (Pin-Connection Members) ........................................... 70

IV. eRKOgbgÁúMrgkarsgát; Compression Members

4>1> esckþIepþIm (introduction) .......................................................................................... 73 4>2> RTwsþIssr(Column Theory) ....................................................................................... 73

4>3> tRmUvkarrbs; AISC (AISC Requirements) ............................................................ 82

4>4> karKNnamuxkat; (Design) ......................................................................................... 89

4>5> esckþIbEnßmsRmab;RbEvgRbsiT§PaB (More on Effective Length) .............................. 92

4>6>karekagedayrmYl nigedayBt;-rmYl (Torsional and Flexural-Torsional Buckling) . 105

4>7> Built-up Member .................................................................................................... 112

V. Fñwm Beams

5>1> esckþIepþIm (Introduction) ........................................................................................ 120

5>2> kugRtaMgBt; nigm:Um:g;)øasÞic (Bending Stress and the Plastic Moment) ...................... 121 5>3> lMnwg (Stability) ...................................................................................................... 127 5>4> cMNat;fñak;rbs;rUbrag (Classification of Shapes) ..................................................... 129

5>5> Bending Strength of Compact Shapes .................................................................. 130

5>6> Bending Strength of Noncompact Shapes............................................................. 140

5>7> Summary of Moment Strength ............................................................................. 144

5>8> ersIusþg;kmøaMgkat;TTwg (Shear Strength) ................................................................. 145

5>9> PaBdab (Deflection) ............................................................................................... 152

5>10> karKNnamuxkat; (Design) ................................................................................... 154

5>11> rn§RbehagenAkñúgFñwm (Holes in Beam).................................................................. 165

5>12> Open-Web Steel Joists ....................................................................................... 167

5>13> bnÞHRTFñwm nigbnÞH)atssr (Beam Bearing Plates and Column Base Plate) ...... 171


matika iii T.Chhay

5>14> Biaxial Bending ................................................................................................. 182

5>15> ersIusþg;m:Um:g;Bt;rbs;rUbragepSg² (Bending Strength of Various Shape) .............. 190

VI. Fñwm-ssr Beam-Columns

6>1> esckþIepþIm (Introduction) ....................................................................................... 197

6>2> smIkarGnþrkmμ (Interaction Formulas) .................................................................. 198

6>3> m:Um:g;bEnßm (Moment Amplification) .................................................................... 201

6>4> Web Local Buckling in Beam-Columns .............................................................. 204

6>5> eRKagBRgwg nigeRKagGt;BRgwg (Braced versus Unbraced Frame).............................. 206

6>6> Ggát;enAkñúgeRKagEdlBRgwg (Members in Braced Frames) ....................................... 207

6>7> Ggát;enAkñúgeRKagEdlminBRgwg (Members in Unbraced Frames) .............................. 217

6>8 KNnamuxkat;Fñwm-ssr (Design of Beam-Column) ................................................ 224

6>9> Trusses With Top Chord Loads Between Joints ................................................... 234

VII. tMNsamBaØ Simple Connections

7>1> esckþIepþIm (Introduction) ..................................................................................... 241

7>2> Bolted Shear Connections: Failure Mode ............................................................ 244

7>3> Bearing Strength, Spacing and Edge-distance Requirements ............................. 246

7>4> b‘ULúgFm μta (Common Bolts) ................................................................................ 253

7>5> b‘ULúgersIusþg;x<s; (High-Strength Bolts)................................................................... 256 7>6> Shear Strength of High-Strength Bolts ................................................................. 258

7>7> Slip-Critical Connections ..................................................................................... 261

7>8> b‘ULúgersIusþg;x<s;rgkarTaj (High-Strength Bolts in Tension) ............................... 277

7>9> kmøaMgpÁÜbrvagkmøaMgTaj nigkmøaMgTajenAkñúgb‘ULúg (Combined Shear and Tension in Fasteners) ............................................................................................................ 287

7>10> tMNpSar (Welded connections)........................................................................... 293

7>11> Fillet Welds........................................................................................................ 295


T.Chhay iv Contents

VIII. tMNcakp©it Eccentric Connections

8>1> ]TahrN_sMrab;tMNcakp©it (Examples of Eccentric Connections) .......................... 306

8>2> tMNcMNakp©itedayb‘ULúg³ EtkmøaMgkat; (Eccentric Bolted Connections: Shear only) .......................................................................................................... 307

8>3> tMNcMNakp©itedayb‘ULúg³ kmøaMgkat;bUknwgkmøaMgTaj Eccentric Bolted Connections: Shear Plus Tension .......................................... 319

8>4> tMNcMNakp©itedaypSar³ EtkmøaMgkat; Eccentric Welded Connections: Shear only........................................................ 323

8>5> tMNcMNakp©itedaypSar³ kmøaMgkat; nigkmøaMgTaj Eccentric Welded Connections: Shear and Tension ........................................... 333

8>6> tMNTb;m:Um:g; (Moment-Resisting Connection)......................................................... 339

8>7> Column Stiffeners and other Reinforcement ...................................................... 348

8>8> End Plate Connection.......................................................................................... 361

8>9> esckþIsnñidæan (Concluding Remarks) ................................................................. 369

IX. eRKOgbgÁúMsmas Composite Construction

9>1> esckþIepþIm (Introduction)........................................................................................ 370

9>2> karsagsg;edaymankarTb; nigedayminmankarTb; Shored Versus Unshored Construction .............................................................. 382

9>3> TTwgsøabRbsiT§PaB (Effect Flange Width ) ............................................................ 384

9>4> Shear Connectors ................................................................................................. 387

9>5> karKNnamuxkat; (Design) ....................................................................................... 390 9>6> PaBdab (Deflections) .............................................................................................. 395 9>7> FñwmsmasCamYynwgkRmalBum<Edk (Composite Beams with Formed Steel Deck) .... 399

9>8> taragsRmab;karviPaK nigkarKNnaFñwmsmas Tables for Composite Beam Analysis and Design.............................................. 412

9>9> FñwmCab; (Continuous Beams).................................................................................... 419

9>10> ssrsmas (Composite Columns) ....................................................................... 421


matika v T.Chhay

X. rtEdkbnÞH Plate Girder

10>1> esckþIepþIm (Introduction) .................................................................................... 428 10>2> karBicarNaTUeTA (General Considerations ) .......................................................... 429

10>3> tRmUvkarrbs; AISC (AISC Requirements) ...................................................... 433

10>4> ersIusþg;rgkarBt; (Flexural Strength) ..................................................................... 435 10>5> ersIusþg;kmøaMgkat; (Shear Strength) ........................................................................ 438 10>6> GnþrGMeBIénkarBt; nigkmøaMgkat; (Interaction of Flexural and Shear) ..................... 444

10>7> Bearing Stiffeners .............................................................................................. 445

10>8> kaKNnamuxkat; (Design) ...................................................................................... 457

Appendix A. karKNna nigkarviPaKedaylkçN³)aøsÞic

Plastic Analysis and Design

A>1> esckþIepþIm (Introduction) ..................................................................................... 478

A>2> AISC Requirements.............................................................................................. 480

A>3> karviPaK (Analysis) ............................................................................................... 481

A>4> karKNnamuxkat; (Design) ....................................................................................... 488 A>5> karsnñidæan (Conclusion Remark)........................................................................... 490

Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat Structural Steel Design Based on Allowable Stress

B>1> esckþIepþIm (Introduction) ...................................................................................... 491

B>2> Ggát;rgkarTaj (Tension members) ...................................................................... 493

B>3> Ggát;rgkarsgát; (Compression members) .............................................................. 494

B>4> Fñwm (Beams) ............................................................................................................ 498

B>5> Beam-Columns...................................................................................................... 505

B>6> snñidæan (Concluding Remarks) ............................................................................... 510


esckþIepþIm 1 T.Chhay

I. esckþIepþIm Introduction

1>1> karsikSaKNnaeRKOgbgÁúM Structural Design

karsikSaKNnaeRKOgbgÁúMsMNg;GKar eTaHCaeRKOgbgÁúMGMBIEdk b¤GMBIebtugBRgwgedayEdkk¾ eday KWeKtRmUv[kMNt; nigeRCIserIsmuxkat;smrmürbs;Ggát;eRKOgbgÁúMTaMgGs; edIm,ITb;Tl;nwg bnÞúk xageRkATaMgGs;EdlmanGMeBImkelIeRKOgbgÁúM. kñúgkrNICaeRcIn sßabtükrmantYnaTIrcnam:UtGKar edayrYmmankarerobcMcMnYnCan;rbs;GKar nigkarerobcMbøg;tamCan;nImYy² ehIyvisVkreRKOgbgÁúMRtUveFVI karkñúgEdnkMNt;énkarrcnaenH. CakarEdlRbesIrbMputKW visVkr nigsßabtükrRtUvshkarKñakñúgdMeNIr karrcna nigsikSaKNnaeRKOgbgÁúMenHedIm,IbBa©b;KMeragedayTTYl)aneCaKC½y. dMeNIrkarénkarsikSa KNnaeRKOgbgÁúMRtUv)ansegçbdUcteTA³ sßabtükrCaGñksMercnUvesaP½NPaBrbs;GKar ehIyvisVkr CaGñksikSaKNnamuxkat;rbs;eRKOgbgÁúMRbkbedaylkçN³esdækic© nigedayFananUvsßirPaBdl;sMNg; GKar. visVkreRKOgbgÁúMRtUvKitCacMbgnUvsuvtßiPaB bnÞab;mkKWkareRbIR)as; niglkçN³esdækic©. lkçN³ esdækic©enAkñúgsMNg;KW sMedAelIkareRbIR)as;nUvsmÖar³ nigkmøaMgBlkm μy:agmanRbsiT§PaB.

karsikSaKNnad¾l¥KWTamTarnUvbøg;eRKagy:ageRcIn edayrYmmankarteRmobGgát; nigkartP¢ab; Ggát;tamEbbEpnxus²Kña ehIyeFIVkareRbobeFobnUvlkçN³esdækic©rbs;va. sRmab;bøg;eRKagnImYy² EdlRtUveFVIkarGegát eKRtUvsikSaKNnamuxkat;rbs;Ggát;nImYy². edIm,IeFVIVdUcenH)an CadMbUgeKRtUv karsikSaviPaKeRKOgbgÁúM ehIyKNnakmøaMg nigm:Um:g;Bt;rbs;Ggát;nImYy². CamYynwgTinñn½yTaMgenH GñksikSaKNnaeRKOgbgÁúMGaceRCIserIsmuxkat;)any:agsmRsb. b:uEnþ munnwgeFVIkarsikSaviPaKRKOg bgÁúM eKRtUvsMercCadMbUgnUvsmÖar³sRmab;eRbIR)as;kñúgeRKOgbgÁúM EdlCaTUeTAmanebtugBRgwgedayEdk eRKOgbgÁúMGMBIEdk nigbnSMénsmÖar³TaMgBIr. CakarRbesIbMput eKKYrerobcMnUvCeRmIsénkarsikSaKNna BIsmÖar³TaMgenH.

enAkñúgesovePAenH manEtkarENnaMBIkarsikSaKNnamuxkat;eRKOgbgÁúMGMBIEdk nigkartP¢ab; rbs;vaEtb:ueNÑaH. visVkreRKOgbgÁúMRtUveRCIserIs nigepÞógpÞat;RbB½n§eRKOgbgÁúMTaMgGs;edIm,ITTYl)annUv karsikSaKNnaRbkbedaylkçN³esdækic© nigsuvtßiPaB.

munnwgerobrab;BIeRKOgbgÁúMGMBIEdk eyIgcaM)ac;RtUvsÁal;RbePTGgát;nImYy²rbs;eRKOgbgÁúMCamun sin. rUbTI 1>1 bgðajBI truss CamYynwgkmøaMgcMcMNucbBaÄrEdlGnuvtþRtg;tMNénGgát;xagelI. eday


T.Chhay 2 Introduction

rkSanUvkarsnμt;énkarviPaK truss ¬tMN pinned nigkmøaMgGnuvtþEtelItMN¦ Ggát;rbs; truss CaGgát; rgkmøaMgBIr (two-force member) EdlrgkmøaMgsgát; b¤kmøaMgTajtamG½kS. sRmab; truss TRm samBaØEdlrgbnÞúkdUcbgðajkñúgrUb 1>1 Ggát;xagelICaGgát;rgkarsgát; ehIyGgát;xageRkamCaGgát; rgkarTaj. Ggát;RTnugGacCaGgát;rgkarTaj b¤rgkarsgát;edayGaRs½yeTAelITItaMg TisTRmuy nig TItaMgrbs;bnÞúk.

RbePTepSgeTotrbs;Ggát;RtUv)anbgðajCamYynwgeRKagtMNrwg (rigid frame) enAkñúgrUbTI 1>2. Ggát;rbs;eRKagenHRtUv)antP¢ab;y:agrwgedayTwkbnSar nwgGacsn μt;CaeRKOgbgÁúMCab;. enARtg; TRm Ggát;RtUv)anpSarP¢ab;eTAnwgbnÞHctuekaNEdlP¢ab;edayb‘ULúgeTAnwgRKwHebtug. edaydak;eRKag enHRsb²Kña ehIyP¢ab;BYkvaedayGgát;bEnßm EdlbnÞab;mkRtUv)anRKbedaysmÖar³dMbUl nigbiT)aMg edaysmÖar³CBa¢aMgedIm,IbegáIt)anCaRbB½n§sMNg;TUeTA. karlMGitsMxan;minRtUv)anerobrab;eT b:uEnþGKar BaNiC¢km μxñattUcRtUv)ansagsg;tamlkçN³EbbenH. karsikSaKNnaeRKOgbgÁúM nigkarsikSaviPaK eRKagnImYy²rbs;RbB½n§cab;epþImCamYynwgeRKagkñúgbøg;dUcbgðajenAkñúgrUbTI 1>2 b. cMNaMfa TRm RtUv)anbgðajCaTRmsnøak; (hinges or pinned) minEmnTRmbgáb; (fixed). RbsinebIeCIgtagman lT§PaBrgmuMrgVilsþÜcesþIg b¤RbsinebIkartP¢ab;manlkçN³bt;Ebn (flexible) RKb;RKan;edIm,IGnuBaØat [manmuMrgVil enaHeKcat;TukvaCaTRmsnøak; (pinned). karsnμt;enAkñúgviFITUeTAénkarsikSaviPaKeRKOg bgÁúMKW kMhYcRTg;RTaymantémøtUc Edlmann½yfamMurgVild¾tictYcrbs;TRmGaceFVI[TRmmanlkçN³Ca tMNsnøak; (pinned) )an. enAeBlEdleKTTYl)annUvragFrNImaRtrbs;eRKag niglkçxNÐTRmehIy eKGackMNt;kardak; bnÞúk)an. karkMNt;bnÞúkenHTak;TgnwgkarEckrMElkbnÞúksrubTaMgGs;eTAeRKagnImYy². RbsinebI eRKagEdlBicarNargbnÞúkdMbUlBRgayes μ I enaHeRKagnImYy²EdlTTYlnUvcMENkrbs;bnÞúkenHnwgman TRmg;CabnÞúkBRgayes μIEdlmanlkçN³CabnÞat;dUcbgðajenAkñúgrUbTI 1>2 b.



sRmab;kardak;bnÞúkEdlbgðajenAkñúgrUbTI 1>2 b eRKagnwgxUcRTg;RTaydUcbgðajenAkñúgrUb edayExSdac;. Ggát;nImYy²rbs;eRKagRtUv)ancat;cMNat;fñak;edayGaRs½yeTAelIRbePTénkareFVIkar EdlsMEdgedayrUbragEdlxUcRTg;RTay. Ggát;edk AB nig BC rgkarBt;begáag (bending or

flexure) RtUv)aneKehAfaFñwm (beam). Ggát;bBaÄr BD Edlrgm:Um:g;KU (couple) EdlbBa¢ÚnBIFñwm nImYy² ¬b:uEnþsRmab;eRKagsIuemRTIdUcbgðaj vamantémødUcKña EtTisedApÞúyKña¦ dUcenHeKGacecal m:Um:g;KU (couple) enH)an. dUcenH Ggát; BD rgEtkmøaMgsgát;tamG½kSEdl)anBIbnÞúkbBaÄr. enA kñúgsMNg; Ggát;rgkarsgát;bBaÄrdUcGVIEdl)anerobrab;RtUv)aneKehAfassr (column). cMENkGgát; bBaÄrBIrepSgeTot AE nig CF minRtwmEtRTnUvkmøaMgsgát;tamG½kSb:ueNÑaHeT b:uEnþvaEfmTaMgTb;Tl; nwgkarBt;begáagEdlmantémøFMeTotpg. Ggát;EbbenHRtUv)aneKehAfa beam-column. Cak;Esþg RKb;Ggát;TaMgGs; eTaHCaRtUv)ancat;cMNat;fñak;CaFñwm b¤ssrk¾eday k¾vaenAEtrgbnÞúktamG½kS nig m:Um:g;Bt;Edr b:uEnþenAkñúgkrNICaeRcIn eKGacecal\T§iBlNaEdlmantémøtUc)an. bEnßmBIelIRbePTGgát;Edl)anBN’naxagelI esovePAenHnwgerobrab;BIkarKNnakartP¢ab; nig Ggát;Biess²dUcteTA³ composite beam, composite column nig plate girder.



1>2> bnÞúk Loads kmøaMg (force) EdlmanGMeBIelIeRKOgbgÁúMRtUv)aneKehAfabnÞúk (load). bnÞúkRtUv)anEckecj CaBIrRbePTFM²KW³ bnÞúkefr (dead load) nigbnÞúkGefr (live load). bnÞúkefrCabnÞúkEdlsßitenACa GciéRnþy_EdlrYmmanTm¶n;rbs;eRKOgbgÁúMxøÜnÉg EdleK[eQ μaHfabnÞúkpÞal;xøÜn (self-weight). bEnßmBI elIbnÞúkpÞal;xøÜn (self-weight) bnÞúkefr (dead load) enAkñúgGKarrYmmanTm¶n;rbs; nonstruc-tural component EdlmandUcCa floor covering, partition nig suspended ceilings ¬CamYynwgRbB½n§ GKÁisnI smÖar³emkanic nigRbB½n§Twk¦. RKb;bnÞúkEdl)anerobrab;CabnÞúkEdlTak;TgeTAnwgTMnajEpn dIehIyRtUv)aneKehAfa gravity loads. bnÞúkGefrEdlGacCa gravity load CabnÞúkEdlminenAsßit esßrdUcbnÞúkefreT. vaGac b¤minGacmanGMeBIelIeRKOgbgÁúMRKb;eBl ehIyTItaMgrbs;vak¾minCab;lab; Edr. bnÞúkGefrrYmman eRKOgsgðarwm smÖar³ Tm¶n;rbs;mnusSEdlrs;enAelIGKar. CaTUeTAeKminGac kMNt;TMhMrbs;bnÞúkGefr (live load) )anCak;lak;dUcbnÞúkefr (dead load) eT dUcenHTMhMrbs;vaCa TMhM)a:n;sμan. kñúgkrNICaeRcIn eKRtUveFVIkarGegáteTAelIGgát;eRKOgbgÁúMsRmab;TItaMgepSg²rbs;bnÞúk Gefr (live load) EdlkareFVIEbbenHeKnwgminemIlrMlgBIlkçxNÐ)ak;d¾eRKaHfñak;eLIy. RbsinebIeKGnuvtþbnÞúkGefreTAelIeRKOgbgÁúMyWt² edaymindkecj b¤dak;eLIgvijsarcuHsar eLIg enaHeKviPaKeRKOgbgÁúMCalkçN³sþaTic. RbsinebIeKGnuvtþbnÞúky:agelOn dUckñúgkrNIeRKOgbgÁúM RT]bkrN_sÞÚccl½t eKRtUvKitbBa©Úl\T§iBlTgÁic. RbsinebIbnÞúkRtUv)andak; nigdkcuHeLIg²eRcIndg kñúgmYyCIvitrbs;eRKOgbgÁúM fatigue stress nwgkøayCabBaðaEdleKRtUvykmksikSa. bnÞúkTgÁicekItman cMeBaHGKarkñúgkMrittictYc dUcCaGKar]sSahkmμ cMENkÉ fatigue load KWkMrnwgekItmanNas; eRBaHmun nwg fatigue køayCabBaða luHRtaEtvdþénkardak;bnÞúkmanrab;Ban;dg. edaymUlehtuenH RKb;lkçxNÐ bnÞúkTaMgGs;EdlmanenAkñúgesovePAenHRtUv)aneKKitCabnÞúksþaTic ehIyeKminBicarNaBI fatigue eT. edaysarFmμCatiminzitefrrbs;xül;bk;xÞb; nigbWtenAelIépÞxageRkArbs;GKar eKcat;Tukxül; kñúgCMBUkbnÞúkGefrEdr. b:uEnþedaysarkarKNnabnÞúkxül;manlkçN³sμ úKsμaj eKcat;TukvakñúgCMBUk dac;edayELk. edaysarbnÞúkxag (lateral load) man\T§iBly:agxøaMgcMeBaHGKarx<s;² dUcenH xül; manlkçN³minsMxan;cMeBaHGKarTab²eT b:uEnþ uplift énRbB½n§dMbUlRsalGacmaneRKaHfñak;. eTaHbICa xül;manvtþmanRKb;eBlk¾eday k¾eKminBicarNavaCajwkjykñúgkarsikSaKNnaEdr ehIyeKk¾mincat; TukvaCa fatigue load eT.



bnÞúkrBa¢ÜydICaCMBUkBiessmYyeTotEdleKcaM)ac;BicarNaBIvasRmab;EtTItaMgPUmisaRsþNaEdl GacekItmanrBa¢ÜydIb:ueNÑaH. karsikSaviPaKeRKOgbgÁúMEdlrg\T§iBlrBa¢ÜydITamTarkarsikSaviPaK structure’s response eTAnwgclnarbs;dIEdlbegáIteLIgedayrBa¢ÜydI. eBlxøHeKeRbIviFIgayRsYl Edl\T§iBlrBa¢ÜydIRtUv)an simulate edayeRbIRbB½n§kmøaMgedk EdlmanlkçN³dUcCasm<aFxül;eday dak;va[manGMeBItamCan;nImYy²rbs;GKar. RBwlCaRbePTbnÞúkGefrmYyEbbeTotEdlRtUvKitkñúgCMBUkdac;edayELk. RBwlGacKrCaBMnUk. bnÞúkGefrepSgeTotk¾RtUv)ancat;TukkñúgCMBUkdac;edayELkEdr dUcCasm<aF hydrostatic nig sm<aFdI. 1>3> Building Codes GKarRtUv)ansikSaKNna (design) nigsagsg;edayGaRs½yelIGVIEdl)anEcgenAkñúg building

code EdlCaÉksarc,ab;EdlmantRmUvkarTak;TgeTAnwgsuvtßiPaBrbs;eRKOgbgÁúM suvtßiPaBelIGKÁIP½y karerobcMRbB½n§Twk karerobcMRbB½n§xül; nigkarsMrYlkareRbIR)as;dl;CnBikar. Building code min)an pþl;nUvlMnaMsikSaKNna (design) eT b:uEnþvakMNt;nUvtRmUvkarkñúgkarsikSaKNna (design). lkçN³ sMxan;sRmab;visVkreRKOgbgÁúMKWbBaØtþBIbnÞúkGefrGb,brmaEdlmanGMeBIelIGKar. bc©úb,nñ eKman building code mYyEdlGacsMrYldl;kargarrbs;visVkrEdlsikSaKNnaeRKOg bgÁúMTaMgenAshrdæGaemric k¾dUcbNþaRbeTsepSg²KW International Building Code (IBC). 1>4> Design Specifications pÞúyBI building code, design specification pþl;nUvkarENnaMlMGitsRmab;karsikSaKNna Ggát;eRKOgbgÁúM nigkartP¢ab;rbs;va. Design Specification tMNag[karGnuvtþvisVkmμd¾l¥EdlQr elIkarsikSaRsavRCavcugeRkaybMput. vaRtUv)anEksMrYl nigeFVI[kan;EtRbesIreLIgtamxYb. dUcKña nwg building code Edr design specification RtUv)aneKsresreLIgkñúgTRmg;c,ab;edayGgÁkarEdlmin rkplcMeNj. Specification EdlvisVkreRKOgbgÁúMcab;Garm μN_eRcInKW specification Edle)aHBum<pSayeday GgÁkardUcxageRkam³



!> American Institute of Steel Construction (AISC): Specification enHpþl;[sRmab; sikSaKNnaeRKOgbgÁúMGMBIEdk nigkartP¢ab;rbs;va. vaCa Specification cMbgEdlykcitþ Tukdak;edayesovePAenH (AISC, 1993).

@> American Association of State Highway and Transportation Officials (AASHTO):

Specification enHRKbdNþb;elIkarsikSaKNnas<an highway nigeRKOgbgÁúMTak;TgepSg² eTot. vapþl;RKb;smÖar³TaMgGs;EdleRbICaTUeTAsRmab;s<anEdlmandUcCa Edk ebtugBRgwg edayEdk nigeQI (AASHTO, 1992, 1994).

#> American Railway Engineering Association (AREA): ÉksarenHRKbdNþb;elIkar sikSaKNnas<ansRmab;rfePøIg nigeRKOgbgÁúMEdlTak;TgepSgeTot (AREA, 1992).

$> American Iron and Steel Institute (AISI): specification enHedaHRsayCamYynwg cold-

formed steel Edlmanerobrab;enAkñúgkfaxNÐ 1>6 kñúgesovePAenH (AISI, 1996). 1>5> eRKOgbgÁúMGMBIEdk Structural Steel eKeRbIR)as;EdkdMbUgbg¥s;sRmab;smÖar³tUc²taMgBIRbEhl 4000qñaMmunRKisþskraC (Murphy, 1957). smÖar³enHmanTRmg;Ca wrought iron EdlplitedaykardutEr:EdkenAkñúgePøIg. enAkñúgGMLúg cugstvtSr_TI 18 nigedImstvtSr_TI 19 cast iron nig wrought iron RtUv)aneRbIsRmab; sMNg;s<an. EdksMNg; (steel) CasMelah³én iron nigkarbUn. Edkmansar³FatuminsuT§ nigkabUn ticCag cast iron EdlRtUv)aneKeRbIsRmab;sMNg;Fn;F¶n;dMbUgkñúgstvtSr_TI 19. CamYynwgkarmk dl;énkarEkERbrbs; Bessemer enAkñúgqñaM 1855 Edkcab;epþImCMnYs wrought iron nig cast iron kñúg sMNg;. lkçN³rbs;EdkEdlvisVkreRKOgbgÁúMcab;GarmμN_xøaMgCageKKWdüaRkaménlT§plEdkTaj. Rb sinebIsMNakKMrUBiesaFn_rgkmøaMgtamG½kS P dUcbgðajenAkñúgrUbTI 1>3 a enaHkugRtaMg (stress) nig bERmbRmYlrageFob (strain) GacRtUv)ankMNt;tamrUbmnþdUcxageRkam³

APf = nig

LLΔ

=ε Edl =f kugRtaMgkmøaMgTajtamG½kS =A RkLaépÞmuxkat; =ε strain tamG½kS



=L RbEvgrbs;sMNakKMrU =ΔL kMhUcRTg;RTay

RbsinebIeKbegáInbnÞúkBIsUnüeTAdl;cMNucdac; (fracture) ¬kugRtaMg nig strain RtUv)aneKKNna tamCMhannImYy²¦ ExSekagTMnak;TMngrvagkugRtaMg nigbERmbRmYlrageFob (stress-strain curve) RtUv)anbgðajenAkñúgrUbTI 1>3 b. ExSekagenHsRmab;RbePTEdksVit (ductile, mild or steel) . TMnak;TMngrvagkugRtaMg nig strain manlkçN³CabnÞat;BIcMNucsUnürhUtdl;EdnkMNt;smamaRt (proportional limit) EdlkñúgcenøaHenHsmÖar³eKarBtamc,ab;h‘Uk (Hook’s law). bnÞab;mkvaeTA dl;cMNuc yield xagelIy:agelOnrYcFøak;mkcMNuc yield xageRkam. bnÞab;BI enaHkugRtaMgenArkSa témøefr eTaHbICa strain enAEtbnþekIneLIgk¾eday. enARtg;tMNak;kalénkardak;bnÞúkenH sMNak KMrUBiesaFn_enAEtbnþlUtEvg eTaHbICaeKminbegáInbnÞúkk¾eday ¬EtbnÞúkk¾minRtUv)andkEdr¦. tMbn;kug RtaMgefrenHRtUv)aneKehAfatMbn;)aøsÞic (plastic range or yield plateau). enARtg; strain Edlman témøRbEhl 12dgén strain enAtMbn; yield, strain hardening cab;epþImekItman ehIyeKRtUvkar



bnÞúkbEnßm ¬b¤kugRtaMgbEnßm¦ edIm,IeFVI[mansac;lUtbEnßm ¬b¤ strain¦. eRkayeBl vaeTAdl;cMNuc kugRtaMgGtibrma sMNakKMrUcab;epþIm neck down EdleFVI[kugRtaMgcab;epþImfycuH Et strain enAEtbnþ ekIneLIgdEdl ehIyekItman fracture. eTaHbICamuxkat;RtUv)ankat;bnßykñúgGMLúgeBldak;bnÞúkk¾eday (Poisson effect) k¾eKenAEt eRbIRkLaépÞmuxkat;edImedIm,IKNnakugRtaMgTaMgGs;. kugRtaMgEdl)anBIkarKNnatamviFIenH RtUv)an eKsÁal;faCa engineering stress. RbsinebIeKeRbIRbEvgedImedIm,IKNna strain enaHvaRtUv)aneKehA fa engineering strain. EdkEdlRtUv)aneKBiesaFedIm,ITTYl)andüaRkamdUcbgðajkñúgrUbTI 1>3 b Ca ductile eRBaHva man lT§PaBrgkMhUcRTg;RTayFMmunnwgeFVIkardl; fracture. eKGacvas;PaBsVit (ductility) edayeRbI sac;lUt (elongation) EdlkMNt;edayrUbmnþ 100×

−=

o

of

LLL

e (1.1)

Edl =e sac;lUt ¬KitCaPaKry¦ =fL RbEvgrbs;sMNakKMrUenAeBldac; =oL RbEvgedIm EdneGLasÞic (elastic limit) rbs;smÖar³CakugRtaMgEdlsßitenAcenøaHEdnsmamaRt nigcMNuc yeild xagelI. smÖar³EdlrgkugRtaMgkñúgtMbn;enH sMNakKMrUnwgminmankMhUcRTg;RTayeRkayeBl eKdkbnÞúkeT. KnøgénkardkbnÞúknwgsßitenAtamKnøgénkardak;bnÞúk ehIyvaminman permanent

strain eT. tMbn;rbs; stress-strain diagram enH RtUv)aneK[eQ μaHfa EdneGLasÞic (elastic rage). eRkABI elastic limit KnøgénkardkbnÞúknwgsßitenAelIExSRtg;EdlRsbeTAnwgKnøgénkardak; bnÞúk ehIyvanwgman permanent strain. ]TahrN_ RbsinebIeKdkbnÞúkRtg;cMNuc A kñúgrUbTI 1>3 b KnøgénkardkbnÞúknwgsßitenAelIExS AB Edlpþl;nUv permanent strain OB . rUbTI 1>4 bgðajBIkMENd¾l¥rbs; stress-strain curve. Proportional limit, elastic limit,

upper nig lower yield point KWsßitenAelIcMNucEtmYyEdleKehAfa yield point EdlkMNt;edaykug RtaMg yF . cMNucmYyeTotEdlvisVkreRKOgbgÁúMRtUvcab;Garm μN_KWkugRtaMgGtibrma EdleK[eQ μaHfa ultimate tensile strength uF . rUbragrbs;ExSekagenHCaKMrUsRmab; mild structural steel TaMgGs; EdlvaxusKñaBImYyeTAmYyedaytémø yF nig uF . pleFobkugRtaMgelI strain kñúgEdneGLasÞic



RtUv)ankMNt;eday E EdleKehAfa young’s modulus or modulus of elasticity. E mantMé;lesμ I MPaksi 5102000,29 ⋅≈ sRmab;RKb;eRKOgbgÁúMEdkTaMgGs;.

rUbTI 1>5 bgðajBIRbePT stress-strain curve sRmab; high-strength steels EdlmanPaBsVit tUcCag mild steels. eTaHbIvamanEpñk linear elastic nig tensile strength k¾eday Etvaminman yield

point b¤ plastic plateau eT. edIm,IeRbI higher strength steel enH[dUcnwgkareRbIR)as; ductile steel eKRtUvkartémøkugRtaMg yF dUcenHeKGaceRbIdMeNIrkar nigrUbmnþdUcKñasRmab;RKb;RbePTEdkTaMg Gs;. dUcEdl)anbgðajBImun sRmab;EdkEdlrgkugRtaMgeRkABItMbn; elastic limit enAeBleKdkbnÞúk vanwgsßitenAelIKnøgExSEdlRsbnwgKnøgdak;bnÞúk EtvamineTAdl;cMNuc strain es μ IsUnüeT. dUcenHva man residual strain b¤ permanent strain eRkayeBldkbnÞúk. Yield stress sRmab;EdkCamYy nwgRbePT stress-strain curve EdlbgðajenAkñúgrUbTI 1>5 RtUv)aneKehAfa yield strength Edl RtUv)ankMNt;Ca kugRtaMgRtg;cMNucénkardkbnÞúkEdlRtUvnwg permanent strain énbrimaNkMNt;Na mYy. eKeRCIserIs yk strain es μ Inwg 002.0 ehIyviFIénkarkMNt; yield strength enHRtUv)aneKehAfa

%2.0 offset method. dUcEdl)anerobrab;BImun CaTUeTAeKRtUvkarlkçN³BIrsRmab; structural

strength design KW yF nig uF edayminKitBIrUbragrbs; stress-strain curve nigminKitBIrebob EdlTTYl)an yF eT. sRmab;mUlehtuenH eKeRbItYTUeTA yield stress ehIyvaGacmann½yCa yield

point b¤ yield strength. lkçN³epSg²rbs;eRKOgbgÁúMEdkEdlrYmbBa¢ÚlTaMg strength nig ductility RtUv)ankMNt;eday smasFatuKImI (chemical composition). Edk (steel) CasMelah³EdlFatupSMcMbgrbs;vaCa iron.



sarFatupSMrbs;eRKOgbgÁúMEdkTaMgGs; ¬eTaHCakñúgbrimaNtictYck¾eday¦ KWkabUnEdlCasarFatucUlrYm kñúgkarbegáIn strength b:uEnþvakat;bnßy ductility. karekIneLIgénPaKrykabUnKWbegáIn strength Etkat;bnßy ductility EdleFVI[karpSarmankarBi)ak. sarFaturYmpSMdéTeTotrbs;EdksMNg;rYm mans<an; (copper), manganese, nickel, chromium, molybdenum nig silicon. eRKOgbgÁúMEdk RtUv)anerobcMCaRkumEdlGaRs½yeTAnwgsarFatupSMrbs;vadUcxageRkam³ !> Plain carbon steel: EdlPaKeRcInCa iron nigkabUnticCag %1 @> Low-alloy steel: man iron nigkabUn EdlrYmpSMCamYynwgsarFatuepSgeTot ¬CaTUeTAtic

Cag %5 ¦. sarFatubEnßmKWedIm,IbegáInersIusþg; Etvanwgkat;bnßyPaBsVit. #> High-alloy or specialty steel: mansarFatupSMRsedogKñanwg low-alloy steel Edr Etman

sarFatubEnßmeRcInPaKryCag. EdkenHmanersIusþg;FMCag plain carbon steel nigman KuNPaBBiessdUcCakarkarBarERcH.

Grade rbs;EdksMNg; (structural steel) RtUv)ankMNt;eday American Society for Testing

and Material (ASTM). GgÁkarenHbegáItbTdæanedIm,IkMNt;smÖar³eTAtamsarFatupSM lkçN³ nigkar eFVIkarrbs;va (ASTM, 1996a). EdkeRKOgbgÁúMEdleKcUlcitþeRbIsBVéf¶Ca mild steel EdlsMKal;Ca ASTM 36A b¤sresry:agxøI 36A . vaman stress-strain curve dUcbgðajenAkñúgrUbTI 1>3 b nig 1>4 ehIymanlkçN³rgkarTajdUcxageRkam³ Yield stress: MPaKsiFy 25036 ≈= Tensile strength: MPaksiFu 40058 ≈= eTA MPaksi 55080 ≈



Edk 36A RtUv)ancat;fñak;Ca plain carbon steel ehIyvamansarFatupSM ¬eRkABI iron¦ dUcxageRkam³ Carbon: %26.0 ¬Gtibrma¦ Phosphorous: %04.0 ¬Gtibrma¦ Sulfur: %05.0 ¬Gtibrma¦ PaKryenHCatémøRbhak;RbEhl témøCak;EsþgGaRs½ynwgTRmg;énkarplitEdk. Edk 36A Ca ductile steel Edlmansac;lUt (elongation) EdlkMNt;edaysmIkar 1.1 KW %20 edayQrelIRbEvg edIm mminLo 200.8 ≈= . eKRtUvplitEdk 36A edayeKarBtambTdæanrbs; ASTM. témø yield strength nig tensile

strength Edl)anbgðajCatRmUvkarGb,brma EtvaGacFMCagtémøenH. Tensile strength RtUv)aneK [enAkñúgcenøaHtémømYy eRBaHlkçN³enHminGacTTYl)anedaysuRkitdUc yield strength eT. CaTUeTA EdkEdlman yield stress FMCag MPaksi 25036 ≈ RtUv)anKitCa high-strength

steel. High-strength steel EdleKniymeRbI eRcInCaRbePTEdkEdlman yield strength MPaksi 34550 ≈ nigman tensile strength MPaksi 45065 ≈ b¤ MPaksi 48070 ≈ ehIyeKk¾man

EdkEdlman yield strength MPaksi 690100 ≈ . Ca]TahrN_ ASTM 242A Ca low-alloy,

corrosion resistant steel Edlman yield strength MPaksi 29042 ≈ / MPaksi 32046 ≈ nig MPaksi 34550 ≈ CamYynwg tensile strength EdlRtUvKñanwg MPaksi 43563 ≈ / MPaksi 46067 ≈

nig MPaksi 48070 ≈ . cMENksmasFaturYmpSMKImIrbs;vamandUcxageRkam³ Carbon: %15.0 ¬Gtibrma¦ Manganese %00.1 ¬Gtibrma¦ Phosphorus: %15.0 ¬Gtibrma¦ Sulfur: %05.0 ¬Gtibrma¦ Copper: %20.0 ¬Gtibrma¦ Edk 242A minEmn ductile dUc 36A . sac;lUtEdlQrelIRbEvgedIm mmin 200.8 ≈ esμ Inwg %18 ebIeRbobeFobCamYysac;lUtrbs; 36A Edlmantémøes μ Inwg %20 . 1>6> rUbragmuxkat;bTdæan (Standard Cross-sectional Shapes) eKalbMNgcMbgkñúgkarsikSaKNnaeRKOgbgÁúMEdkKWkareRCIserIsmuxkat;EdlsmRsbsRmab;



Ggát;nImYy². CaTUeTA kareRCIserIsenHtRmUv[eRCIserIsrUbragmuxkat;tambTdæanEdleRbIR)as;y:ag TUlMTUlayCagkartRmUv[plitrUbragEdlmanxñat niglkçN³Biess. kareRCIserIsrUbragEdkEdl manRsab; (off-the shelf) CaCMerIsEdlmanlkçN³esdæikc©Cag eTaHbICavaeRbIsmÖar³eRcInCagbnþicbnþÜc k¾edaykþI. RbePTénrUbragbTdæanEdlFMCageKRtUv)anplitedaykarhUtekþA (hot-rolling). enAkñúg dMeNIrplitkm μEdleFVIeLIgenAkñúgeragcRkplitEdk (mill) EdkEdlrlayEdl)anBILsøEdkRtUv)an cak;cUleTAkñúgRbB½n§Bum<EdlCab; edayTuk[EdkeLIgrwg b:uEnþeKminGnuBaØat[vaRtCak;eBj eljeT. EdkekþAqøgkat; roller Caes‘rI EdlKab[eTACarUbragEdlcg;)an. karhUtEdkkñúgeBlEdlvaenAekþA GnuBaØat[vaxUcrUbragedaymin)at;bg; ductility rbs;va dUckrNIhUtRtCak;eT. kñúgGMLúgeBlhUt Ggát;EdllUtRbEvgehIyRtUv)ankat;tamRbEvgbTdæan EdlCaTUeTAmanRbEvgGtibrma BI mft 2065 ≈ eTA mft 2375 ≈ ehIyEdlvaRtUv)ankat;CabnþbnÞab;eTAtamRbEvgrbs;eRKOgbgÁúMenA eragCageTAtam karkMNt;rbs;bøg;.



muxkat;xøHrbs; hot-rolled shape EdlRtUv)aneRbICaTUeTARtUv)anbgðajenAkñúgrUbTI 1>6. xñat nigkMNt;sMKal;rbs;rUbragbTdæanRtUv)ankMNt;enAkñúg ASTM standard (ASTM, 1996). W-shape

EdleKGacehA)anfa rUbragsøabTUlay (wide flange shape) EdlpSMeLIgedaysøabBIrEdlEjk edayRTnugmYy. rUbragenHmanG½kSsIuemRTIBIr. kMNt;sMKal;KMrUrbs;vaKW 5018×W Edl W bgðajBI RbePTrUbrag/ elx 18 Ca nominal depth EdlRsbeTAnwgRTnug nig 50 CaTm¶n;rbs;EdkkñúgmYy ÉktþaRbEvg. W-shape én nominal size TaMgGs;RtUv)andak;CaRkumEdlmankm<s;BIsøabxagkñúgeTA søabxagkñúgdUcKña b:uEnþmankMras;søabxusKña. American Standard b¤ S-shape KWRsedogKñaeTAnwg W-shape Edr edaymansøabBIrRsbKña RTnugmYy nigmanG½kSsIuemRTIBIr. PaBxusKñarbs;vaKWsmamaRtrbs;muxkat;³ søabrbs; W FMCagRTnug cMENkÉsøabrbs; S tUcCagRTnug. elIsBIenH épÞxagkñúg nigépÞxageRkArbs;søabén W-shape man lkçN³RsbKña EtépÞxagkñúgénsøabrbs; S-shape eTrEdleFVI[kMras;xagcugtUcCagkMras;enAEk,r RTnug. kMNt;sMKalrbs; S-shape KW 7018×S Edl S bgðajBIRbePTrbs;rUbrag nigelxTaMg BIrtYCakm<s; nigTm¶n;kñúgmYyÉktþaRbEvg erogKña. rUbragenHRtUv)aneKehAfa I-beam. EdkEkg (angle shape) GacmaneCIges μI b¤eCIgmines μI. kMNt;sMKal;KMrUKW 4

366 ××L b¤ 8

536 ××L . elxTaMgbItYKW RbEvgeCIgTaMgBIrrbs;vaEdlvas;BIcugeTAEkgxageRkA nigkMras;rbs;va. kñúgkrNIEdkEkgEdlmaneCIgminesμ I eCIgEvgRtUv)ansresrmun. kMNt;sMKal;rbs;EdkEkgmin)an R)ab;BITm¶n;eT.

American Standard Channel b¤ C-shape mansøabBIr nigRTnugmYy EtmanG½kSsIuemRTIEt mYy. kMNt;sMKal;KMrUrbs;vaKW 209×C . nimitþsBaØaenHKWRsedogKñanwg W- nig S-shape Edr Edl manelxmYytYtMNag[km<s; nigmYytYeTottMNag[Tm¶n;kñúgmYyÉktþaRbEvg. b:uEnþsRmab; channel km<s;manRbEvgCak;EsþgCag. épÞxagkñúgrbs;søabKWdUcKñanwg S-shape Edr. eKenAman Miscellaneous Channel EdlCa]TahrN_ 2510×MC KWRsedogKñanwg American Standard

Channel Edr. Structural Tee RtUv)anpliteLIgedaykat; W-, M- b¤ S-shape Rtg;km<s;Bak;kNþal.

eBlxøHeKehArUbragenHfa split-tee. buBVbTénnimitþsBaØarbs;rUbragenHKW WT, MT b¤ ST GaRs½y eTAelIrUbragedImrbs;vamuneBlkat;. ]TahrN_ 11518×WT man nominal depth .18in nigmanTm¶n;

ftlb /115 ehIyvaRtUv)ankat;ecjBI 23036×WT . dUcKñasRmab; ST- nig MT-shape.



edaymin)anbgðajkúñgrUbTI 1>6 eKenAman hot-rolled shapes EdlmanlkçN³RsedogeTAnwg W-shape EdrKW³ HP- nig M-shapes. eKeRbI HP shape sRmab;ssrRKwH EdlvamanépÞsøabRsbKña nigmanTTwgesμ Inwgkm<s; ehIykMras;søabdUcKñanwgkMras;RTnug. GkSr M tMNag[ Miscellaneous ¬epSg²¦ EdlrUbragenHminRtUvKñanwgRbePTrUbragén W, HP b¤ S eT. TaMg M- nig HP-shape

RtUv)ansMKal;kñúgTRmg;dUcKñanwg W-shape Edr ]TahrN_ 1814×M nig 11714×HP . rUbragEdlRtUv)aneKeRbICajwkjab;Edr RtUv)anbgðajenAkñúgrUbTI 1>7. Edkr)ar (bar) Gac

manmuxkat; mUl kaer nigctuekaNEkg. RbsinebITTwgrbs;muxkat;ctuekaNEkgmanRbEvgtUcCag cmin 20.8 ≈ eKcat;TukrUbragenHCaEdkr)ar (bar) ehIyvaRtUv)ansMKal;edayTTwgmunkMras; ( 4

38× )

EtpÞúymkvijvaRtUv)ancat;TukCaEdkbnÞH (plate) ehIykMNt;sMKal;rbs;vaRtUv)annaMmuxedaykMras; munTTwg ( 102

1 × ). Edkr)ar (bar) nigEdkbnÞH (plate) RtUv)anpliteday hot-rolling.

rUbTI 1>7 k¾bgðajBImuxkat;RbehagEdr EdlGacplitBIEdkbnÞH (plate) EdlRtUv)anBt;eTACa rUbragEdlcg;)anehIypSartamefñr b¤eday hot-working edIm,IplitrUbragEdlK μanefñr. rUbragenH RtUv)ankt;sMKal;eday HSS sRmab;muxkat;EdkRbehag. muxkat;RbehagrYmman TIbmUl nigTIbRCug EdlmanrUbragkaer nigctuekaN. eKenAmanrUbragepSg²eTot b:uEnþeyIgelIkykEtrUbragEdleKniymeRbICaTUeTAmkbgðaj b:ueNÑaH. kñúgkrNICaeRcIn rUbragbTdæanmYynwgbMeBjtRmUvkarsRmab;karsikSaKNna. Rbsinvamin manrUbragbTdæanEdlRtUvnwgkarsikSaKNnaeT eKcaM)ac;eFVI built-up section dUcbgðajenAkñúgrUbTI 1>8. eBlxøH standard shape RtUv)anbEnßmeday cross-sectional element dUckrNIEdleKpSar cover plate P¢ab;eTAnwgsøabmYy b¤søabTaMgBIrrbs; W-shape. kareFVI built-up section CaviFId¾man



RbsiT§PaBkñúgkarbegáInlT§PaBRTRTg;rbs; standard shape. eBlxøHeKRtUveRbI built-up shape

edaysarK μan standard rolled shape NaEdlmuxkat;rbs;vamanRkLaépÞ b¤m:Um:g;niclPaBFMlμm. enA kñúgkrNIEbbenH eKeRbI plate girder EdlGacmanrUbragCa I-shaped section EdlmansøabBIr nig RTnugmYy b¤muxkat;RbGb; EdlmansøabBIr nigRTnugBIr. eKGacpSarFatupSMbBa©ÚlKñaedayrcnaedIm,I TTYl)annUvlkçN³Edlcg;)an. eKGacbegáIt built-up shape edayP¢ab; standard rolled shape BIr b¤eRcInbBa©ÚlKña. bnSMénrUbragEdleRbICaTUeTAKWEdkEkgDubEdlRtUv)andak;xñgTl;xñg ehIyRtUv)an P¢ab;tamcenøaHénRbEvgrbs;va.

RbePTepSgeTotrbs;EdksRmab;eRKOgbgÁúMKW cold-formed steel. Structural steel RbePTenH

RtUv)anbegáIteLIgedaykarBt;snøwkbnÞHEdkesþIgedaymineRbIkMedA. muxkat;KMrURtUv)anbgðajenAkñúgrUb TI 1>9. Cold-formed shape RtUv)aneRbIsRmab;RTTm¶n;Rsalb:ueNÑaH. Cold-working nwgbegáIn yield point b:uEnþvanwgkat;bnßyPaBsVitrbs;Edk nigeRkamlkçxNÐCak;EsþgeKGaceRbIvakñúgkarsikSa KNna (AISI, 1993). KuNsm,tþirbs;vaKWrUbragrbs;vagayRsYlkñúgkarbegáIt. edaysarmuxkat; rbs;vaesþIg instability CaktþacMbgkñúgkarsikSaKNna cold-formed structure.


T.Chhay 16 Concepts in Structural Steel Design

II. eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁÁúMEdk Concepts in Structural Steel Design

2>1> TsSnviC¢akñúgkarsikSaKNnamuxkat; Design Philosophies karsikSaKNnaGgát;eRKOgbgÁúMtMrUvnUvkareRCIserIsmuxkat;EdlmansuvtßiPaB nigmanlkçN³ esdækic© edIm,ITb;Tl;nwgkmøaMgEdlGnuvtþBIxageRkA. CaTUeTA lkçN³esdækic©mann½yfabrimaNEdk Gb,brma. brimaNenHRtUvnwgmuxkat;EdlmanTm¶n;kñúgmYyÉktþaRbEvgRsalCageK ehIyRtUvnwgmux kat;EdlmanRkLaépÞtUcCageKpgEdr. edIm,ITTYl)annUveKalbMNgenH visVkreRKOgbgÁúMk¾RtUvsMerc eFVIy:agNaeGayvamanlkçN³suvtßiPaBpgEdr. eKmanviFIkñúgkarKNnabIsMxan;xus²KñaKW³ !> sRmab; allowable stress design eKRtUveRCIserIsGgát;EdlmanlkçN³muxkat;dUcCa RkLa

épÞ nigm:Um:g;niclPaBFMRKb;RKan;edIm,IkarBarkugRtaMgGtibrmakMueGayFMCagkugRtaMg GnuBaØat. kugRtaMgGnuBaØatKWsßitenAkñúgtMbn;eGLasÞicrbs;smÖar³ ehIyvamantémøtUcCag yield stress yF ¬emIlrUbTI 1>4¦. témørbs;kugRtaMgGnuBaØatGacesμ Inwg yF6.0 . eKTTYl )ankugRtaMg GnuBaØatedayEck yield stress yF b¤ ultimate tensile stress uF CamYynwg emKuNsuvtßiPaB. eKGacehAviFIkñúgkarKNnaenHfa elastic design b¤ working stress

design. Working stress CakugRtaMgEdl)anBIbnÞúkeFVIkar (working load or service

load). Ggát;Edl)anKNnarYcehIy GacrgkugRtaMgmineGayFMCagkugRtaMgGnuBaØatenAeBl rgbnÞúkeFVIkar.

@> Plastic design KWQrelIkarsn μt;lkçxNÐ)ak; (failure) CaglkçxNÐbnÞúkeFVIkar. Ggát; RtUv)aneRCIserIsedayeRbIlkçxNÐvinicä½yeGayeRKOgbgÁúM)ak;eRkambnÞúkEdlFMCagbnÞúkeFVI kar. kar)ak; (failure) k¾mann½yfavamanPaBdabFMelIslub. eKeRbIBakü plastic enATI enHeRBaH enAeBl)ak; Epñkrbs;Ggát;nwgrg strain FM EdlvamantémøFMRKb;RKan;edIm,I eGay Ggát;sßitenAkñúgtMbn;)aøsÞic ¬emIlrUbTI 1>3 b¦. enAeBlEdlmuxkat;TaMgmUlrbs;Ggát; køayeTACa)aøsÞicenATItaMgRKb;RKan; plastic hinge nwgekIteLIgenATItaMgenaH Edl begáIt)anCa collapse mechanism. edaysarbnÞúkCak;EsþgtUcCag failure load edaymanemKuNsuvtßiPaBEdleKsÁal;faCa emKuNbnÞúk (load factor). Ggát;EdlKNna


eKalKMnitkñúgkarsikSaKNnaeRKOgbgÁúMEdk 17 T.Chhay

tamviFIenH nwgmansuvtßiPaB eTaHbICakarKNnaQrelIGVIEdlekItmanenAeBl)ak;k¾eday. dMeNIrkarénkarsikSaKNnaenHRtUv)ansegçbdUcteTA³

KuN working load b¤ service load CamYynwgemKuNbnÞúkedIm,ITTYl)an failure load.

kMNt;lkçN³muxkat;EdlcaM)ac;edIm,ITb;Tl; failure eRkamGMeBIénbnÞúkem KuN. Ggát;EdlmanlkçN³EbbenHKWmanersIusþg;RKb;RKan; ehIyvanwgCit² nwg)ak; enAeBlEdlGgát;rgbnÞúkemKuNEbbenH.

eRCIserIsrUbragmuxkat;EdlRsalCageKEdlmanlkçN³EbbenH. Ggát;EdlKNnaedayRTwsþI)aøsÞicnwgeTAdl;cMNuc)ak;eRkamGMeBIbnÞúkemKuN Etvamansuvtßi-PaBeRkamGMeBIbnÞúkeFVIkarCak;Esþg.

#> Load and resistance factor design (LRFD) manlkçN³RsedogKñanwg plastic design Rtg;eKKitlkçxNÐeBl)ak;. eKGnuvtþemKuNbnÞúkeTAelIbnÞúkeFVIkar ehIyeKRtUveRCIserIs Ggát;EdlmanersIusþg;RKb;RKan;edIm,IkarBarbnÞúkemKuN. elIsBIenH ersIusþg;Edl)anBIRTwsþI RtUv)ankat;bnßyedaykarGnuvtþemKuNersIusþg;. lkçN³vinicä½yEdlRtUvbMeBjkñúgkareRCIs erIsGgát;enHKW³

bnÞúkemKuN (factored load) ≤ ersIusþg;emKuN (factored strength) (2.1)

CaTUeTA enAkñúgsmIkarenH bnÞúkemKuNCaplbUkénbnÞúkeFVIkarTaMgGs;EdlRtUv)anTb;Tl; edayGgát;eRKOgbgÁúM edayKuNnwgemKuNbnÞúkeTAtamRbePTbnÞúk. Ca]TahrN_ bnÞúkefr RtUv)anKuNedayemKuNbnÞúkEdlxusBIbnÞúkGefr. ersIusþg;emKuNCaersIusþg;RTwsþIEdl KuNCamYynwgemKuNersIusþg;. dUcenHeKGacsresrsmIkar 2.1 dUcxageRkam³ ∑ ¬bnÞúk × emKuNbnÞúk¦ ≤ ersIusþg; × emKuNersIusþg; (2.2)

bnÞúkemKuNCa failure load EdlmantémøFMCagbnÞúkeFVIkarsrubCak;Esþg dUcenHCaTUeTAem

KuNbnÞúkEtgEtFMCag 1.0. b:uEnþ ersIusþg;emKuNRtUv)ankat;bnßy dUcenHemKuNersIusþg;



EtgEttUcCag 1.0. bnÞúkemKuNCabnÞúkEdlnaMeGayeRKOgbgÁúM b¤Ggát;eTAdl;cMNucEdn kMNt;. kñúgn½ysuvtßiPaB sßanPaBkMNt;GacCa fracture, yielding b¤ buckling ehIyersIusþg;emKuN CaersIusþg;EdlmanRbeyaCn_rbs;Ggát;Edlkat;bnßyBIersIusþg;RTwsþI edayemKuNersIusþg;. sßanPaBkMNt;k¾GacCasßanPaBkMNt;énkareRbIR)as; dUcCaPaBdab GnuBaØatGtibrma.

2>2> American Institute of Steel Construction Specification sRmab;karsikSaKNnamuxkat;Ggát;rbs;eRKOgbgÁúMGMBIEdk nigkartP¢ab;rbs;va specification

of the American Institute of Steel Construction Ca design specification Edlmansar³sMxan;. vaRtUv)aneKsresr nigeFVIkarEkERbtamsm½ykaleday AISC committee EdlrYmmanvisVkreRKOg bgÁúM GñksikSaRsavRCavBIsMNg;Edk plitkr nigGñksagsg;sMNg;Edk. Allowable stress design CaviFIdMbUgEdlRtUv)aneKeRbIsRmab;sMNg;EdleFVIBIeRKOgbgÁúMEdktaMgBIkare)aHBum<pSayrbs; AISC

Specification elIkTImYy kñúgqñaM 1923. enAqñaM 1986 AISC )ane)aHpSay specification dMbUg sRmab; load and resistance factor design sRmab;sMNg;GMBIEdk rYmCamYynwg Manual of Steel Construction. eKalbMNgénÉksarTaMgBIrKWpþl;nUvCeRmIssRmab;karKNnatam allowable stress

design eGay)aneRcIndUc karKNnatam plastic design. kare)aHBum<elIkTIBIrrbs; Manual (AISC,

1994) rYmman AISC Specification 1993. Load and resistance factor design minEmnCaKMnitf μIeT. taMgBIqñaM 1974 vaRtUv)aneKeRbIenA RbeTskaNada EdlenATIenaHeKehAviFIenHfa limit state design. ehIyvak¾CaeKalkarN_rbs; European building code pgEdr. enAshrdæGaemric LRFD CaviFIénkarKNnaEdlRtUv)anGnuBaØat sRmab;ebtugBRgwgedayEdkCaeRcInqñaMmkehIy ehIyvaCaviFIdMbUgEdlGnuBaØatenAkñúg American

Concrete Institute’s Building Code EdlvaRtUv)aneKsÁal;Ca Strength design (ACI, 1995). Highway bridge design standard pþl;eGayTaMg allowable stress design (AASHTO, 1992) nig load and resistance-factor design (AASHTO, 1994).



2>3> emKuNersIusþg; nigemKuNbnÞúkEdleRbIR)as;enAkñúg AISC Specification Load and Resistance Factors Used in the AISC Specification

smIkar 2.2 GacRtUv)aneKsresreGaykan;EtmanlkçN³suRkitEfmeTotdUcxageRkam³

nii RQ φγ ≤∑ (2.3)

Edl iQ = bnÞúk ¬kmøaMg b¤m:Um:g;¦ iγ = emKuNbnÞúk nR = nominal resistance or strength

φ = emKuNersIusþg; nRφ RtUv)aneKehAfa ersIusþg;KNna (design strength). GgÁxageqVgénsmIkar 2.3, iiQ∑γ KWCa

plbUkéncMnYnbnÞúkKNna ¬bnÞúkemKuN¦ TaMgGs;EdlmanGMeBIelIeRKOgbgÁúM. emKuNbnÞúk γ GaRs½y eTAnwgRbePTbnÞúk nigkarbnSMbnÞúk (load combination). bnÞúkemKuN RtUv)anykeTAeFVIkarsikSa KNnasRmab;témøEdlFMCageKkñúgcMeNamsmIkarpSMbnÞúkTaMg ^ xageRkam. xageRkamCakarbnSMbnÞúuk EdleGayeday “General Provision” enAkñúgCMBUk A

D4.1 ¬A$-!¦ )(5.06.12.1 orSorRLLD r++ ¬A$-@¦

)8.05.0()(6.12.1 WLororSorRLD r ++ ¬A$-#¦ )(5.05.03.12.1 orSorRLLWD r+++ ¬A$-$¦

SLED 2.05.00.12.1 ++± ¬A$-%¦ )13.1(9.0 EWorD ± ¬A$-^¦

Edl D = bnÞúkefr (Dead load)

L = bnÞúkGefr (Live load) rL = bnÞúkdMbUlGefr (Roof live load)

S = bnÞúkRBwl (Snow load)

R = bnÞúkePøóg b¤Twkkk (Rain or ice load) W = bnÞúkxül; (Wind load) E = bnÞúkrBa¢ÜydI (Earthquake load)



eyIgeXIjfa smIkar A$-@/ γ sRmab;bnÞúkGefr L es μ I 6.1 EtsRmab;smIkar A$-@ vij 5.0=γ . mUlehtuKWbnÞúkGefr RtUv)aneKepþatsMxan;sRmab;smIkar A$-@ ÉbnÞúkmYykñúgcMeNam

bnÞúkTaMgbI rL / S b¤ R RtUv)aneKepþatsMxan;sRmab;smIkar A$-#. ÉemKuNersIusþg; φ mantémøenAcenøaHBI 75.0 eTA 1.

]TahrN_ 2>1³ ssr ¬Ggát;rgkarsgát;¦ enACan;xagelIrbs;GKarrgbnÞúkdUcxageRkam³ bnÞúkefr (Dead load): kN485 bnÞúkGefrelIkRmal (Floor live load): kN205 bnÞúkGefrelIdMbUl (Roof live load): kN5.84 bnÞúkRBwl (Snow): kN89

a. kMNt;karbnSMbnÞúktam AISC Edllub nigtémøbnÞúkemKuNEdlRtUvKña b. RbsinebIemKuNersIusþg; 85.0=φ . etI nominal strength EdlRtUvkares μ Ib:unμan?

dMeNaHRsay³ a. bnSMbnÞúkEdllubCabnSMbnÞúkEdlbegáItbnÞúkemKuNFMCageK. eyIgnwgBinitüsmIkarnImYy²

EdlmanBak;B½n§nwgbnÞúkefr D / bnÞúkGefrEdl)anBI]bkrN_ smÖar³ nigmnusSEdlmanGMeBI elIkRmal L / bnÞúkGefrEdlmanGMeBIelIdMbUl rL nigbnÞúkRBwl S . (A4-1): ( ) kND 6794854.14.1 == (A4-2): rLLD (5.06.12.1 ++ b¤ S b¤ )R . eday rLS > ehIy 0=R dUcenHeyIg

caM)ac;sikSakarbnSMbnÞúkEtmþgKt; edayeRbI S =++ SLD 5.06.12.1 ( ) ( ) ( ) kN5.954895.02056.14852.1 =++ (A4-3): rLD (6.12.1 + b¤ S b¤ LR 5.0() + b¤ )8.0 W

sRmab;bnSMbnÞúkenH eyIgeRbI S CMnYseGay rL ehIy 0==WR ( ) ( ) ( ) kNLSD 9.8262055.0896.14852.15.06.12.1 =++=++ (A4-4): rLLWD (5.05.03.12.1 +++ b¤ S b¤ )R . smIkarenHRtUv)ankat;bnßymk

Rtwm SLD 5.05.02.1 ++ ehIytamkarGegÁt eyIgeXIjfasmIkarenHpþl;nUv lT§pltUcCagbnSM (A4-2) nig (A4-3).



(A4-5): SLED 2.05.00.12.1 ++± . edaysar 0=E dUcenHsmIkarenHRtUv)ankat; bnßymkRtwm SLD 2.05.02.1 ++ EdllT§plTTYl)anBIsmIkarenHtUcCag lT§plEdlTTYl)anBIsmIkar (A4-4).

(A4-6): WD 3.1(9.0 ± b¤ )0.1 E . smIkarenHmanemKuNbnÞúkefrtUcCagsmIkard¾éT naMeGaylT§plrbs;smIkarenHtUcCaglT§plrbs;smIkard¾éT.

cemøIy³ bnSMbnÞúkEdllubKW (A4-2) ehIybnÞúkemKuNKW kN5.954 . b. RbsinebIeKCMnYsbnÞúkemKuNxagelIeTAkñúgsmIkar 2.3 eyIgTTYl)an

nii RQ φλ ≤∑ nR85.05.954 ≤

kNRn 1123≥ cemøIy³ nominal strength EdlRtUvkarKW kN1123 . 2>4> mUldæanRbU)ab‘ÍlIetrbs ; Load and Resistance Factors Probabilistic Basis of Load and Resistance Factors TaMgemKuNbnÞúk TaMgemKuNersIusþg;EdlkMNt;eday AISC KWQrelIeKalkarN_RbU)ab‘ÍlIet. emKuNersIusþg;karBarPaBminCak;lak;énlkçN³rbs;smÖar³ RTwsþIénkarsikSaKNna nigkarsagsg;. Tinñn½yénkarBiesaFRtUv)anbgðajkñúgTMrg; histogram b¤ bar graph dUcbgðajenAkñúgrUbTI 2>1 EdlmanG½kSGab;sIustMNageGaytémørbs;sMNakKMrU b¤RBwtþikarN_ (event) nigG½kSGredaentMNag eGaycMnYnsMNakKMrUEdlmantémøCak;lak; b¤PaBjwkjab; (frequency) énkarekIteLIgéntémøCak; lak;. r)ar (bar) nImYy²GactMNageGaytémøsMNakKMrUmYy² b¤EdnéntémømYy. RbsinebIGredaen KitCaPaKry RkaPicnwgtMNageGaykarEbgEck relative frequency. kñúgkrNIEbbenH plbUkrbs; Gredaennwges μ I %100 . RbsinebIG½kSGab;sIusCaRBwtþikarN_ ehIyeRbInUvsMNakKMrURKb;RKan; Gredaen nImYy²GacsMEdgCaRbU)ab‘ÍlIetedaysresrCaPaKryéntémøsMNakKMrU b¤RBwtþikarN_EdlekItman. Relative frequency k¾GacsresrCaTMrg;TsSPaKpgEdr EdlmantémøenAcenøaHBI 0 nig 0.1 . dUcenH plbUkrbs;Gredaennwgesμ I 0.1 ehIyRbsinebIr)ar (bar) nImYy²manTTwgÉktþa dUcenHRkLaépÞsrub rbs;düaRkamk¾nwges μI 0.1 pgEdr. lT§plenHbBa¢ak;faRbU)ab‘ÍlIetEdles μInwg 0.1 nwgnaMeGayRBwtþi- karN_sßitenAkñúgEdnkMNt;rbs;düaRkam. elIsBIenH Rb)ab‘ÍlIeténtémøCak;lak;EdltUcCag Edlnwg



ekIteLIgnwgesμ IRkLaépÞrbs;düaRkamEdlenAxageqVgrbs;témøenaH. RbU)ab‘ÍlIeténRBwtþkarN_Edl mantémøsßitenAcenøaH a nig b enAkñúgrUbTI 2>1 esμ InwgRkLaépÞrbs;düaRkamenAcenøaH a nig b .

munnwgdMeNIrkarsikSaKNna eyIgRtUvsÁal;BIrUbmnþxøH²EdleRbIenAkñúgRbU)ab‘ÍlIet. mFümPaK (mean) x énsMnMutémøsMNakKMrU b¤ population CatémømFümnBVnþEdl

∑=

=n

iix

nx

1

1

Edl ix CatémøsMNakKMrU ehIy n CacMnYnrbs;témø. Median CatémøkNþalrbs; x ehIy mode CatémøEdlekItmanjwkjab;CageK. Variance v CaxñatEdlvas;BIbERmbRmYlénTinñn½yTaMgGs;BI mean ehIyRtUv)ankMNt;dUcxageRkam³

( )∑=

−=n

ii xx

nv

1

21

Standard deviation s Cab¤skaerén variance

( )∑=

−=n

ii xx

ns

1

21

dUcKñanwg variance Edr standard deviation CargVas;énbERmbRmYlTaMgmUl b:uEnþvamanxñat niglMdab;én GaMgtg;sIuetCa data. Coefficient of variation V CaplEckrvag standard deviation elI mean.

xsV =



RbsinebIeKCMnYskarEbgEck frequency Cak;EsþgedayGnuKmn_Cab;tamRTwsþIEdlesÞIrEtes μ IKñanwgTinñ-n½y (data) enaHeKehAGnuKmn_enHCa probability density function. GnuKmn_EbbenHRtUv)an bgðajenAkñúgrUbTI 2>2. GnuKmn_RbU)ab‘ÍlIetRtUv)anKNnaedayeGayRkLaépÞsrubEdlenABIeRkam ExSekagesμ IcMnYnÉktþa. sRmab;GnuKmn_ ( )xf

( )∫+∞

∞−= 0.1dxxf

Edlmann½yfaRbU)ab‘ÍlIeténtémøsMNakKMrU b¤RBwtþikarN_EdlnwgekIteLIgesμInwg 0.1 . RbU)ab‘ÍlIetén RBWtþikarN_enAcenøaH a nig b enAkñúgrUbTI 2>2 es μ InwgRkLaépÞeRkamExSekagcenøaH a nig b

( )∫b

adxxf

enAeBlEdleKeRbI probability density function eKsn μt;eRbInimitþsBaØaxageRkam =μ mean =σ standard deviation

eKalkarN_RbU)ab‘ÍlIetrbs;emKuNbnÞúk nigemKuNersIusþg;EdleRbIeday AISC RtUv)anbgðaj enAkñúg ASCE structural journal (Ravindra and Galambos, 1978). \T§iBlbnÞúk Q nigersIusþg; R CaGBaØat ehIyvaGaRs½yeTAnwgemKuNCaeRcIn. eK)a:n;s μan nigTTYl)anbnÞúkBIkarvas;eRKOgbgÁúMCak; Esþg ehIyersIusþg;RtUv)anKNna nigkMNt;edaykarBiesaF. Q nig R RtUv)anbMEbkeGaydac;BIKña



ehIy GacbgðajCa frequency distribution histogram b¤bgðajCa theoretical probability density

function. RbsinebIeKsg;düaRkamén probability density sRmab;\T§iBlbnÞúk Q nigersIusþg; R enAelI RkaPicEtmYy dUcenAkñúgrUbTI 2>3 tMbn;EdlRtUvKñanwg RQ > bgðajBI failure ehIy RQ < bgðajBI survival. RbsinebIkarEbgEck Q nig R RtUv)andak;bBa©ÚlKñaeTAkñúgGnuKmn_EtmYy témøviC¢manén

QR − RtUvKñanwg survival. dUcKña RbsinebIeKeRbI probability density function QR / ¬emKuN suvtßiPaB¦ survival RtUv)ansMEdgedaytémø QR / FMCag 0.1 . RbU)ab‘ÍlIetEdlRtUvKñanwg failure

CaRbU)ab‘ÍlIetEdl QR / tUcCag 0.1 .

⎥⎦

⎤⎢⎣

⎡<⎟⎟

⎠

⎞⎜⎜⎝

⎛= 1

QRPPF

edaydak;elakarItenEBeTAelIGgÁsgxagénvismIkarxagelIeyIgTTYl)an

⎥⎦

⎤⎢⎣

⎡<⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎥

⎦

⎤⎢⎣

⎡<⎟⎟

⎠

⎞⎜⎜⎝

⎛= 0ln1lnln

QRP

QRPPF

ExSekagEbgEck frequency én ( )QR /ln RtUv)anbgðajenAkñúgrUbTI 2>4. eKGackMNt;TMrg;Edlman lkçN³sþg;daénGBaØat ( )QR /ln Ca

( )QR

mQR

QR

U/ln

lnln

σ

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟⎠

⎞⎜⎜⎝

⎛

=



Edl =⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

mQRln témømFüm (mean value) én ⎟⎟

⎠

⎞⎜⎜⎝

⎛QR

( ) =QR /lnσ standard deviation én ⎟⎟⎠

⎞⎜⎜⎝

⎛QR

eyIgGacsresrRbU)ab‘ÍlIetén failure Ca

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛<

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎥

⎦

⎤⎢⎣

⎡<⎟⎟

⎠

⎞⎜⎜⎝

⎛= 0ln0ln /ln

mQRF Q

RUPQRPP σ

( )⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−<=)/ln(/ln

lnln

QR

mu

QR

m QR

FQR

UPσσ

Edl uF Ca cumulative distribution function én U b¤CaRbU)ab‘ÍlIetEdl U minFMCag argument rbs;GnuKmn_. RbsinebIeyIgyk

( )QR

mQR

/ln

ln

σβ

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

= (2.4)

enaH ( )QRmQ

R/lnln βσ=⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛



eKGacbgðajGBaØat β CacMnYnén standard deviations BIeKalén mean value ( )QR /ln . edIm,I suvtßiPaB/ mean value RtUvEttUcCagsUnü ehIyCavi)ak β RtUv)aneKehAfa safety index b¤ reliability index. témøenHkan;EtFM kMritsuvtßiPaBkan;EtFM. enHmann½yfaRbU)ab‘ÍlIetén failure Edl bgðajedayépÞqUtenAkñúgrUbTI 2>4 nigmankMNt;sMKal; FP nwgmantémøtUc. Reliability index CaGnuKmn_én\T§iBlbnÞúk Q nigersIusþg; R . kareRbI reliability index dUcKñasRmab;RKb;RbePTGgát; EdlrgRKb;RbePTbnÞúk dUcKñanwgkarpþl;eGayGgát;nUversIusþg;RKb;RbePTEdr. témøkMNt; (target

value) rbs; β EdlbgðajenAkñúgtarag 2>1 RtUv)aneRCIserIs nigeRbIenAkñúgkarKNnaemKuNbnÞúk nigemKuNersIusþg;sRmab; AISC Specification EdlQrelIkaresñIeLIgeday Ravindra and

Galambos (1978) ehIyk¾)anbgðajfa

RV

n

m eRR βφ 55.0−= (2.5)

Edl =mR mean value énersIusþg; R =nR nominal resistance b¤ersIusþg;tamRTwsþI =RV emKuNbERmbRmYlrbs; R smIkar 2.5 CasmIkarsRmab;emKuNersIusþg; φ EdleGayenAkñúg Commentary to the

Specification.

2>5> Manual of Steel Construction

Manual manBIrPaK EdlPaKTImYymancMNgeCIgfa “Structural Members, Specifications

and Codes” man 7Epñk Edlerobrab;BIkarKNnaGgát; ehIyPaKTIBIrmancMNgeCIg “connections”

tarag 2>1 Edntémø (target value) rbs; β lkçxNÐbnÞúk

RbePTeRKOgbgÁúM LD (+ b¤ )S SLD ++ ELD ++

Ggát; 3.0 2.5 1.75

tMN 4.5 4.5 4.5



man 5Epñk EdlniyayBIkarKNnatMN. esovePAenHepþatCasMxan;eTAelIPaKTImYyEdlEckecjCa 7Epñk.

Part1. Dimensions and Properties: EpñkenHmanB½t’manlMGitBI standard rolled-shapes,

pipe nig structural tubing EdlrYmmanTMhMmuxkat; niglkçN³sMxan;²TaMgGs; dUcCaRkLaépÞ nigm:Um:g;niclPaB. EdkEdlmanerobrab;enAkñúg manual enHRtUv)anGnuBaØateday AISC

Specification sRmab;eRbIR)as;enAkñúgsMNg;GKarEdlrYmmandUcxageRkam³

ASTM A36: Carbon structural steel ASTM A529: High-strength, carbon-manganese structural steel ASTM A572: High-strength, low-alloy structural steel ASTM A242: Corrosion-resistant, high-strength, low-alloy structural steel ASTM A588: Corrosion-resistant, high strength, low-alloy structural steel ASTM A852: Quenched and temped low-alloy structural plate ASTM A514: High-strength, quenched and tempered alloy structural steel plate

Part2. Essentials of LRFD: EpñkenHENnaMy:agsegçbBImUldæanrbs; load and resistance

factor design rbs;eRKOgbgÁúMEdk nigman]TahrN_CaelxbgðajpgEdr. Part3. Column Design: EpñkenHmantaragCaeRcInsRmab;sRmYlldl;karKNnaTaMgGgát; rgkarsgát;tamG½kS nig beam-columns. taragPaKeRcInKWsRmab;EdkEdlman yield stress

MPaksi 25036 ≈ nig MPaksi 34550 ≈ . Part4. Beam and Girder Design: EpñkenHk¾dUcEpñkTI 3EdrKWvaman design aid CaeRcInrYm mantarag nigRkaPic. Design aid PaKeRcInmanniyayBItMrUvkarrbs; AISC Specification b:uEnþ design aid xøHdUcCa Beam diagrams and Formula KWTak;Tgnwg structural analysis. kñúgEpñkenHk¾manerobrab;BIdMeNIrkarKNnaFñwm nig girder ehIyman]TahrN_bgðajBIkarsikSa KNnaeTotpg. Part5. Composite Design: EpñkenHerobrab;BIeRKOgbgÁúMsmas EdlCaTUeTACaFñwm b¤ssr. eRKOgbgÁúMsmaspSMeLIgedaysmÖar³BIrRbePTKW EdkeRKOgbgÁúM nigebtugGarem:. CaFm μta eK eRbIFñwmsmasenAeBlEdlRbB½n§FñwmRsbRTkMralxNÐebtugGarem:. enAkñúgkarGnuvtþ element EdlpSarP¢ab;eTAnwgsøabxagelIRtUv)anbgáb;enAkñúgebtugedIm,IP¢ab;smÖar³TaMgBIr. ssrsmas



GacCaEdkeRKOgbgÁúMbgáb;enAkñúgebtugGarem: b¤EdkRbehagEdlbMeBjedayebtug. EpñkenH man design aid nig]TahrN_bgðajpgEdr. Part6. Specifications and Codes: EpñkenHman AISC Specification nig Commentary,

specification sRmab;b‘ULúgersIusþg;x<s; (RCSC, 1994) nigÉksardéTeTot. Part7. Miscellaneous Data and Mathematical Tables: EpñkenHniyayBI wire, sheet

steel niglkçN³epSg²rbs;Edk nigsmÖar³sMNg;déTeTot. ehIyk¾manrYmbBa©ÚlTaMgrUbmnþ KNitviTüa nigemKuNsRmab;bMElgxñat. PaKTIBIr ¬EdlpSMeday 5Epñk¦ mantaragsRmab;CYykñúgkarKNnakartP¢ab;edaykarpSar

nigedayb‘ULúgCamYynwgtaragEdlpþl;eGayy:aglMGitelI standard connection. AISC Specification RKan;EtCaEpñkd¾tUcmYyrbs; Manual. Bakü nigtémøefrCaeRcInEdleRbI

enAkñúgEpñkxøHrbs; Manual RtUv)anbgðajedIm,IsRmYldl;dMeNIrkarsikSaKNna ehIyvaminmansresr enAkñúg specification eT.


cMeNaT 29 T.Chhay

cMeNaT cMNaM³ bnÞúksmμtikm μTaMgGs;CabnÞúkeFVIkar (service load). @>#>!> ssrenACan;xagelIrbs;GKarrgbnÞúksgát;Edl)anBI³ bnÞúkefr kN137= / bnÞúkGefr kN5.7= / bnÞúkGefrEdlmanGMeBIelIdMbUl kN85= nigbnÞúkRBwl kN90= . k> kMNt;karbnSMbnÞúkEdlmanlkçN³lub nigbnÞúkemKuN. x> RbsinebIemKuNersIusþg;es μInwg 85.0 . etI nominal strength tRmUvkarrbs;ssrmantémøb:unμan? @>#>@> ssrrgbnÞúkEdl)anBI³ bnÞúkefr kN115= / bnÞúkGefr kN67= / bnÞúkGefrEdlmanGMeBIelI dMbUl kN22= / bnÞúkRBil kN35= / bnÞúkePøóg kN22= nigbnÞúkxül; kN35 . bnÞúkTaMgGs;CabnÞúk sgát;elIkElgEtbnÞúkxül;EdlGacCabnÞúkTaj b¤bnÞúksgát;. k> kMNt;karbnSMbnÞúkEdlmanlkçN³lub nigbnÞúkemKuN. x> RbsinebIemKuNersIusþg;es μInwg 85.0 . etI nominal strength tRmUvkarrbs;ssrmantémøb:unμan? @>#>#> bnÞúkenAelIFñwmdMbUlrYmmanbnÞúkGefr mkN /9.2 / bnÞúkGefrEdlmanGMeBIelIdMbUl mkN /9.1 nigbnÞúkRBwl mkN /0.2 . kMNt;bnÞúkemKuNEdleKeRbIsRmab;sikSaKNnaFñwmenH. etIbnSMbnÞúkmYy NaEdllub? @>#>$> eKnwgsikSaKNnaFñwmsRmab;RbB½n§dMbUl nigRbB½n§kRmalsRmab;GKarkariyal½y. kMNt;bnSM bnÞúkEdllub nigbnÞúkemKuNsRmab;krNIxageRkam³ k> dMbUl³ bnÞúkefr 2/4.1 mkN / bnÞúkefrEdlmanGMeBIelIdMbUl 2/0.1 mkN / bnÞúkRBil 2/0.1 mkN nigbnÞúkTwkePøógEdl)anBIkm<s;Twk cm10 . x> kRmal³ bnÞúkefr 2/0.3 mkN nigbnÞúkGefr 2/8.3 mkN @>#>%> CaerOy² eKEtgsikSaKNnasMNg;GKarGMBIEdkCamYynwgRbB½n§BRgwgGgát;RTUg (diagonal bracing system) edIm,ITb;Tl;nwgbnÞúkxag ¬kmøaMgtamTisedkEdlekItBIbnÞúkxül; nigbnÞúkrBa¢ÜydI¦. kMNt;bnSMbnÞúk nigbnÞúkemKuNEdllubsRmab;bnÞúkEdl)anBI³ bnÞúkefr kN59= / bnÞúkGefr kN31= / bnÞúkGefrEdlmanGMeBIelIdMbUl kN8.5= / bnÞúkRBil kN8.5= bnÞúkxül; kN670= nigbnÞúkrBa¢ÜydI

kN717= .


T.Chhay 30 Tension Members

III. eRKOgbgÁúMrgkarTaj Tension Members

3>1> esckþIepþIm (Introduction)

eRKOgbgÁúMrgkarTaj CaeRKOgbgÁúMsMNg;EdlrgkmøaMgTajtamG½kS. vaRtUv)aneKeRbIsRmab; eRKOgbgÁúMeRcInRbePT rYmbBa©ÚlTaMgeRKOgbgÁúM truss ExSkabsRmab; suspension bridge nig cable-

stayed bridge, RbB½n§BRgwgGKar nigs<an ExSkabsRmab;RbB½n§dMbUlBüÜrpgEdr. sRmab;Ggát;rg karTaj RkLaépÞmuxkat;CaGñkkMNt;lT§PaBTb;Tl;eTAnwgkmøaMgxageRkA. EdkEdlmanmuxkat;mUl nig EdkEkghUtekþA (rolled angle shape) RtUv)aneKeRbICaTUeTA. eBlxøH muxkat; built-up BI muxkat;hUtekþA (rolled shape) b¤muxkat;pSMKñaBImuxkat;hUtekþACamYynwgEdkbnÞH (plate) RtUv)aneK eRbIR)as;kñúgkrNITb;Tl;CamYybnÞúkFM. muxkat; built-up PaKeRcInCa double-angle section ¬rUb TI3>1¦ CamYynwgmuxkat;KMrUepSg²eTot. edaysarEtkareRbIR)as;muxkat;enHmanPaBTUlMTUlay taraglkçN³énbnSMmuxkat;Ekg (combinations of angles) epSg²k¾RtUv)anbB©ÚaleTAkñúg AISC

Manual of steel Construction.

kugRtaMgenAkñúgGgát;rgkarTajtamG½kSKW

APf =

RbsinebIRkLaépÞmuxkat;rbs;Ggát;rgkarTajERbRbYltamRbEvg enaHkugRtaMgnwgERbRbYltam muxkat;Edr. CaFmμta eRKOgbgÁúMrgkarTajEdlP¢ab;edayb‘ULúg EtgEtmanRbehag. vtþmanrbs;Rb

Figure 3.1


eRKOgbgÁúMrgkarTaj 31 T.Chhay

ehagEtgman\T§iBleTAelIkugRtaMg. enAkñúgkrNIenH eKecalmuxkat;Rbehag. RkLaépÞmuxkat;suT§ (net area b¤ net section) Camuxkat;suT§EdlminKitmuxkat;Rbehag ÉRkLaépÞeBj (gross area) Camux kat;eBjEdlKitrYmTaMgmuxkat;Rbehag. CaerOy² Ggát;rgkarTajEtgP¢ab;edayb‘ULúgenAxagcug ¬rUb TI3>2¦. karsikSaKNnaeRKOgbgÁúMrgkarTaj KWCakareRCIserIsGgát;Edlmanmuxkat;RKb;RKan; edIm,ITb; Tl;nwgkugRtaMgEdl)anBIbnÞúkemKuN. kñúgkrNIEdleKsÁal;muxkat;Ggát; eKGacKNnaersIusþg;KNna (design strength) ehIyeKeFVIkareRbobeFobvaCamYybnÞúkemKuN. CaTUeTA karsikSaviPaK (analysis)

CadMeNIrkarKNnaviPaK ÉcMENkkarsikSaKNnamuxkat; (design) CadMeNIrkarKNnasarcuHsareLIg ehIyRtUvkarkarsakl,g nigmankMhusecosminput. 3>2> ersIusþg;KNna (Design strength)

eRKOgbgÁúMrgkarTajGacminCab;edaysßanPaBkMNt; (limit state) BIry:ag³ - kMhUcRTg;RTayelIslb; (excessive deformation)³ edIm,IkarBarsßanPaBEbbenH bnÞúkenAelI

muxkat;eBj (gross section) RtUvEtmantémøtUcRKb;RKan; EdlnaM[kugRtaMgenAelImuxkat; eBj (gross section) man témøtUcCagkugRtaMgyal (yield stress) yF .

gyn AFP <

Figure 3.2



Edl nP = nominal strength in yielding yF = yield strength gA = gross section area

- kardac; (fracture)³ edIm,IkarBarsßanPaBEbbenH kugRtaMgenAelImuxkat;suT§ (net section) RtUv EtmantémøtUcCagersuIsþg;dac; (tensile strength) uF .

eun AFP <

Edl nP = nominal strength in yielding uF = tensile strength

eA = RkLaépÞmuxkat;suT§RbsiT§PaB (effective net area). kñúgkrNIxøH eA mantémø esμ IRkLaépÞmuxkat;suT§ (net section) nA EtkñúgkrNIxøHvamantémøtUcCag nA .

eTaHbICa enAelImuxkat;suT§ (net section) ekItmanyal (yield) munk¾eday EtkMhUc RTg;RTayenAelIRbEvgéntMNmantémøtUcCagkMhUcRTg;RTayenAelIEpñkrgkarTajEdlenAsl;. mUlehtuKWsac;lUtsrub (total elongation) CaplKuNrvagRbEvgedIm nigsac;lUteFob (strain) ¬GnuKmn¾eTAnwgkugRtaMg¦. sßanPaBkMNt; (limit state) seRmc[muxkat;eBj (gross section)

rgkugRtaMgyal (yield stress) KWedaysarEtsac;lUtsrubmantémøFMCag minEmneday sarkaryal (yielding) muneT.

emKuNersIusþg; 9.0=tφ sRmab;karyal (yielding)

emKuNersIusþg; 75.0=tφ sRmab;kardac; (fracture)

BIsmIkar !># eyIgGacsresr

ntii PQ φγ ≤∑

b¤ ntu PP φ≤

Edl uP CabnSMbnÞúkemKuNEdlmantémøFMCageK. edaysareKmansßanPaBkMNt; (limit state) cMnYnBIr dUcenHsßanPaBTaMgBIrRtUvbMeBjlkçxNÐ

xageRkam³



gyu AFP 9.0≤ sRmab;;muxkat;eBj (gross section)

euu AFP 75.0≤ sRmab;muxkat;suT§ (net section)

témøtUcCageKkñúgcMeNamtémøTaMgBIrCaersIusþg;KNnarbs;Ggát;rgkarTaj. RkLaépÞBitR)akdEdldkecjBIRkLaépÞmuxkat;eBj (gross area) edaymanvtþman

RbehagKWGaRs½yeTAnwgdMeNIrkarplit. sRmab;karGnuvtþTUeTA rn§EdlecaHedaylkçN³bTdæan drill or punch oversized holes eKRtUvbUkbEnßm mm2 eTAelIGgát;p©itrbs;b‘ULúg. sRmab; drill or

punch standard holes eKRtUvbUkbEnßm mm4 eTAelIGgát;p©itrbs;b‘ULúgEdleKeRbIR)as;. sRmab; rn§RTEvg (slotted holes) eKRtUv)aneKbUkbEnßm mm2 eTAelIGgát;p©itrbs;b‘ULúg. xageRkamCatarag bgðajBIGgát;p©itb‘ULúg nigGgát;p©itrn§.

Nominal Hole Dimensions, mm

xñatRbehag Hole Dimensions Ggát;p©itb‘ULúg Bolt Diameter Standard

(Dia.) Oversize

(Dia.) Short-Slot

(Width × Length) Long-Slot

(Width × Length) M16 18 20 18×22 18 ×40 M20 22 24 22×26 22×50 M22 24 28 24×30 24×55 M24 27 [a] 30 27×32 27×60 M27 30 35 30×37 30×67 M30 33 38 33×40 33×75 ≥M36 d + 3 d + 8 (d + 3)×(d + 10) (d + 3)× 2.5d

[a]Clearance provided allows the use of a 1-in. bolt if desirable. (RtUvKña mm25 )

]TahrN_3>1³ r)arEdkm:ak A36 Edlmanmuxkat; 25.12125 mm× RtUv)aneRbICaGgát;rgkarTaj. vaRtUv)antP¢ab;eTAnwg gusset plate CamYynwgb‘ULúg M16 cMnYn 4 RKab; ¬rUbTI3>3¦. edaysnμt;fa effective net area eA esμ Inwg net area cUrkMNt;ersIusþg;KNna (design strength).



dMeNaHRsay³

EdkEdlmanm:ak A36 man MPaFy 250= nig MPaFu 400= sRmab; yielding én gross section

25.15625.12125 mmAg =×=

ersIusþg; nominal kNAFP gyn 3905.1562250 =×==

ersIusþg;KNna (design strength) kNPnt 3513909.0 =×=φ

sRmab; fracture én net section

holesgn AAA −= 25.1062)205.12(25.1562 mm=××−=

25.1062 mmAA ne == ¬sRmab;Et]TahrN_enHb:ueNÑaH¦ ersIusþg; nominal

kNAFP eun 4255.1062400 =×==

ersIusþg;KNna (design strength) kNPnt 75.34842575.0 =×=φ

dUcenH ersIusþg;KNna (design strength) kNPnt 75.348=φ ¬témøtUcCagCacemøIy¦ \T§iBlénkugRtaMgpþúM (stress concentration) minRtUv)aneKBicarNakñúgkrNIenHeT EtFatuBit kugRtaMgenARtg;rn§mantémøRbEhlbIdgkugRtaMgmFümEdlekItmanenAelI net area ehIykugRtaMgenA

Figure 3.3



Rtg; fillet énmuxkat;hUtekþA mantémøFMCagkugRtaMgmFümelIsBIrdg. edaysarEtPaBsVit b¤PaB hUtlYs (ductile) rbs;EdkEdlTItaMgEdlman overstress RtUv)anecalsRmab;karKNnaTUeTA. eRkamlkçxNÐCak;Esþg EdkGac)at;bg;PaBsVitrbs;va ehIy stress concentration GaceFVI[r)ar dac;Pøam². sßanPaBenHrYmman fatigue loading nigeRkamsItuNðPaBTabEmnETn. ]TahrN_3>2³ r)arrgkarTajmuxkat;EkgeTal 5.98989 ××L Rtv)anP¢ab;eTAnwg gusset plate CamYynwgb‘ULúg M22 cMnYn 3 RKab; ¬rUbTI3>4¦. r)arEdkenH manm:ak A36 . bnÞúkefr kNDL 155= nigbnÞúk kNLL 67= . viPaKmuxkat;enH edaysnμt; effective net area eA esμ IeTAnwg 85% rbs; net

area . dMeNaHRsay³

bnSMbnÞúk (load combination)

(A4-1): kNDL 2171554.14.1 =×=

(A4-2): kNkNLLDL 2172.293676.11552.16.12.1 >=×+×=+

⇒ kNPu 2.293=

ersIusþg;KNna (design strength)

gross section: 21610mmAg = kNAFP gytnt 25.36216102509.0 =××== φφ

net section: 21363)265.9(1610 mmAn =×−= 255.1158136385.0 mmAe =×= kNkNAFP eutnt y

25.36257.34755.115840075.0 <=××== φφ

Figure 3.4



eday ntu PP φ< ( )kNkN 57.3472.293 < dUcenH r)armansuvtßiPaBedaybMeBjlkçxNÐ. enAkñúg]TahrN_xagelIenH eyIgeXIjfabnSMMbnÞúk (A4-2) RtUv)anykmkeFVIkarKNna. enA

eBlmanEtbnÞúkefr nigbnÞúkGefreFVIGMeBIelIeRKOgbgÁúM ehIybnÞúkefr tUcCagbnÞúkGefr *dg enaHeKeRbI bnSMbnÞúk (A4-2) edIm,IeFVIkarKNna. sRmab;]TahrN_xagmux eyIgnwgmineFVIkarepÞógpÞat;bnSMbnÞúk

D4.1 (A4-1) eT edaysarEtvaminGacFMCagbnSMbnÞúk (A4-2)eT.

3>3> RkLaépÞmuxkat;suT§RbsiT§PaB (Effective net area)

kñúgcMeNamktþaCaeRcInEdlman\T§iBleTAelIkareFVIkarrbs;r)arrgkarTaj rebobénkartP¢ab; CaktþamYyEdlsMxan;CageK. tMNPaKeRcInEtgEteFVI[r)arcuHexSay karKNnanUv\T§iBlrbs;vaRtUv )aneKehAfa Joint efficiency . ktþaenHCaGnuKmn_eTAnwgPaBsVitrbs;smÖar³ (ductility of material)

KMlatrbs;eRKOgP¢ab; (fastener spacing) kugRtaMgpþúMenARtg;Rbehag (stress concentra-tion) TRmg; énkarplitrYmTaMg)atuPUtEdleKsÁal;faCa shear leg. ktþaTaMgenHnaM[mankarkat;bnßyRbsiT§PaB rbs;r)ar b:uEnþ shear lag CaktþamYyEdlsMxan;CageK. Shear lag ekItmanenAeBlEdlmuxkat;r)arTaMgmUlminRtUv)antP¢ab; dUcCaenAeBlEdleCIg mçagrbs;EdkEkgRtUv)anP¢ab;edaysarb‘ULúgeTAnwg gusset plate ¬rUbTI3>5¦. sar³sMxan;rbs;kart P¢ab;edayEpñk eFVI[Epñkrbs;r)arEdltP©ab;rgbnÞúkFM (overload) ehIyEpñkEdlmintP¢ab;minrg kugRtaMgeBjelj. karbnøayRbEvgtMbn;tP¢ab;CYykat;bnßy\T§iBlenH. karRsavRCavEdleFVIeLIg eday Munse nig Chesson (1963) )ansMNUmBr[Kit shear lag kñúgkarkat;bnßy net area. edaysarEt shear lag man\T§iBleTAelIkartP¢ab;edayb‘ULúg nigkartP¢ab;edaykarpSar enaH effec-

tive net area RtUv)aneKGnuvtþcMeBaHtMNTaMgBIrRbePTenH. Effective net area sRmab;tMNb‘ULúg

ne UAA =

Effective net area sRmab;tMNpSar

ge UAA =



U CaemKuNkat;bnßyRbsiT§PaB (reduction factor) 9.01 ≤−=

LxU (AISC Equation B3-2)

x CacmøayBITIRbCMuTm¶n;rbs;muxkat;eTAbøg;énkartP¢ab;. L CaRbEvgénkartP¢ab;. RbsinebIr)artP¢ab;edaymanlkçN³sIuemRTI x RtUveRCIserIsyktémøtUcCageK ¬rUbTI3>6¦. L CaRbEvgtP¢ab;tamTisedAbnÞúkeFVIGMeBI ¬rUbTI3>7¦. sRmab;tMNb‘ULúg L RtUv)aneKvas;BI

cugmçagrbs;G½kSb‘ULúg eTAcugmçageTotrbs;G½kSb‘ULúg. sRmab;tMNpSar L RtUv)anvas;BIcugtMNmçag eTAtMNmçag. RbsinebI kMNat;EdlpSarmanRbEvgtamTisedAkmøaMg RbEvgkMNat;EdlmanRbEvgEvg CagRtUv)anykmkKNna.

Figure 3.5

Figure 3.6



témømFüm

Lx sRmab;kartP¢ab;edayb‘ULúgsRmab;Ggát;rgkarTajepSg² Commentary to

AISC B3 [témø U CMnYs[karKNna Lx

−1 . témømFüm U sRmab;tMNb‘ULúgmanBIrRbePT³ sRmab;kartP¢ab;eday fastener BIrkñúgmYyCYrtamTisedAbnÞúkeFVIkar nigsRmab;karP¢ab;eday fastener

bIb¤ eRcInkñúgmYyCYr. eK[témø U bIepSgKña EdleKaeBtamlkçxNÐxageRkam³ !> sRmab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkm<s;y:agtic 3

2 ¬nigsRmab; muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøabCamYynwg fastener y:agticbIkúñgmYyCYrtamTisedAbnÞúkeFVIGMeBI

9.0=U @> sRmab;RKb;TRmg;muxkat;epSgeTot ¬rYmTaMgmuxkat; built-up¦ CamYynwg fastener y:agtic

bIkúñgmYyCYr

Figure 3.7



85.0=U #> sRmab;RKb;Ggát;TaMgGs; CamYynwg fastener y:agticBIrkúñgmYyCYr

75.0=U rUbxageRkamnwgbgðajnUv beRmIbRmas;c,ab;TaMgenH ¬rUbTI3>8¦. eKk¾GaceRbIR)as;témø U mFümsRmab;tMNpSarEdr. ebIeTaHCamin)anbriyaykñúg Com-

mentary k¾eday EtvaCaectnarbs; ¬AISC, 1989b¦. c,ab;enHdUcKña EtelIkElgsRmab;karpþl;[ EdleqøIytbeTAnwg fastener BIrminRtUv)anGnuvtþ. témømFüm U sRmab;tMNpSarmandUcxageRkam³

!> sRmab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkm<s;y:agtic 32 ¬nig

sRmab;muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøab 9.0=U

@> sRmab;RKb;TRmg;muxkat;epSgeTot 85.0=U

krNIBiesssRmab;kartedaykarpSar

eA mantémøtUcCag nA enAeBlEdlmuxkat;rbs;Ggát;xøHb:ueNÑaHminRtUv)antP¢ab;. sRmab; Ggát;rgkarTajdUcCa bnÞHEdk b¤r)ar ¬dUcbgðajkñúg]TahrN_3>1¦ effective net area RtUv)anyk eBj dUckarKNna net area. EteTaHCay:agNa vamankrNIelIkElgsRmab;c,ab;enH³ sRmab;bnÞH Edk b¤Edkr)arEdltP¢ab;edaykarpSartambeNþay (longitudinal weld) Epñkxagcugrbs;va ¬rUbTI 3>9¦ .

ne UAA =

Edl 1=U sRmab; wl 2≥ 87.0=U sRmab; wlw 25.1 <≤ 75.0=U sRmab; wlw 5.1<≤ l = RbEvgkarpSar w> w = cmøaycenøaHkarpSar ¬EdlGacykTTwgrbs; plate b¤ bar¦



AISC B3 k¾[nUvkrNIBiessmYysRmab;Ggát;edaykarpSarEt transverse weld b:ueNÑaH eA = RkLaépÞmuxkat;EdlpSar

Figure 3.8



¬rUbTI3>10¦ bgðajBIPaBxusKñarvagkarpSartambeNþay (longitudinal weld) nigkarpSar

tamTTwg (transverse weld). karEdlpSarEt transverse weld CakarxusFmμta EdleKmineRbIkñúg plitkmμeT.

]TahrN_TI3>3³ kMNt; effective net area sRmab;Ggát;rgkarTaj ¬rUbTI3>11¦. dMeNaHRsay³ holesgn AAA −= ( ) 2363 10212.3102207.121072.3 mAn

−−− ×=×××−×= eCIgEtmçagb:ueNÑaHrbs;muxkat;RtUv)anP¢ab; dUcenH net area RtUvEtkat;bnßy. BItaraglkçN³

kñúgEpñkTI1 rbs; Manual cmøayBITIRbCMuTm¶n;eTAépÞxageRkAéneCIgrbs; 7.12152152 ××L KW mx 21025.4 −×=

RbEvgtP¢ab;KW mmL 150275 =×=

Figure 3.9

Figure 3.10



9.0717.0150

5.421 <=−=U 233 103.210212.3717.0 mUAA ne

−− ⋅=⋅×== eKGaceRbItémømFüm U BI Commentary . edaysarEtmuxkat;minEmn W, M, S b¤ GkSr T

ehIymanb‘ULúgeRcInCagBIrkñúgmYyCYrtamTisbnÞúkeFVIGMeBI 85.0=U 233 1073.210212.385.0 mAe

−− ⋅=⋅×= témø U TaMgBIrGacTTYlyk)anTaMgBIr Ettémø U Edl)anBIkarKNnatam AISC Equation

B3-2 mantémøsuRkitCag. EteTaHCay:agNak¾eday k¾témømFüm U manRbeyaCn_sRmab;karKNna dMbUg (preliminary design) enAeBlEdlmuxkat;BitR)akd nigB½t’manlMGitGMBIkarpSarminTan;RtUv )andwgenaH.

]TahrN_TI3>4³ RbsinebIGgát;kñúg]TahrN_TI3>3 RtUv)anpSardUcbgðajkñúgrUbTI3>12 cUrkMNt; effective net area

dMeNaHRsay³ dUckñúg]TahrN_TI3>3 manEtEpñkmuxkat;tP¢ab; nig reduced effective net area

RtUv)aneRbI. karP¢ab;RtUv)aneFIVeLIgCamYynwgkarpSartambeNþay nigtamTTwg dUcenHvaminEmnCa krNIBiesssRmab;Ggát;pSareT.

9.07.0140

5.4211 <=⎟⎠⎞

⎜⎝⎛−=⎟

⎠⎞

⎜⎝⎛−=

LxU

cemøIy³ 233 10604.21072.37.0 mUAA ge−− ⋅=⋅×==

Figure 3.11



3>4> karteRmobtamEbbqøas; (Staggered fasteners)

RbsinebIkartP¢ab;Ggát;eFIVeLIgCamYynwgb‘ULúg enaH net area nwgmantémøGtibrmakñúgkrNI EdleRKOgP¢ab; (fastener) RtUv)andak;EtmYyCYr. eBlxøH edaysarEtKMlatRtUv)ankMNt; dUcCaTMhM a enA kñúgrUbTI3>13 (a) caM)ac;eFVI[eKRtUvEteRbIeRKOgP¢ab;eRcInCagmYyCYr. RbsinebIdUcenH kar kat;bnßyRkLaépÞmuxkat;RtUv)ankat;bnßy RbsinebIeRKOgP¢ab;RtUv)anteRmobtamEbbqøas; staggered

pattern dUcbgðaj. eBlxøH Staggered fasteners RtUv)aneKtRmUv[erobtamlkçN³FrNImaRtdUc bgðajkñúgrUbTI13 (b). kñúgkrNIepSgeTot muxkat;xøHEdlkat;tamrn§nwgkat;tamrn§EdlmancMnYntic CagRbsinebIeRKOgP¢ab;minRtUv)anteRmobtamEbbqøas;eTenaH.

RbsinebIcMnYnén stagger mancMnYnticlμm enaHkarP¢ab;Gacdac;tamExSKnøg abcd dUckñúgrUbTI 3>13 (c). kñúgkrNIEbbenH eKminGacGnuvtþTMnak;TMng A

Pf = )aneT ehIykugRtaMgenAkñúgmuxkat; tamExSeRTt bc KWCabnSMénkugRtaMgTaj nigkugRtaMgkmøaMgkat;. viFIsaRsþRbhak;RbEhl (approxi-

mate) CaeRcIn RtUv)aneKesñIeLIgedIm,IBnül;GMBIRbsiT§PaBrbs; staggered hole. elak Cochran

(1922) )anesñInUvkar eRbIR)as;RkLaépÞsuT§ (net area) Edlesμ InwgplKuNrvagkRmas;bnÞH nig TTwgsuT§ (net width). karKNnaRkLaépÞRtUv)aneFVIeLIgdUcteTA³ kMNt;ExSdac;EdlGacekIteLIg)an edIm,IeFVIkarGegát nig[TTwgsuT§ (net width) esμ InwgTTwgdk[

gsdd4

'2

−= (2-1)

sRmab;muxkat;dac;tam staggered hole b¤dk d sRmab;muxkat;dac;tam unstaggered hole. d Ca Ggát;p©itRbehag s (pitch) CaRbEvgKMlatrvagrn§BIrCitKñatamTisedARsbnwgbnÞúk nig g (gage) Ca

Figure 3.12



RbEvgKMlatRbehagtamTTwg. AISC specification k¾eRbInUvviFIsaRsþdUcKñaenHEdr b:uEnþkñúgTRmg;xus Kñabnþic. Epñk B2 tRmUv[TTwgsuT§RtUv)anKNnaedaydkplbUkGgát;p©itRbehagBITTwg ehIybUk bEnßmExSeRTt tamCYrmYy²Edlmantémø

gs4

2

.

gsdww gn 4

2

∑+∑−=

enAeBlEdlkardac;GacekIteLIgtamTRmg;eRcIn eKRtUveFVIkarGegátRKb;lT§PaBénkardac;TaMg Gs; ehIy (net width) EdlmantémøtUcCageKbMputRtUv)anykmkeRbI. cMNaMfa viFIsaRsþenHmin)an pþl;nUvTRmg;nwgkardac;CamYyExSRsbeTAnwgTisedAbnÞúkeFVIGMeBIenaHeT. ]TahrN_TI3>5³ KNna net area EdltUcbMputsRmab;bnÞHEdlbgðajkñúgrUbTI3>14 . RbehagTaMg Gs;sRmab;b‘ULúgGgát;p©it mm25 .

Figure 3.13



dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaB (effective hole diameter) KW mm30 sRmab;ExSbnÞat; abcd

mmwn 350)30(2410 =−= sRmab;ExSbnÞat; abcde

mmwn 6.341)130(4

)75(2)30(34102

=+−= mm350< cemøIy³ 268326.34120 mmtwA nn =×== edaysarEteRKOgP¢ab; (fastener) nImYy²Tb;Tl;kmøaMges μ I²Kña ¬karsnμt;EdleRbIenAkñúgkar KNnatMNsamBaØ kñúgCMBUkTI 7¦ sñamExSdac;EdlmanlkçN³epSgKña GaceFVI[muxkat;Rtg;kEnøg dac;rgkmøaMgepSgKña. ]TahrN_ ExS abcde kñúgrUbTI3>14 muxkat;rbs;Ggát;Rtg;kEnøgdac;rgkmøaMg eBj %100 EdlExS ijfh eFVI[muxkat;rbs;Ggát;Rtg;kEnøgdac;Tb;Tl;Et 11/8 énkmøaMgEdl Gnuvtþ. mUlehtuKW kmøaMg 11/3 EdlbBa¢ÚnBIGgát;RtUv)anTb;edayeRKOgP¢ab; munnwg ijfh TTYlbnÞúk. enAeBlEdl eRKOgP¢ab; (fastener) RtUv)anP¢ab;CaCYrenAelIeCIgTaMgBIrrbs;EdkEkg ehIykar P¢ab;manlkçN³qøas; (staggered) KñaeTAvijTAmk enaHedIm,ITTYl)anRkLaépÞ net area dMbUgeKRtUv BnøatEdkEkgedIm,ITTYl)anbnÞHEdksmmUl. bnÞHEdkenHRtUv)anviPaKdUcbnÞHEdkdéTeTotEdr. karBnøatRtUv)aneFVIeLIgtamRTnugEdkEkgEdlpþl;[nUvTTwgEdkbnÞHes μ IeTAnwgplbUkRbEvgeCIgrbs;

Figure 3.14



vadknwgkRmas;EdkEkg. AISC B2 kMNt;faRbEvg g Edlkat;tamRTnugEkgrbs;EdkEkgRtUv)andk edaykRmas;EdkEkg. dUcenH RbEvg g enAkñúgrUbTI3>15 EdlRtUv)anykeTAeRbIkñúgtY gs 4/2 nwgman témøes μ Inwg mm113125075 =−+ . ]TahrN_TI3>6³ cUrrk design tensile strength rbs;EdkEkgdUcbgðajkñúgrUbTI 3>16. Edk A36

RtUv)aneKykmkeRbIEdlmanRbehagsRmab;b‘ULúg 22mm. dMeNaHRsay³ KNna net width

mmwg 3.3427.12152203 =−+=

Ggát;p©itRbehagRbsiT§PaB effective hole diameter esμ I 28mm

sRmab;ExSbnÞat; abdf mmwn 3.286)282(3.342 =×−= sRmab;ExSbnÞat; abceg mmwn 98.263

5.634)38()283(3.342

2=

×+×−=

Figure 3.15

Figure 3.16



edaysarEt bnÞúk 10/1 RtUv)anepÞrBIGgát;edayeRKOgP¢ab;enARtg;cMNuc d enaHExSrdac; potential failure line enHRtUvEtTb;nwgbnÞúkEt 10/9 . dUcenH net width mm98.263 RtUvEtKuNnwg

9/10 edIm,ITTYl)an net width EdlGaceRbobeFobCamYynwgExSbnÞat;EdlTb;nwgbnÞúkeBj %100 . dUcenHExSbnÞat; abceg man mmwn 31.2939/1098.263 =×= sRmab;ExSbnÞat; degabc

mmgcd 3.1207.125776 =−+= mmwn 74.243

764)38(

1204)38(

5.634)38()284(3.342

222=

×+

×+

×+×−=

eday net width Edldac;tamExS degabc mantémøtUcCageK dUcenHkrNIenHRtUv)aneKykmk KNna net area

25.309574.2437.12 mmAn =×= edaysarEteCIgTaMgBIrrbs;EdkEkgRtUv)anP¢ab; dUcenH

25.3095 mmAA ne == ersIusþg;KNnaKW kNAFP eunt 65.9285.309540075.075.0 =××==φ

kNAFP nynt 75.98743902509.05.0 =××==φ cemøIy³ ersIusþg;KNnaKW kN65.928

cMNaMfa plKuNrvag gross width nwgkRmas;EdkEkgKWCa gross area krNIRtwmRtUvRbsinebI eCIgrbs;EdkEkgmanragctuekaNEkg. mUlehtuKWfa eKGacTTYl)anragctuekaNEkgedaydképÞ enARtg;rbt;Ekg nigbUkbEnßmépÞenARtg;cugEdkEkg.

AISC Specification min)anpþl;karENnaMsRmab;karerobeRKOgP¢ab;tamEbbqøas;enAelI rolled shape eRkABIEdkEkgeT. bnÞHEdksmmUlmanPaBs μ úKsμajedaysarkRmas;Ggát;manPaBxus Kña dUckrNIEdk channel nig wide flange . enAkñúgkrNIEbbenH eKesñI[eRbIRkLaépÞ ¬RbesIrCag TTWg¦ nigdkGgát;p©itrn§ Edl[edaysmIkar (2-1).

enAkñúg]TahrN_TI3>7 RKb;rn§RbehagTaMgGs;sßitenAEtmYyEpñkénmuxkat;.



]TahrN_TI3>7³ kMNt;RkLaépÞmuxkat;suT§Gb,brma (smallest net area) sRmab;Edk American

Standard Channel dUcbgðajenAkñúgrUbTI3>17. RbehagsRmab;b‘ULúgEdlmanGgát;p©it 16mm.

dMeNaHRsay³ ∑ ×−= (dtAA wgn b¤ )' d

mmd 20= ExSbnÞat; abc

22238201.112460 mmdtAA wgn =×−=−= ExSbnÞat; abcd

dtAA wgn (−= sRmab;RbehagRtg; '() dtb w− sRmab;RbehagRtg; )c 2

21.2064

75450221.11221.112460 mm=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

×−×−×−=

cemøIy³ RkLaépÞmuxkat;Gb,brma (smallest net area) KW 21.2064 mm enAeBlEdlEpñkCaeRcInrbs;muxkat;manRbehag eKeRbIviFIsaRsþedaHRsayxusKñabnþic. eTaHbICa EdkEdlmanrUbragepSgBIEdkEkgminGacBnøattamviFIEdlEdkEkgBnøatk¾eday k¾eKmanviFIsaRsþ epSgeTotkñúgkarBnøatrUbragEdkTaMgenaHEdr. viFIsaRsþkñúgkarBnøatEdkTaMgenaHRtUv)anbgðajkñúgrUbTI 3>18 nigkñúg]TahrN_TI3>8.



]TahrN_TI3>8³ kMNt;ersIusþg;KNnarbs;Edk S-Shape dUcbgðajkñúgrUbTI3>19. RbehagKWsRmab;b‘U LúgEdlmanGgát;p©it mm20 . eRbIEdk 36A . dMeNaHRsay³ KNnaRkLaépÞ net area

×−= ∑ tAA gn ( Ggát;p©itRbehag ) Ggát;p©itRbehagRbsiT§PaB mm24= sRmab;ExS ad

22.79538.152449470 mmAn =××−= sRmab;ExS abcd RbEvg g sRmab;eRbIenAkñúgtY

gs4

2 KW

Figure 3.18

Figure 3.19



mmtgg w 5.1072

14702

8922 1 =−+=−+

edayKitRbehagRtg; b nigRtg; c CaRbehagEdlerobqøas; eKTTYl)an 2

223.7375

5.10743824142248.1549470 mmAn =⎟

⎟⎠

⎞⎜⎜⎝

⎛

×−××−××−=

kardac;tamExS abcd mantémøtUcCageK. edaysarRKb;EpñkTaMgGs;rbs;muxkat;RtUv)anP¢ab; dUcenH 223.7375 mmAA ne ==

sRmab; net section

kNAFP eunt 57.221223.737540075.075.0 =××==φ kNAFP nynt 75.213094702509.05.0 =××==φ

cemøIy³ ersIusþg;KNnaKW kN75.2130 3>5> Block shear

sRmab;rUbsNæanénkartP¢ab;xøH kMNat; b¤bøúkénsmÖar³enAxagcugénGgát;GacrEhk. ]Ta-hrN_ kartP¢ab;rbs;Ggát;ragEkgeTalrgkarTaj dUcbgðajkñúgrUbTI3>20 gayrg)atuPUtEbbenH Edl eK[eQ μaHfa block shear ¬kardac;TaMgbøúk¦. sRmab;krNIEdl)anbgðajkñúgrUb épÞEdlqUtGac dac;edaykmøaMgkat;TTwg (shear) tammuxkat;beNþay ab nigkmøaMgTaj (tension) tammuxkat;TTwg bc. RbFanbT enHmin)anbgðajy:agc,as;kñúg AISC Chapter D (“Tension Members”) eT b:uEnþkfaxNÐdMbUg )anENnaMeyIgeTAkan; Chapter J (“Connections, Joints, and Fasteners”),

Section J4.3 (“Block Shear Rupture Strength”). nitiviFIKWQrenAelIkarsnμt;fa muxkat;dac;mYyKWdac;eday fractures nigmYyeTotdac;eday yielding. enHmann½yfa muxkat;EdlrgkugRtaMgTaj yield naM[muxkat;EdlrgkugRtaMgkmøaMgkat; TTwg fracture b¤pÞúymkvij. muxkat;TaMgBIrenH naMmknUvPaBFn;srub ehIyersIusþg;rbs; block shear

KWCaplbUkénPaBFn;énmuxkat;TaMgBIr. PaBFn;Fmμta (nominal strength) enAkñúgGgát;rgkarTajKW ntu AF sRmab; fracture nig

gty AF sRmab; yield Edl ntA KWCa net area nig gtA KWCa gross area tambeNþaymuxkat;rgkar Taj ¬ bc enAkñúgrUbTI3>20¦. edayykkugRtaMg yield sRmab;møaMgkat; nigkugRtaMg ultimate sRmab;



kmøaMgkat;esμ I 60% énkugRtaMgkmøaMgTaj enaHersIusþg;dac;Fmμta (nominal fracture strength) sRmab; kmøaMgkat;KW nvu AF6.0 nigersIusþg; yield sRmab;kmøaMgkat;KW gvy AF6.0 Edl nvA KWCa net area nig

gvA KWCa gross area tambeNþaymuxkat;rgkmøaMgkat; ¬ ab enAkñúgrUbTI20¦. eKGacmanTRmg;énkardac;Ca2rebob. sRmab;kmøaMgkat; yield nigkmøaMgTaj fracture ersIusþg;KNnaKW

]6.0[ ntugvyn AFAFR += φφ (AISC Equation J4-3a)

sRmab;kmøaMgTaj yield nigkmøaMgkat; fracture ersIusþg;KNnaKW

]6.0[ gtynvun AFAFR += φφ (AISC Equation J4-3a)

sRmab;krNITaMgBIr 75.0=φ . BIeRBaH sßanPaBkNt; (limit state) KW fracture smIkarEdl lub KWsmIkarNaEdlmantY fracture FMCag.

]TahrN_TI3>9³ kMNt;ersIusþg; block shear rbs;Ggát;rgkarTajdUcbgðajenAkñúgrUbTI 3>21. rn§RbehagRtUv)aneRbIsRmab;Ggát;p©it 22mm nigEdkRbePT A36RtUv)aneRbI.

dMeNaHRsay³ RkLaépÞmuxkat;kmøaMgkat;KW

218051905.9 mmAgv =×=

Figure 3.20



edaysarEtman 2.5 Ggát;p©itrn§

[ ] 21140285.21905.9 mmAnv =×−×= RkLaépÞmuxkat;kmøaMgTaj

25.370395.9 mmAgt =×= [ ] 25.237285.0395.9 mmAnt =×−×=

edayeRbI AISC Equation J4-3a eKTTYl)an ]6.0[ ntugvyn AFAFR += φφ

( )( )[ ]5.23740018052506.075.0 ×+×= [ ] kN3.2749500027075075.0 =+×= edayeRbI AISC Equation J4-3b eKTTYl)an

]6.0[ gtynvun AFAFR += φφ ( )( )[ ]5.37025011404006.075.0 ×+×= [ ] kN7.2749262527360075.0 =+×= smIkarTI 2 mantY fracture FM ¬tYEdlman uF ¦ dUcenHsmIkarTI 2 lub.

cemøIy³ ersIusþg;KNnasRmab; block shearKW kN7.274 . 3>6> karKNnaGgát;rgkarTaj Design of tension members

karKNnaGgát;rgkarTaj KWkarKNnark gross area nig net area RKb;RKan;sRmab;Ggát;Edl rgkarTaj. RbsinebIGgát;enaHRtUv)anP¢ab;edaytMNb‘ULúg enaHeKRtUvkarnUvmuxkat;smRsbsRmab;Rk

Figure 3.21



LaépÞEdl)an)at;bg;edaysarrn§tMN. sRmab;Ggát;Edlmanmuxkat;ctuekaNEkg karKNnaman lkçN³RsYlCag. RbsinebImuxkat; rolled shape RtUv)aneRbImuxkat;EdlRtUvkat;bnßyminGacRtUv)an BüakrN_TukCamun)an BIeRBaHkRmas;rbs;muxkat;enARtg;cMNucrn§minRtUv)andwg. karBicarNabnÞab;kñúgkarKNnaGgát;rgkarTajKW PaBrlas; (slenderness). RbsinebIGgát; rbs;eRKagbgÁúMmanmuxkat;tUceFobeTAnwgRbEvgrbs;va enaHGgát;enaHmanlkçN³Rsav (slender). kar KNnaEdlmanlkçN³suRkit KWpleFobrlas; (slenderness ration)

RL Edl L CaRbEvgrbs;Ggát;

nig r Ca kaMniclPaB (radius of gyration) énRkLaépÞmuxkat;Gb,brma. kaMniclPaB (radius of

gyration) Gb,brma KWRtUvKñanwgG½kS minor principal énmuxkat;. témørbs; radius of gyration

RtUv)anerobCataragsRmab;muxkat; rolled shape TaMgGs;enAkñúgtaraglkçN³ (properties tables)

enAkñúgEpñkTI1 én Manual. sRmab;Ggát;rgkarsgát; slenderness mansar³sMxan;sRmab;ersIusþg; (strength) b:uEnþ slender-

ness minsUvCasMxan;sRmab;Ggát;rgkarTajb:unμaneT. eTaHCay:agNak¾eday enAkñúgsßanPaBxøH vaCa karRbesIrsRmab;karkMNt;nUv slenderness sRmab;Ggát;rgkarTaj. RbsinebIbnÞúkcMG½kSenAkñúg Ggát; rgkarTajRsav (slender tension member) ehIyrgbnÞúktamTTwg (transverse load) eTaHtUckþI k¾rMjr½EdleKminR)afñacg;)an b¤PaBdabnwgekItmaneLIg. Ca]TahrN_ krNIenHGacekIteLIgsRmab; EdkBRgwg (bracing rod) EdlmanlkçN³mintwgRbQmnwgkmøaMgxül;. sRmab;krNIenH AISC B7

)anesñInUv slenderness ratio Gtibrmaes μInwg 300. témøenHRKan;EtCatémøesñI (commended value) BIeRBaH slenderness minmanPaBsMxan;sRmab;Ggát;rgkarTajeT ehIytémøenHGacRtUv)anykFMCag enHenAeBlEdlkal³eTs³BiessGnuBaØat[. EdntémøenHminRtUv)anGnuvtþeTAelIExSkabeT ehIy specification k¾)anelIkElgcMeBaHEdksrésEdr. bBaðasMxan;kñúgkarKNnaRKb;muxkat;TaMgGs; rYmbBa©ÚlTaMgkarKNnaGgát;rgkarTaj KWkarrk muxkat; EdlplbUkbnÞúkemKuNTaMgGs;minRtUvelIsersIusþg;rbs;Ggát;. Edl

∑ ≤ nRQ φγ

sRmab;Ggát;rgkarTaj smIkarenHmanrag



ntu PP φ≤ b¤ unt PP ≥φ

Edl uP KWCaplbUkbnÞúkemKuN. edIm,IKNna yielding

ugy PAF ≥9.0 b¤ y

ug F

PA90.0

≥

edIm,IeCosvag fracture

ueu PAF ≥75.0 b¤ u

ue F

PA75.0

≥

Slenderness ratio RtUv)anbMeBjRbsinebI

300Lr ≥

Edl r Ca radius of gyration Gb,brma nig L CaRbEvgGgát;.

]TahrN_TI3>10³ Ggát;rgkarTajEdlmanRbEvg mm1750 RtUvTb;nwgbnÞúkefreFVIkar (service dead

load) kN80 nigbnÞúkGefreFVIkar (service live load) kN233 . eRCIserIsGgát;Edlmanmux kat;ctuekaNEkg. eRbIEdk 36A nigtMNRtUv)ansnμt;eRbIb‘ULúgEdlmanGgát;p©it mm24 mYyCYr. dMeNaHRsay³

kNPu 8.4682336.1802.1 =×+×= muxkat;caM)ac; 2

36.2083

2509.0108.468

9.0mm

FPA

y

ug =

×⋅

==

muxkat;caM)ac; 23

7.156240075.0108.468

75.0mm

FPA

u

ue =

×⋅

== edaysarEt ne AA = sRmab;Ggát;enH gross area EdlRtUvKñanwg muxkat;caM)ac; net area

enHKW holeng AAA +=

t×+= 287.1562



sakl,g mmt 25= 27.226225287.1562 mmAg =×+=

edaysarEt 6.20837.2262 > dUcenHmuxkat;caM)ac;KW 27.2262 mm mm

tA

w gg 5.90

257.2262===

sakl,gmuxkat; 9225× epÞógpÞat; slenderness ratio

43

min 7.11979112

2592 mmI =×

=

23009225 =×=A

BI 2ArI = eyIgTTYl)an mm

AIr 22.7

23007.119791min

min === 3004.242

22.71750

<==rL (OK)

cemøIy³ eRbIEdkEdlmanmuxkat; 9225× . Ggát;enAkñúg]TahrN_TI3>10 manTTwgtUcCag mm20 EdlRtUv)aneKcat;fñak;vaCaEdkr)ar (bar) CaCagEdkbnÞH (plate). Edkr)arKYrRtUv)ankMNt;eday[TTwgrbs;vaERbRbYlmþg mm5 nig kRmas;rbs;vaERbRbYlmþg mm2 ¬RbB½n§cMNat;fñak;Cak;lak;RtUv)anpþl;[kñúgEpñkTI1 én Manual

eRkamcMNgeCIg “Bars and Plates”. RbsinebIEdkEkgRtUv)aneRbICaGgát;rgkarTaj ehIykartP¢ab;RtUv)aneFVIeLIgedayeRbIb‘ULúg

enaHvacM)ac;RtUvmanépÞ ¬TMhM¦ RKb;RKan;sRmab;b‘ULúg. vaGacekItmanbBaðaenAeBlEdleKeRbIb‘ULúgBIr CYrenAelIeCIgmYy. rn§RbehagRtUv)aneKecaHenATItaMgdUcbgðajenAkñúgrUbTI3>22 (a) sRmab;karplit TUeTA eday)andkecjBIrUbTI 9-5 enAkñúgEpñkTI9 én Manual (VOL. II). cmøayKMlat Rbehag tamTTwg gage 1g RtUv)aneKeRbIenAeBlEdleKmanb‘ULúgmYyCYr ehIy 2g nig 3g RtUv)aneKeRbIenA eBlEdleKmanb‘ULúgBIrCYr. rUbTI3>22 (b)bgðajfaeCIgEdkEkgRtUvmanRbEvgy:agxøIbMput mm127 edIm,IGnuBaØat[eRbIb‘ULúgBIrCYr)an.



]TahrN_TI3>11³ KNnaGgát;rgkarTajEdlmanmuxkat;EdkEkgeCIgmines μ IKña (unequal-leg angle) RbEvg m6.4 Tb;nUv service dead load kN155 nig service live load kN310 . eRbIEdkRbePT

36A . kartRtUv)anbgðajenAkñúgrUbTI23. dMeNaHRsay³ bnÞúkemKuN (factored load) ( ) ( ) kNLDPu 6823106.11552.16.12.1 =+=+=

KMlatRbehagtamTTWgsRmab;EdkEkg )(mm

Leg 203 178 152 127 102 89 76 64 51 44 38 35 32 25 g1 114 102 89 76 64 51 44 35 26 25 22 22 19 16 g2 76 64 57 51 g3 76 76 64 44

(b)

Figure 3.22

Figure 3.23



nigmuxkat;caM)ac; ( )21.3031

2509.0682 mm

FPA

yt

ug ===

φ

ehIymuxkat;caM)ac; ( )23.2273

40075.0682 mm

FPA

ut

ue ===

φ

kaMniclPaB (radius of gyration) KYrmantémøy:agtUcbMput mmLr 33.15

3004600

300===

edIm,IrknUvmuxkat;RsalbMputsRmab;bMeBjlkçxNÐTaMgenH eyIgrkEdk (unequal-leg angle) Edlman RkLaépÞeBj (gross area) EdlGacTTYlyk)anmantémøtUcbMput rYcehIyepÞógpÞat; effective net

area. kaMniclPaB (radius of gyration) k¾GacRtUv)anepÞógpÞat;edaykarRtYtBinitüpgEdr. eday sarkarteFVIeLIgedaymanb‘ULúgBIrCYr enaHeCIgEdlRtUv)aneFVIkartP¢ab;RtUvmanTTwgtUcbMput mm127 ¬emIlkñúgtaragKMlatRbehagtamTTWgsRmab;EdkEkg rUbTI3>22¦. eyIgcab;epþImBItaraglkçN³ sRmab;EdkEkgeTal (table of properties for single angle) enAkñúgEpñkTI1 én Manual nigerobnUv muxkat;EdkRsalCageKtamlMdab;BItUceTAFM ¬minEmnlMdab;dUcKñaenAkñúgtarageT¦. muxkat;xageRkam GacRtUv)anerob.

23060:7.12102152 mmAL g =×× nig mmr 1.22min = 23180:9.1589127 mmAL g =×× nig mmr 20min =

23300:1.11102203 mmAL g =×× nig mmr 1.22min = 23400:7.12102178 mmAL g =×× nig mmr 15.22min =

¬cMNaMfa sRmab;EdkEkg G½kS X nig Y Edl)anbgðajenAkñúgtaragminEmnCaG½kSem (principal

axes)eT EtG½kS Z eTIbCaG½kSem (principle axis) zrr =min . EtsRmab;EdkEkgDub (double-angle

shape) G½kS X nig Y KWCaG½kSem.¦ sakl,g 7.12102152 ××L . muxkat;enHman gross area EdlRtUvKñaBitR)akdeTAnwgRkLaépÞcaM)ac; ¬RbesIrCagmuxkat;bIeTot RkLaépÞrbs;vaRtUv)an[enAkñúgtarag¦. ( )( ) 24.24507.122423060 mmAAA holesgn =−=−= edaysarRbEvgtminRtUv)andwg AISC Eq. B3-2 minGacRtUv)aneKeRbIedIm,IKNna shear lag factor

U . dUcenH eyIgeRbI 85.0=U / témømFümEdl)anBI Commentary. ¬]TahrN_TI8 kñúgCMBUkTI 7 tMNsamBaØbgðajlMGitGMBItMN nigtémø U mFümGacRtUv)aneKeRbIedIm,ITTYl)annUvmuxkat;sakl,g



bnÞab; témø U BI AISC Eq. B3-2 GacRtUv)aneKKNna¦. 22 3.227384.20824.245085.0 mmmmUAA ne <=×== ¬minl¥ N.G.¦ sakl,g 9.1589127 ××L ( )( ) 28.24169.152423180 mmAn =−= 22 3.227328.20548.241685.0 mmmmAe <=×= ¬minl¥ N.G.¦ eTaHbICamuxkat;enHman gross area FMCagmuxkat;munk¾eday Etvamin)anbegáIn net area eT. mUlehtu KWRkLaépÞEdlRtUvdksRmab;rn§mantémøFM edaysarEtkRmas;eCIg. sakl,g 1.11102203 ××L

( )( ) 22.27671.112423300 mmAn =−= 22 3.227312.23522.276785.0 mmmmAe >=×= (OK)

cemøIy³ muxkat;enHbMeBjRKb;lkçxNÐtRmUvkar dUcenHeRbI 1.11102203 ××L ttameCIgEdlman RbEvg mm203 . enAeBlEdlEdkrag (structural shape) b¤EdkbnÞHRtUv)aneRbIedIm,IpÁúMCa built-up shape vamin RtwmEtRtUv)anpÁúMenAEtxagcugGgát;b:ueNÑaHeT b:uEnþvak¾RtUv)anpÁúMenAcenøaHtamRbEvgbeNþayrbs;vapg Edr. eKminRtUvkarkarpÁúMEdlmanlkçN³Cab;rhUteT. karpÁúMEbbenHRtUv)aneKehAfa stitching ehIy eRKOgP¢ab;rbs;vaRtUv)aneKehAfa stitch bolts. karGnuvtþTUeTAKWkMNt;TItaMg stitching Edl rL / sM rab;EpñkpÁúMnImYy² minelIs rL / sRmab;muxkat; built-up. AISC D2 ENnaMfa Edkrag built-up Edl EpñkpÁúMrbs;vaRtUv)anEckeday filler EdlRtUv)aneRbIsRmab;P¢ab;enAcenøaH filler enaH témøGtib,rma

rL / sRmab;EpñkmYy²minRtUvelIs 300. Edkrag built-up EdlekIteLIgedayEdkbnÞH b¤edaykarpÁúM rvagEdkbnÞH nigEdkragRtUv)aneBalenAkñúg AISC Section J3.5 of Chapter J (“Connections joints,

and Fasteners”). CaTUeTA KMlatrbs;eRKOgP¢ab; b¤karpSarminKYrelIs 24dg énkRmas;EpñkesþIgbMput rbs;bnÞHEdk b¤ mm300 . RbsinebIGgát;CaEdk weathering EdlsßitenAkñúgbriyakasgayrgERcHsIu enaHKMlatGtibrmaKW 24dg énkRmas; b¤ mm175 .



3>7> EdksrésEdlmaneF μj nigExSkab Threaded rods and Cables

enAeBl slenderness minRtUv)anBicarNaEdksrés rod Edlmanmuxkat;mUl nigExSkab (cable) RtUv)aneKeRbIR)as;CaTUeTAsRmab;Ggát;rgkarTaj. Edksrés nigExSkabxusKñaRtg; Edk sréstan; EtExSkabekItBIExSlYskabCaeRcInv½NÐbBa©ÚlKñaehIymanrUbragdUcExSBYr. Edksrés nig ExSkab RtUv)aneKeRbICaerOy²sRmab;RbB½n§dMbUlBüÜr k¾dUcCa hanger nig suspension member

sRmab;s<an. Edksrésk¾RtUv)aneRbIenAkñúgRbB½n§ bracing enAkñúgkrNIxøH vaRtUv)aneKeFVIeRbkugRtaMg edIm,IkarBarvaBIPaBrlg; (slack) enAeBlEdlbnÞúkxageRkARtUv)andk. rUbTI3>24 bgðajBIviFItEdk srés nigExSkabKMrU. enAeBlcugmçagrbs;EdksrésRtUv)aneFVI[maneFμj (thread) eBlenaH upset end RtUv)an eRbI. EpñkEdlmaneFμjRtUv)ankat;ecjedIm,IBRgIkmuxkat;. enAkEnøgeFμj muxkat;EdkRtUv)ankat; bnßy EtkareFVI upset end )anbegáInmuxkat;Edk[FM. tambTdæan upset end EdlmaneFμj CaTUeTA man net area enARtg;kEnøgeFμj eRcInCagRtg;EpñkEdlKμaneFμj. eTaHCa upset end mantémøéføk¾ eday EteKk¾mincaM)ac;eRbIvaRKb;krNIeT. RkLaépÞmuxkat;RbsiT§PaB (effective cross-sectional area) enARtg;EpñkeFμjRtUv)aneK[ eQ μaHfa stress area ehIyvaCaGnuKmn_eTAnwgGgát;p©it unthreaded nigcMnYneFμjkñúg inch1 . pleFob rvag stress area nig nominal area ERbRbYl b:uEnþvamantémøtUcbMputRbEhl 75.0 . dUcenH ersIusþg; rgkarTaj nominal rbs;Edk threaded GacRtUv)ansresrdUcxageRkam³

usn FAP = ubFA75.0=

Edl =sA stress area =bA nominal (unthreaded) area

smIkarenHpþl; nominal strength EdlRtUv)anbgðajenAkñúgtarag Table J3.2 enAkñúg Section

J3.6 én AISC Specification. emKuNersIusþg; (resistance factor) enAkñúgkrNIenH 75.0=tφ . RbsinebI upset end RtUv)aneKeRbI enaHlT§PaBrgkarTajenAGgát;eFμjEdlFMRtUvFMCag yF KuNnwg unthreaded body area (AISC Table J3.2, footnote c).



]TahrN_TI3>12³ Edk threaded RtUv)aneKeRbICaGgát;sRmab;BRgwgEdlRtUvEtTb;Tl;nwg service tensile load EdlbnÞúkefr kN9 nigbnÞúkGefr kN5.26 . etIGgát;p©itEdkTMhMb:uNÑaRtUv)aneRbI RbsinebIeKeRbI A36?

dMeNaHRsay³ bnÞúkemKuN (factored load) ( ) ( ) kNPu 2.535.266.192.1 =+=

edaysar unt PP ≥φ ( ) ugut PAF ≥75.0φ

muxkat;caM)ac; ( ) ( )244.236

40075.075.02.53

75.0mm

FPA

ut

ug ===

φ

BI 4

2dAgπ

=

Ggát;p©itcaM)ac; mmd 35.1744.2364=

×=

π

cemøIy³ eRbIEdk threaded EdlmanGgát;p©it mm18 ( )247.254 mmAg = . edIm,IkarBarkarxUcxatkñúgeBlsagsg; EdksrésminRtUvRsav b¤rlas; (slender) eBkeT. eTaHbIminmankarTamTarBI specification k¾eday EtsRmab;karGnuvtþTUeTA Ggát;p©itGb,brmaEdlRtUv eRbI RtUvmantémø mm16 .

Figure 3.24



ExSkabkñúgrUbragCa strands b¤ wire rope RtUv)aneKeRbIenAkñúgkarGnuvtþEdlTamTar high

strength EtPaBrwg (rigidity) minmanlkçN³sMxan;eT. bEnßmBIelIkareRbIR)as;vaenAkñúgRbB½n§s<anBüÜr nigdMbUl vak¾RtUv)aneKeRbIenAkñúgeRKOgelIkdak;dUcCa hoist nig derrick EdleKeRbIvadUcCaExSeyag sRmab;GKarx<s;² nigsRmab;BRgwgtambeNþayenAkñúgGKarEdleFVIBIEdk. PaBxusKñarvag strand nig

wire rope KWbgðajenAkñúgrUbTI3>25. Strand CakarrYmpSMKñaénsréslYsCaeRcInrMuv½NÐKña ehIy wire

rope CakarrYmpSMKñaén strand CaeRcInrMuv½NÐKña. kareRCIserIsExSkabEdlRtwmRtUvsRmab;bnÞúkEdl[CaTUeTAQrenAelIkarBicarNaGMBI ersIu sþg; (strength) nigkMhUcRTg;RTay (deformation). bEnßmBIelIsac;lUteGLasÞicFmμta karlUtdMbUg EdlbNþalmkBI seating b¤ shifting énsréslYsmYy² EdlCalT§plvaeFVI[ExSkabmankarlUt Gcié®nþy_. sRmab;mUlehtuenH CaTUeTAExSkabRtUv)aneKTajBnøÚtmun (prestretched). Wire rope

nig strand RtUv)aneKpliteLIgBIEdkEdlmanesIusþg;x<s;CagEdksMNg;Fmμta ehIyminmanEcgenAkñúg AISC Specification eT. ersIusþg;dac;rbs;ExSkabnImYy² k¾dUcCakarlMGitBIkarttMNr GacTTYl)an BI manufacturer’s literature. Tinñn½ymanRbeyaCn_sRmab;RbePTenHmanenAkñúg Cable Roof

structures (Bethlehem Steel, 1968).

3>8> Ggát;rgkarTajenAkñúgdMbUl Tension members in roof trusses

Ggát;rgkarTajCaeRcInEdlvisVkrKNna CaeRKOgbgÁúM trusses. enAeBleRKOgbgÁúM trusses

RtUv)aneRbIR)as;enAkñúgsMNg; CaTUeTAvamannaTIcMbgkñúgkarRTRbB½n§dMbUlEdleKRtUvkarElVgEvg. va RtUv)aneKykmkeRbIenAeBlEdléfø nigTm¶n;Fñwmmantémøx<s;. ¬eRKOgbgÁúM trusses RtUv)anKitCaFñwm CeRmA (deep beam) EdlykecjnUvEpñénRTnugy:ageRcIn¦. dMbUl trusses RtUv)aneRbICaerOy²enAkñúg



sMNg;shRKas eTaHbICasMNg;RbePTenHRtUvkareRKagrwg (rigid frame) k¾eday. dMbUl trusses KMrU EdlRTeday load-bearing wall RtUv)anbgðajenAkñúgrUbTI 3>26. sMNg;RbePTenH CaTUeTA cugmçag rbs; trusses EdlP¢ab;eTAnwgCBa¢aMgRtUv)aneKKitCaTRm pinned nigTRmmçageTotRtUv)aneKKitfaCa TRm roller. dUcenH trusses GacRtUv)aneKviPaKCaeRKOgbgÁúMsþaTickMNt;. CBa¢aMgEdlCaTMrGaceFVIBI ebtugBRgwgedayEdk bøúkebtug \dæ b¤bnSMénsmÖar³TaMgenH. CaFm μta dMbUl trusses EtmanKMlatesμ IKñatambeNþayGKar nigcgP¢ab;KñaeTAvijeTAmkeday sarFñwmbeNþayEdleKehAfa édrENg (purlin) nigedayEdkExVg (X-bracing). tYnaTIcMbgrbs;éd rENgKWbBa¢ÚnbnÞúkeTAGgát;xagelI (top chord) rbs; trusses b:uEnþvak¾GaccUlrYmedayEpñkxøHkñúgkar BRgwgRbB½n§. CaTUeTAEdkBRgwg (bracing) RtUv)andak;enAkñúgbøg;énGgát;xagelI nigGgát;xageRkam b:uEnþvamincaM)ac;enARKb;ElVg (bay) TaMgGs;eT edaysarkmøaMgxag (lateral forces) GacRtUv)anbBa¢ÚnBI ElVgEdlTb;mYyeTAElVgEdlTb;mYyeTot edaysarédrENg. vaCakarRbesIrbMputEdlédrENgRtUv)andak;enAelItMNrbs; trusses. dUenH trusses Gac RtUv)anKitCaeRKOgbgÁúMtMNsnøak; (pin-connected structure) EdlRTbnÞúkEtRtg;tMN. EteBlxøH kRmaldMbUlminGaclatsn§WgelIcmøayrvagtMN dUcenHeKRtUvkarédrENgkNþal (intermediate

purlin). enAkñ μ úgkrNIEbbenHGgát;xagelInwgrgm:Um:g;Bt;FM k¾dUcCakmøaMgsgát;tamG½kS (axial

compression) ehIy vaRtUv)aneKKNnaedayKitCa Fñwm-ssr (beam-column) EdlmanBnül;kñúg CMBUkTI6. Sag rod CaGgát;rgkarTajEdlRtUv)aneRbIedIm,Ipþl;TRmxagsRmab;édrENg. bnÞúkPaKeRcIn EdlGnuvtþmkelIédrENgmanTisQr dUcenHvanwgmanbgÁúMkmøaMgRsbeTAnwgmMuCMraldMbUlEdlnwgeFVI [édrENgekagenAkñúgTisedAenaH ¬rUbTI 3>27¦. Sag rod GacRtUv)andak;enAcMNuckNþal b¤ cMNucmYyPaKbI b¤GacjwkenAtambeNþayédrENg GaRs½yeTAnwgcMnYnTRmEdlRtUvkar. KMlatrbs; sag rod CaGnuKmn_eTAnwgKMlat trusses, mMuCMralrbs;Ggát;xagelI/ ersuIsþg;rbs;édrENgTb;nwg karBt;RbePTenH ¬rUbragPaKeRcInrbs;EdkEdleRbICaédrENgmanlkçN³exSayNas;sRmab;karBt; tamTisenH¦ nigcMnYnTRmEdlpþl;edaydMbUl. RbsinebIeKeRbI bnÞHEdk CaTUeTAvaRtUv)aneKP¢ab;y:ag rwgCamYyédrENg dUcenHeKmincaM)ac;RtUvkar sag rod eT. EteBlxøH EtTm¶n;pÞal;rbs;édrENgKWva RKb;RKan;kñúgkarbgábBaðaenH dUcenHeKcaM)ac;dak; sag rod edIm,IRT kñúgGMLúgeBlsagsg;muneBldak;



kRmaldMbUl.



RbsinebIeKeRbI sag rod eKcaM)ac;KNnavaedIm,IRTbgÁMúbnÞúkdMbUlEdlRsbeTAnwgdMbUl. Ggát; nImYy²cenøaHédrENgRtUv)ansnμt;[RTGVI²TaMgGs;BIxageRkamva dUcenHGgát;xagelIRtUv)anKNna sRmab;bnÞúkenAelIépÞdMbUlEdlmanGMeBIelIGgát;enaH BIcugdMbUldl;kMBUldMbUldUcbgðajenAkñúg rUbTI 3> 28. eTaHbICakmøaMgenAkñúgGgát;nImYy²xusKñak¾eday EtCakarGnuvtþTUeTAeKeRbITMhMEtmYysRmab; RKb;Ggát; sag rod enaH. kareRbIR)as;nUvmuxkat;dUcKñasRmYldl;kargarsagsg; ÉbrimaNEdkelIs minCaFMb:unμaneT.

rUbTI 3>29 a bgðajBIkarcgP¢ab;édrENgenARtg;RBMdMbUl. Tie rod cenøaHédrENgxagRtUvTb;

nwgbnÞúkBIRKb; sag rod TaMgGs;EdlenAsgçagsøabdMbUl. kmøaMgTajenAkñúgGgát;edkmYyCabgÁúMkmøaMg rbs;Ggát; sag rod EdlenAxagelI. düaRkamGgÁesrI (free-body diagram) rbs;édrENgkMBUl RtUv)anbgðajenAkñúgrUbTI 3>29 b .

]TahrN_TI3>13³ Fink trusses EdlmanKMlat m6 KitBIG½kSeTAG½kS ehIyRTédrENg

18.0150×W dUcbgðajenAkñúgrUbTI 3>30 a. édrENgRtUv)anRTeday sag rod enAcMNuckNþal. edayeRbIEdk A36 KNna sag rod nig tie rod enAédrENgkMBUlsRmab;bnÞúk service load dUcxag



eRkam³ kRmaldMbUlEdk (metal deck)³ 2/1.0 mkN Built-up roof: 2/25.0 mkN RBwl³ 2/85.0 mkN elIbøg;edk Tm¶n;édrENg³ kN18.0 kñúgmYyEm:RtRbEvg

dMeNaHRsay³ KNnabnÞúk³

TTwgrgbnÞúksRmab; sag rod nImYy² mm 32/6 == RkLaépÞrgbnÞúksRmab;kRmaldMbUl nig Built-up roof 242143 m=×= bnÞúkefr ¬kRmaldMbUl nig Built-up roof¦ kN7.1442)25.01.0( =×+= Tm¶n;édrENgsrub kN86.49318.0 =××= bnÞúkefrsrub kN56.1986.47.14 =+= épÞrgbnÞúkRBwl 28.406.133 m=×= bnÞúkRBwlsrub kN68.34=



RtYtBinitübnSMbnÞúk³ (A4-2)³ kNSD 8.4068.345.056.192.15.02.1 =×+×=+

(A4-3)³ kNSD 7968.346.156.192.16.12.1 =×+×=+ bnSMbnÞúk A4-3 lub. ¬tamkarGegát A4-1, A4-4 nig A4-5 nwgminmantémøFMeT¦.

sRmab;bgÁMúkmøaMgRsbeTAnwgépÞdMbUl ¬rUbTI 3>30 b¦ kNT 3.20

146.379 ==

muxkat;EdkEdlRtUvkar ( )2

32.90

40075.075.0103.20

)75.0(mm

FTA

utg =

×⋅

==φ

cemøIy eRbIEdk threaded rod Ggát;p©it mm16 ¬ 2201mmAg = ¦ Edk tie rod EdlP¢ab;édrENgenARBMdMbUl ¬rUbTI 3>30 c¦

kNP 9.206.13

143.20 ==

muxkat;EdkEdlRtUvkar ( )2

32.90

40075.075.0103.20

)75.0(mm

FTA

utg =

×⋅

==φ

cemøIy eRbIEdk threaded rod Ggát;p©it mm16 ¬ 2201mmAg = ¦ sRmab;ragFrNImaRtrbs; truss nigkardak;bnÞúk Ggát;xageRkam (bottom chord) nwgrgkug RtaMgTaj ehIyGgát;xagelI (top chord) nwgrgkugRtaMgsgát;. Ggát;RTnugxøHrgkugRtaMgTaj nigxøH eTotrgkugRtaMgsgát;. enAeBleKbBa¢Úl\T§iBlxül;kñúgkarviPaK Tisxül;epSgKñaRtUv)aneKykmk BicarNa eBlenaHkmøaMgenAkñúgGgát;RTnug (web member) xøHGacnwgERbRbYlcenøaHkugRtaMgsgát; nigkugRtaMgTaj. kñúgkrNIEbbenH Ggát;EdlrgGMeBIRtUv)anKNnaeday[mannaTICaGgát;rgkarsgát; pg nigrgkarTajpg. sRmab; truss Edlcab;b‘ULúg (bolted truss) muxkat;EdkEkgDub (double-angle section)

RtUv)aneRbICajwkjab;sRmab;Ggát;xagelI (top chord) nigGgát;RTnug (web member) . karKNnaenH sRmYldl;karP¢ab;Ggát;EdlCYbKñaenARtg;dMNedayGnuBaØatnUvkareRbIR)as;bnÞHEdkeTal (single

gusset plate) dUcbgðajenAkñúgrUbTI 3>31. enAeBlGgát;xagelIrbs;eRKOgbgÁúM truss EdlpSareRbI Edkmuxkat;GkSret EdkRTnugEdlmanmuxkat;EdkEkgGacpSarP¢ab;CamYyeCIg (stem) rbs;Edkmux kat;GkSret. RbsinebI kmøaMgenAkñúgGgát;RTnug (web member) mantémøtUc eKGaceRbIEdkEkgeTal



(single angle) ebIeTaHbIkareFVIkarEbbenaH)ankat;bnßybøg;sIuemRTIBI truss ehIybNþal[Ggát;RTnug rgbnÞúkcakp©itk¾eday. CaTUeTAGgát;xagelI nigGgát;xageRkam (chord member) CaGgát;Cab; ehIy eKGackat;vaCakMNat;²RbsinebIcaM)ac;.

CakarBitEdlfa chord member CaGgát;Cab; ehIytMNRtUv)ancab;b‘ULúg b¤pSarEdleKmin Gacsnμt;fa truss CaeRKOgbgÁúMtMN pin-connected )aneT. PaBrwgrbs;tMNBitCanaMmknUvm:Um:g;Bt;enA kñúgGgát; b:uEnþCaTUeTAvamantémøtUc ehIyRtUv)anBicarNavaCakmøaMgrg (secondary effect) dUcenH kñúgkarGnuvtþTUeTAeK)anecalva. EtkarBt;EdlbNþaledaysarbnÞúkxageRkAEdlGnuvtþedaypÞal; eTAelIGgát;cenøaHtMN RtUvEtykmkKitBicarNadac;xat. eyIgKitkrNIenHenAkñúgemeronTI 6. ExSeFVIkar (working line) énGgát;rbs;eRKOgbgÁúM truss TaMgGs;RtUvkat;KñaRtg;tMNnImYy². sRmab; truss EdlP¢ab;edayb‘ULúg CYrrbs;b‘ULúg (bolt line) Ca working line ehIysRmab; truss pSar G½kSTIRbCMuTm¶n;rbs;TwkbnSarCa working line. karsnμt;kñúgdMeNIrkarviPaK truss RbEvgGgát;RtUv)an vas;BIcMNuceFVIkar (working point) eTA working point. ]TahrN_TI3>14³ eRCIserIsmuxkat;GkSretsRmab;Ggát;xageRkam (bottom chord) rbs;eRKOgbgÁúM dMbUl Warren truss dUcbgðajenAkñúgrUbTI 3>32 a. Truss RtUv)anpSar nigmanKMlatcmøay m6 . snμt;fakarP¢ab;rbs;Ggát;xageRkamRtUv)aneFVIeLIgdaykarpSarbuitkaMtambeNþay (longitudinal fillet

weld) enAnwgsøabRbEvg mm230 . edayeRbIEdk A36 CamYynwgTinñn½ybnÞúkxageRkam ¬xül;minRtUv )anBicarNaenAkñúg]TahrN_enHeT¦. édrENg (purlin)³ 097.0200×M RBwl³ 2/95.0 mkN elIbøg;edk



kRmaldMbUlEdk (metal deck): 2/1.0 mkN dMbUl³ 2/2.0 mkN kRmalGIusULg;³ 2/15.0 mkN

dMeNaHRsay³ KNnabnÞúk³ RBwl kN4.6812695.0 =××=



bnÞúkefr ¬elIkElgédrENg¦ =

bnÞúkefrsrub kN4.3212645.0 =××= Tm¶n;édrENgsrub kN7126097.0 =××=

snμt;faTm¶n; truss esμ I %10 énbnÞúkepSg² ( ) kN78.1074.324.681.0 =++

bnÞúkenAelItMNxagkñúgKW kND 66097.0

878.10

84.32

=×++= kNS 55.8

84.68==

enAelItMNxageRkA RkLaépÞrgbnÞúkKWesμ InwgBak;kNþalRkLaépÞrgbnÞúkrbs;tMNxagkñúg. bnÞúkenAelI tMNxageRkAKW kND 28.36097.0

8278.10

824.32

=×+×

+×

= kNS 3.4

824.68=

×=

karbnSMbnÞúk A4-3 nwgTTYl)antémøFMCageK³ SDPu 6.12.1 += enAelItMNxagkñúg kNPu 88.2055.86.162.1 =×+×= enAelItMNxageRkA kNPu 82.103.46.128.32.1 =×+×= Truss EdlrgbnÞúkRtUv)anbgðajenAkñúg rUbTI 3>32 b. Ggát;xageRkamRtUv)anKNnaedaykMNt;kmøaMgkñúgGgát;nImYy²rbs;Ggát;xageRkam nigeFVIkar eRCIserIsmuxkat;smrmüedIm,ITb;nwgkmøaMgEdlFMCageK. enAkñúg]TahrN_enH kmøaMgenAkñúgGgát; IJ mantémøFMCageK. GgÁesrI (free body) enAxageqVgmuxkat; a-a RtUv)anbgðajenAkñúg rUbTI 3>32 c.

kRmaldMbUlEdk dMbUl kRmalGIusULg;

2/1.0 mkN 2/2.0 mkN

2/15.0 mkN srub 2/45.0 mkN



( ) ( ) ( )∑ =−++−−= 02.15.10.35.488.20682.1069.83 IJE FM kNFIJ 8.208=

sRmab;muxkat;eBj (gross section) muxkat;EdlRtUvkar 2

3928

2509.0108.208

9.0mm

FFA

y

IJg =

×⋅

==

sRmab; net section muxkat;EdlRtUvkar 2

3696

40075.0108.208

75.0mm

FFA

u

IJe =

×⋅

== sakl,g 09.0125×WT 22 9281140 mmmmAg >= kartP¢ab;eFVIeLIgedaykarpSartambeNþay ehIyGgát;minEmnCaEdkbnÞH b¤Edksrés dUcenHkartP¢ab; enHminsßitenAkñúgkrNIBiessNamYysRmab;Ggát;EdlpSarEdlrg shear leg. 9.085.0

2305.3411 <=⎟⎠⎞

⎜⎝⎛−=⎟

⎠⎞

⎜⎝⎛−=

LxU

22 696969114085.0 mmmmUAA ge >=×== (OK) RbsinebIGgát;xageRkamRtUv)anBRgwgenA panel point

3004.759.19

1500<==

rL (OK)

cemøIy eRbIEdk 09.0125×WT 3>9> Ggát;EdltPa¢b;edayknøas ; (Pin-Connection Members)

enAeBlGgát;RtUv)antP¢ab;edayknøas; rn§RbehagRtUv)aneFVIeLIgenAcugTaMgsgçagrbs;Ggát; nigEpñkEdlvaRtUvP¢ab; ehIyknøas;RtUv)ans‘ktamrn§enaH. kareFVIEbbenHedIm,IkMu[Ggát;rgm:Um:g;Bt;. Ggát;rgkarTajEdltP©ab;tamTRmg;EbbenHRbQmnwgkar)ak;eRcInRbePT EdlRtUv)anerobrab;enAkñúg AISC D3 nigRtUv)anBnül;dUcxageRkam. Eyebar CaRbePTBiessrbs;Ggát;EdlP¢ab;edayknøas; (pin-connected member) EdlenA xagcugrbs;vamanrn§knøas; dUcbgðajkñúgrUbTI 3>33. ersIusþg;KNnaKWQrelIersIusþg;yalrbs;mux kat;eBj. k,ÜnlMGitsRmab;KNnaTMhM eyebar manenAkñúg AISC D3 EtminRtUv)anykmkerobrab;enA



TIenHeT. Eyebar RtUv)aneRbIy:agTUlMTUlayenAeBlmun vaCaGgát;rgkarTajEdleRbIenAkñúg truss s<an b¤enAkñúgs<anBüÜr. vaminRtUv)aneKeRbIeT naeBlbc©úb,nñ. Ggát;EdltP¢ab;edayknøas;KYrRtUv)anKNnasRmab;sßanPaBkMNt;dUcxageRkam ¬rUbTI 3>34¦

!> kugRtaMgTajenAelI net effective area ¬rUbTI 3>34 a ¦

75.0=tφ / ueffn FtbP 2= (ASIC Equation D3.1)

@> kugRtaMgkmøaMgkat;enAelI net effective area ¬rUbTI 3>34 b¦

75.0=sfφ / usfn FAP 6.0= (ASIC Equation D3.21)

#> kugRtaMg bearing. tRmUvkarenHmanenAkñúg chapter J (“Connections, Joints and

fastener”) ¬rUbTI 3>34 c¦

75.0=φ / pbyn AFP 8.1= (ASIC Equation J8-1)

$> kugRtaMgTajenAelI gross area

9.0=φ / gyn AFP = (ASIC Equation D1-1)

Edl =t kRmas;rbs;EpñkEdltP¢ab; btbeff ≤+= 162 ¬KitCa mm ¦ =b cmøayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlEkgeTAnwgTisrbs;kmøaMg ( )2/2 datAsf += =a cm¶ayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlRsbeTAnwgTisrbs;kmøaMg =d Ggát;p©itknøas; =pbA projected bearing area dt= tRmUvkarbEnßmsRmab;karkMNt;TMhMrbs;knøas; nigGgát;manbkRsayenAkñúg AISC D3.




eRKOgbgÁúMrgkarsgát; 73 T.Chhay

IV. eRKOgbgÁúMrgkarsgát; Compression Members

4>1> esckþIepþIm (introduction) eRKOgbgÁúMrgkarsgát; CaeRKOgbgÁúMsMNg;EdlrgEtkmøaMgsgát;tamG½kS. bnÞúkEdlGnuvtþtam G½kSbeNþaykat;tamTIRbCMuTm¶n;rbs;muxkat;Ggát; ehIykugRtaMg (stress) Gaces μ Inwg APfa = Edl

af RtUv)anKitfamantMéles μ IKñaelImuxkat;TaMgmUl. b:uEnþCak;EsþgeKminEdlTTYl)ansßanPaBl¥Ebb enHeT eKminGaceCosputBIkmøaMgcakp©itxøH)aneLIy. CalT§pleKnwgTTYl)ankarBt; b:uEnþvaGac RtUv)aneKKitkmøaMgrg (secondary load) nigGacRtUv)anecalRbsinebIlkçxNÐénkardak;bnÞúkesÞIrEt dUcKñanwgRTwsþI. karBt;minGacRtUvecaleT RbsinebIvaCam:Um:g;Bt;Edl)anBIkarKNna. eyIgnwgKit sßanPaBenHenAkñúgCMBUkTI6.

CaTUeTA Ggát;rgkarsgát;EdlekItmanenAkñúgGKar nigs<anKW ssr ¬CaGgát;bBaÄrEdlman tYnaTIcMbgKWRTnUvbnÞúkbBaÄr¦. Ggát;rgkarsgát;k¾RtUv)aneRbIenAkñúgeRKOgbgÁúM truss nigCaeRKOgbgÁúMén RbBn§½BRgwgpgEdr. Ggát;rgkarsgát;EdlmanRbEvgxøIminRtUv)aneKcat;cMNat;fñak;Ca column eT Etva RtUv)aneKehAfa strut.

4>2> RTwsþIssr (Column Theory)

edayBicarNaGgát;rgkarsgát;Evg ehIyRsavdUcbgðajenAkñúgrUbTI 4>1 a . RbsinebIbnÞúktam G½kS P RtUv)andak;yWt² enAeBlmYybnÞúkenaHnwgmantémøRKb;RKan;edIm,IeFVI[Ggát;KμansßirPaBehIy


T.Chhay 74 Compression members

ragrbs;Ggát;nwgekagdUcbgðajedayExSdac;. bnÞúkEdleFVI[Ggát;ekagRtUv)aneKehAfa critical

buckling load. RbsinebI Ggát;manRbEvgxøI ehIyFat;dUcbgðajenAkñúgrUbTI 4>2 b enaHeKRtUv karbnÞúk EdlmantémøFMCagmunedIm,IeFVI[Ggát;enaHsßitkñúgsßanPaBK μansißrPaB. RbsinebIGgát;enaH kan;EtxøI kar)ak;nwgekIteLIgeday compressive yielding Cageday buckling. munnwg)ak; kugRtaMgsgát; AP nwgrayesμ IenAelImuxkat;RKb;cMNucTaMgGs;énbeNþayRbEvgrbs;ssr eTaHCa)ak;eday yielding b¤ k¾)ak;eday buckling. bnÞúkEdleFVI[ buckling ekItman CaGnuKmn_eTAnwg slendernesss ehIy sRmab;Ggát;EdlRsavxøaMg bnÞúkenHnwgmantémøtUcNas;. RbsinebIGgát;manlkçN³RsavxøaMg EdlkugRtaMgmunnwg buckling EdltUcCagEdnsmamaRt (proportional limit) ¬EdlGgát;sßitenAkñúglkçN³eGLasÞic¦ critical buckling load RtUv)an[dUc xageRkam³ 2

2

LEIPcr

π= ¬$>!¦

Edl E Cam:UDuleGLasÞic (modulus of elasticity), I Cam:Um:g;niclPaBénRkLaépÞmuxkat; (moment

of inertia of the cross-sectional are) EdleFobnwgG½kSemEdltUc (minor principal axis), L CaRb Evgrbs;Ggát;cenøaHTRm. edIm,I[smIkar ¬$>!¦ mann½y luHRtaEtGgát;sßitkñúgsßanPaBeGLasÞic ehIycugrbs;vaGacviledayesrI EtminRtUvrMkileTAxageT. cugTRmenHbMeBjlkçxNÐedayTRmsnøak; (hinge) b¤ pinned dUcbgðajkñúgrUbTI 4>2 . TMnak;TMngd¾KYr[cab;Garm μN_enHRtUv)anrkeXIjdMbUgbMput edayGñkR)aCJKNitviTüaCnCatisVIseQμaH Leonhard Euler Edle)aHBum<enAkñúgqñaM 1759. bnÞúkeRKaH fñak; (critical load) enH enAeBlxøHRtUv)aneKehAfa Euler load b¤ Euler buckling load . smIkarTI $>! RtUv)aneKbgðajedIm,IeFVI[eCOedaykarBiesaFy:ageRcIn. karsMraybBa¢ak;rbs;smIkarenH RtUv)an [edIm,IbgðajBIPaBsMxan;rbs;lkçxNÐcugTRm.



edIm,IgayRsYlkñúgkarbkRsay Ggát;RtUv)andak;[edkelIG½kS x dUcEdl[kñúgrUbTI 4>3. TRm roller Edldak;enATIenHedIm,ITb;Ggát;min[cl½teTAelI b¤cuHeRkam. bnÞúksgát;tamG½kS RtUv)anGnuvtþ ehIyekIneLIgsnSwm². bnÞúkxagbeNþaHGasnñRtUv)andak;edIm,IeFVI[Ggát;dabdUcrUb ragEdlbgðajedayExSdac; ehIyGgát;nwgRtLb;eTArkrUbragedImvijenAeBlEdlbnÞúkbeNþaHGsnñ enaHRtUv)aneKdkecjRbsinebIbnÞúktamG½kSmantémøtUcCag critical buckling load . Critical

buckling load, crP RtUv)ankMNt;CabnÞúkEdlmantémøFMRKb;RKan;edIm,IrkSarUbragdabrbs;Ggát;enA eBlEdlbnÞúkxagbeNþaHGasnñRtUv)aneKdakecj.

smIkarDIepr:g;Esül (differential equation) sRmab;rUbragdabrbs;Ggát;eGLasÞicEdlrgkar Bt;KW³

IEM

dxyd

−=2

2 ¬$>@¦

Edl x Cacm¶ayrbs;cMNucEdlsßitenAelIG½kSbeNþayrbs;Ggát;/ y CaPaBdabrbs;Ggát;enARtg; cMNucenaH/ nig M Cam:Um:g;Bt;enARtg;cMNucenaH. E nig I RtUv)anbgðajBIxagelI b:uEnþm:Um:g;niclPaB I enATIenHKWeFobnwgG½kSénkarBt;. smIkarenHRtUv)anTajeday Jacob Bernoulli ehIyRtUv)an bMEbkeday Euler EdleRbIR)as;vasRmab;bBaðaekagrbs;ssr. BI rUbTI 4>3 eyIgeXIjfaenAeBl EdlGgát;ekagedaysarbnÞúktamG½kS crP enAcm¶ay x BITRmxageqVgeyIgmanPaBdab y ehIy m:Um:g;Bt;enARtg;cMNucenaHKW yPcr . enaHsmIkar $>@ GacsresrdUcxageRkam³ 0" =+ y

EIPy cr

Edl RBIm KWCaDIepr:g;Esültam x . smIkarenHCa second order, linear, ordinary differential

equation CamYynwgemKuNefr ehIymandMeNaHRsay



)sin()cos( cxBcxAy += Edl

EIPc cr=

ehIy A nig B Catémøefr. témøefrTaMgenH RtUv)ankMNt;edayGnuvtþnUvlkçxNÐRBMEdndUcxageRkam³ Rtg; 0=x / 0=y ³ )0sin()0cos(0 BA += enaH 0=A Rtg; Lx = / 0=y ³ )sin(0 cLB= lkçxNÐcugeRkayenHtRmUv[ 0)sin( =cL RbsinebI 0≠B ¬cemøIyminsMxan; EdlRtUvKñanwg 0=P ¦. sRmab; 0)sin( =cL / ,0=cL ,π ,2π ,3π ... ,πn= ,0=n ,1 ,2 ,3 ... BI

EIPc cr=

eyIgTTYl)an ,πnLEIPcL cr =⎟⎟

⎠

⎞⎜⎜⎝

⎛= 222 πnL

EIPcr = ehIy 2

22

LEInPcr

π=

témøCaeRcInrbs; n RtUvKñanwgrUbragekag (buckling mode) epSg². 1=n bgðajnUvrUbragekagTImYy (first mode). 2=n KWrUbragekagTIBIr (second mode).l. témø 0=n CakrNIK μanbnÞúk EdlCa krNIminsMxan;. rUbragénkarekagTaMgenHRtUv)anbgðajenAkñúgrUbTI 4>4. témø n minGacFMCagmYy elIkElgEtGgát;rgkarsgát;RtUv)anTb;BIkardabenARtg;cMNucEdleFVI[kMeNagbt;Ebn.

dUcenHdMeNaHRsayrbs;smIkarDIepr:g;EsülKW



⎟⎠⎞

⎜⎝⎛=

LxnBy πsin

ehIyemKuN B CatémøminkMNt;. lT§plenHRtUv)aneRbICacemøIy linear kñúgsmIkarDIepr:g;EsültM Nag)atuPUt nonlinear. sRmab;krNIFm μtarbs;Ggát;rgkarsgát;EdkK μanTRmenAcenøaHcugsgçagrbs;va 1=n enaH smIkar Euler RtUv)ansresrCa 2

2

LEIPcr

π= ¬$>#¦

vamanlkçN³gayRsYlCagkñúgkarsresrsmIkar $># kñúgTRmg;dUcxageRkam

( )22

2

22

2

2

/ rLEA

LEAr

LEIPcr

πππ===

Edl A CaRkLaépÞmuxkat; nig r CakaMniclPaB (radius of gyration) EdleFobnwgG½kSEdlekag. pleFob rL / Ca slenderness ratio. Ggát;EdlmanlkçN³kan;EtRsav témø slenderness ration kan;EtFM. RbsinebI critical load RtUv)anEckedayRkLaépÞmuxkat; enaHeKnwgTTYl)an critical

buckling stress dUcxageRkam³

( )22

/ rLE

APF cr

crπ

== ¬$>$¦

sRmab;kugRtaMgrgkarsgát; karekagnwgekIteLIgtamG½kSEdlRtUvKñanwg r . karekagnwgekIteLIg Pøam² enAeBlEdlbnÞúkEdlGnuvtþmkelIGgát;esμ InwgbnÞúkEdl[kñúgsmIkar $># ehIyssrnwgKμanesßr PaBeFobG½kSem (principal axis) EdleFVI[ slenderness ratio mantémøFMCageK. CaTUeTAvaCa G½kSEdlmanm:Um:g;niclPaBtUcCageK ¬eyIgnwgBinitükrNIenHenAeBleRkay¦. dUcenHm:Um:g;niclPaB Gb,brma nigkaMniclPaBGb,brmaRtUv)aneRbIenAkñúgsmIkar $># nig $>$. ]TahrN_4>1³ ssrEdlmanmuxkat 73.0300×W RtUv)aneRbIedIm,IRTbnÞúksgát;tamG½kS kN645 . ssrenHmanRbEvg m6 nigmanTRm pinned enAcugsgçag. edaymikKitBIemKuNbnÞúk nigemKuN ersIusþg; cUreFVIkarGegátBIesßrPaBrbs;Ggát;enH. ¬eKminRtUvkardwgBIm:akrbs;EdkeT edaysar critical

buckling load CaGnuKmn_énm:UDuleGLasÞic minEmn yield stress b¤ ultimate tensile strength¦.



dMeNaHRsay³ sRmab; 73.0300×W témøGb,brmarbs; mmrr y 8.49== témøGtibrmarbs; 5.120

8.496000

==rL

( )

kNrLEAPcr 7.128810

5.1201048.910200 3

2

332

2

2=⋅

⋅×⋅×== −ππ

cemøIy³ edaysarbnÞúkGnuvtþKW kN645 tUcCag crP enaHssrrkSasßirPaBehIymanemKuNsuvtßiPaB RbqaMgnwg bucklinges μ Inwg 0.2645/7.1288 = . eRkaymkeK)anrkeXIjfa smIkarrbs; Euler minGaceRbICamYyGgát;rgkarsgát;EdlFat; xøI nigminRsav. mUlehtuKWfa slenderness ratio tUcrbs;Ggát;bNþal[man buckling stress FM ¬BIsmIkar $>$¦. RbsinebI buckling stress FMCag proportional limit rbs;smÖar³ enaHTMnak;TMng rvag stress nig strain nwgminmanlkçN³Ca linear eT ehIym:UDuleGLasÞic E nwgminGacyk mkeRbI)aneT. ¬kñúg]TahrN_ 4>1 buckling stress KW MPaAPcr 13648.9/7.1288/ == EdltUc Cag proportional limit sRmab;RKb;eRKOgbgÁúMEdkTaMgGs;. enAkñúgqñaM 1889 Friedrich

Engesser )anesñIeLIgdMbUgkñúgkareRbIR)as; tangent modulus tE enAkñúgsmIkar $>#. sRmab;smÖar³ EdlmanExSekag stress-strain dUckñúgrUbTI 4>5/ E ElgCatémøefrsRmab;kugRtaMgEdlFMCag proportional limit plF . Tangent modulus tE RtUv)ankMNt;Ca slope énbnÞat;b:HeTAnwgExSekag stress-strain sRmab;témørbs; f EdlsßitenAcenøaH plF nig yF . RbsinebI buckling stress APcr / sßitenAkñúgtMbn;enH vaRtUv)anbgðajdUcxageRkam³ 2

2

LIEP t

crπ

= ¬$>%¦ smIkar $>% dUcKñanwgsmIkar Euler RKan;EtCMnYs E eday tE .

ExSekag stress-strain EdlbgðajenAkñúgrUbTI 4>5 manlkçN³xusKñaBIrUbEdl)anbgðajBImun sRmab; ductile steel ¬enAkñúgrUbTI 1>3 nig1>4¦ edaysarEtvamantMbn; nonlinear . ExSekag enHCaRbePTénkarBiesaFkarsgát;rbs;Edk W-shape RbEvgxøI EdleKehAfa stub column. Nonlinearity CalT§pldMbUgénvtþmanrbs; residual stress enAkñúg W-shape. enAeBlEdlEdk hot-

rolled shape Tuk[RtCak; muxkat;TaMgmUlrbs;EdkminRtUv)anRtCak;edayGRtadUcKñaeT. ]TahrN_



enAcugsøabrbs;EdkRtCak;elOnCagkEnøgCYbKñarvagsøab nigRTnug. karRtCak;minRBmKñaEbbenH begáIt[ mankugRtaMgenACab;kñúgEdkrhUt. ktþaepSgeTotdUcCakarpSar nigkarBt;RtCak;edIm,IbegáIt Fñwmekag GacCaktþabNþal[man residual stress b:uEnþdMeNIrkareFVI[RtCak;CaktþacMbg.

cMNaMfa tE mantémøtUcCag E ehIysRmab; rL / EdlmantémødUcKñaRtUvKña eKnwgTTYl)an

critical load crP tUc. edaysarEtPaBERbRbYlrbs; tE karkMNt;témø crP enAkñúg inelastic range

edayeRbIsmIkarTI $>% BitCamankarBi)ak. CaTUeTA trial-and-error approach RtUv)aneRbICamYynwg ExSekag stress-strain dUcbgðajkñúgrUbTI 4>5 edIm,IkMNt; tE sRmab;témøsakl,grbs;témø crP . sRmab;mUlehtuenH design specification CaeRcIn rYmTaMg AISC Specification manrUbmnþEdl)an BIkarBiesaF (empirical formulas) sRmab; inelastic column.

sRmab;RKb;smÖar³TaMgGs; critical buckling stress RtUv)ansg;CadüaRkamCaGnuKmn_eTAnwg slenderness dUcbgðajenAkñúgrUbTI 4>6 . ExSekag tangent modulus b:HeTAnwgExSekag Euler Rtg; cMNucEdlRtUvKñanwg proportional limit rbs;smÖar³. bnSMExSekagenH RtUv)aneKehAfa column

strength curve EdlBN’naBIesßrPaBrbs;RKb;ssrTaMgGs;. eRkABI ,yF E nig tE EdlCalkçN³ rbs;smÖar³ ersIusþg;CaGnuKmn_nwg slenderness ratio.



RbEvgRbsiT§PaB (effective Length) TaMgsmIkar Euler nigsmIkar tangent modulusQrelIkarsnμt;dUcxageRkam³

!> ssrmanlkçN³Rtg;l¥ @> bnÞúkGnuvtþtamG½kS K μancMNakp©it #> ssrmanTRm pinned enAcugsgçag

lkçxNÐBIrdMbUgmann½yfa K μanm:Um:g;Bt;enAkñúgGgát;mugeBlekag (buckling). dUc)anerobrab; BIxagedIm m:Um:g;écdnüxøHnwgekItman b:uEnþvaRtUv)anecalkñúgkrNICaeRcIn. tRmUvkarsRmab;TRm pinned CakarkMNt;mYyEdlBi)ak Edlkarpþl;[RtUv)aneFVIsRmab;lkçxNÐTRmepSg²eTot. lkçxNÐ TRm pinned tRmUv[Tb;Ggát;BIkarrMkilxag b:uEnþminTb;nwgkarvilCMuvijTRmeT. CakarBit karbegáIttMN pinned EdlK μankkitKWminGaceFVIeTA)anl¥enaHeT dUcenHlkçxNÐTRmenHRKan;EtmanlkçN³Rbhak; RbEhlb:ueNÑaH. Cak;EsþgssrTaMgGs;RtUvEtxUcRTg;RTaytamG½kSedayesrI.

lkçxNÐcugepSgeTotGacRtUv)anBnül;enAkñúgsmIkarTI $>#. CaTUeTA m:Um:g;Bt;GacCaGnuKmn_ én x EdlCalT§plenAkñúg nonhomogeneous differential equation. vamanlkçxNÐRBMEdnxusBI smIkaredIm EtviFIsaRsþKNnadUcKñaTaMgRsug. smIkarEdlCacemøIysRmab; crP manTRmg;dUcKña. ]TahrN_ edayBicarNaGgát;rgkarsgát;EdlmanTRmmYyCa pinned nigmYyeTotCa fixed Tb;nwg karvil nigkarrMkil dUcbgðajenAkñúgrUbTI 4>7 . smIkar Euler sRmab;krNIenH EdlRtUv)anbkRsay tamrebobdUcsmIkar $># eKTTYl)an



2

205.2L

EIPcrπ

=

b¤ 2

2

2

2

)/70.0()/(05.2

rLEA

rLEAPcr

ππ==

dUcenHGgát;rgkarsgát;enHmanlT§PaBRTbnÞúkes μ InwgGgát;EdlmanTRm pinned sgçagEdr Et RbEvgrbs;vaRtUv)anKitRtwm %70 bueNÑaH. eKnwgTTYl)ansmIkarkñúgTRmg;RsedogKñaenHsRmab; ssrEdlmanlkçxNÐTRmepSg². Column-buckling problem GacRtUv)anbegáItCarUbmnþkñúgTRmgCa forth-order differential

equation CMnYs[smIkar $>@. kareFVIEbbenHedIm,IgayRsYlkñúgkaredaHRsayCamYylkçxNÐRBMEdn eRkABITRm pinned . edIm,IPaBgayRsYl smIkarsRmab; critical buckling load nwgRtUv)ansresrkñúg TRmg;dUcxageRkam³

( )22

/ rKLEAPcr

π= b¤

( )22

/ rKLAEP t

crπ

= ¬$>^ a/ $>^ b¦

Edl KL CaRbEvgRbsiT§PaB (effective length) nig K CaemKuNRbEvgRbsiT§PaB (effective length

factor). emKuNRbEvgRbsiT§PaBsRmab;Ggát;rgkarsgát; fixed-pinned KW 70.0 . sRmab;cugsgçag manTRm fixed Tb;nwgkarvil nigrMkil enaH 50.0=K . témørbs; K sRmab;krNITaMgenH nigkrNI epSgeTotmanenAkñúgtarag C_C2.1 enAkúñg Commentary to the AISC Specification. enAkñúg taragenaH eK[témørbs; K cMnYnBIr³ mYyCatémøtamRTwsþI nigmYyeTotCatémøsRmab;karKNna



(recommended design value) EdlRtUv)anykmkeRbIenAeBlEdleKmanlkçxNÐTRmesÞIrl¥\tex©aH. dUcenH luHRtaEtTRm fixed KWbgáb;\tex©aHeTIbtémøKNnaEdlmanlkçN³snSMsMécCagRtUv)anykmk eRbI. EtcMNaMfa témøtamRTwsþI nigtémøsRmab;karKNnamantémødUcKñasRmab;lkçxNÐ (d)nig (f) enAkñúg Commentary Table C-C2.1. mUlehtuKWfaPaBEdlminGaceFVI)anrbs;TRmsnøak;Kμankkit Edll¥\tex©aH b¤rbs;TRm pinned )anbegáIt[mankarTb;nwgkarvil nigeFVI[témø K fycuH. dUcenH kareRbItémøtamRTwsþIkñúg krNITaMgBIrKWmantémøtUc. kareRbIRbEvgRbsiT§PaB KL CMnYs[RbEvg L min)aneFVI[mankarpøas;bþÚrTMnak;TMng Edl)an erobrab;knøgmkeT. ExSekagersIusþg;ssr (column strength curve) Edl)anbgðajenAkñúg rUbTI 4>6 minmankarpøas;bþÚreT ebIRKan;EteFVIkarpøas;bþÚreQ μaHG½kSGab;sIusmk KL enaH. Critical buckling

stress EdlRtUvKñanwgRbEvgEdl[ eTaHCaRbEvgBitR)akd b¤RbEvgRbsiT§PaBk¾eday k¾eQ μaHrbs;vaelI G½kSGredaenenArkSadEdl.

4>3> tRmUvkarrbs; AISC (AISC Requirements)

tRmUvkarCamUldæansRmab;Ggát;rgkarsgát;RtUv)anerobrab;enAkñúg Chapter E of the AISC

Specification. TMnak;TMngrvagbnÞúk nigersIusþg; ¬smIkar @>#¦ manTRmg; ncu PP φ≤ Edl =uP plbUkbnÞúkemKuN =nP nominal compressive strength crg FA= =crF critical buckling stress

=cφ emKuNersIusþg;sRmab;Ggát;rgkarsgát; 85.0= CMnYs[kareRbIsmIkar critical buckling stress crF CaGnuKmn_én slenderness ration rKL / specification eRbInUv slenderness parameter

EF

rKL y

c πλ = (AISC Equation E2-4)

vaCa)a:ra:Em:RtK μanxñat ebIeTaHCasmIkarmanlkçN³smÖar³cUlrYmk¾eday. sRmab;ssreGLasÞic (elastic column) smIkar $>$ GacRtUv)ansresrCa

( ) yc

cr FrLK

EF 22

2 1/ λ

π==



edIm,IKitbBa¢ÚlnUv\T§iBlrbs;PaBminRtg;dMbUg (initial crookedness) smIkarxagelIRtUv)ankat;bnßy dUcxageRkam y

ccr FF 2

877.0λ

=

sRmab; inelastic column EdleRbI tangent modulus equation ¬smIkar $>^ b¦ RtUv)anCMnYseday ( ) ycr FF c

2

658.0 λ= Edl)anKitpgEdrnUv initial crookedness. dUcenHdMeNaHRsayedaypÞal;GacTTYl)an edayeCos vagnUv trial-and error approach EdlmanCab;CamYynwgkareRbIR)as; tangent modulus equation. RbsinebIeKyk 5.1=cλ CaRBMEdnrvagssreGLasÞic nigssrminEmneGLasÞic enaH AISC equation

sRmab; critical buckling stressGacRtUv)ansegçbdUcxageRkam³ sRmab; 5.1≤cλ ( ) ycr FF c

2

658.0 λ= (AISC Equation E2-2)

sRmab; 5.1>cλ y

ccr FF 2

877.0λ

= (AISC Equation E2-3)

tRmUvkarTaMgenHRtUv)anbgðajCalkçN³RkaPicenAkñúgrUbTI 4>8.

AISC Equation E2-2 nig E2-3 RtUv)ansegçbBIsmIkarcMnYn 5 Edlman cλ 5 lMdab;

(Galambos, 1988). smIkarTaMgenHQrelIkarBiesaF nigRTwsþIEdlKitbBa¢ÚlnUv residual stress nig initial out-of straightness esμ Inwg 1500/L / Edl L CaRbEvgGgát;.



AISC esñInUvpleFobPaBrlas;Gtibrma (maximum slenderness ration) rKL / esμ Inwg 200 sRmab;Ggát;rgkarsgát;. eTaHbICamankarkMNt;EtmYyk¾eday EtenAkñúgkarGnuvtþn_eKGacyk pleFobkMNt;FMCagenH edaysarssrEdlmanlkçN³RsavCag nigmanersIusþg;tUc ehIyvanwgmin manlkçN³esdækic©.

]TahrN_4>2³ kMNt;ersIusþg;sgát;KNnarbs; 08.1360×W EdlmanRbEvg m6 nigmanTRm pinned. eRbIEdk 36A . dMeNaHRsay³ Slenderness ratio³

témøGtibrmarbs; ( ) 20024.956360000.1

<===yr

KLr

KL (OK)

072.1200000

25024.95===

ππλ

EF

rKL y

c sRmab; 5.1<cλ

( ) ( ) ( ) MPaFF yc

cr 5.154250658.0658.02072.12

=== λ kNFAP crgn 2177105.15414100 3 =××== −

kNPnc 1850217785.0 =×=φ cemøIy³ ersIusþg;sgát;KNna (design compressive strength) kN1850= . enAkñúg]TahrN_ 4>2/ eday xy rr < enaHvanwgmanersIusþg;FMCagtamTis x . EdkTIbRCugmux kat;kaer: Camuxkat;EdlmanRbsiT§PaBCageKsRmab;Ggát;rgkarsgát; edaysar xy rr = enaHersIusþg; rbs;vanwges μ IKñaTaMgBIrTis. eBlxøHEdkTIbmUlRbehagk¾RtUv)aneRbICaGgát;egkarsgát;sRmab;mUl ehtudUcKña. rUbragénkar)ak;Edl)anBicarNayUrmkehIyKWsMedAeTAelIkarekagedaykarBt; (flexural

buckling) dUcGgát;rgkarBt; enAeBlEdlvaK μanesßrPaB. sRmab;muxkat;xøH Ggát;nwg)ak;edayrmYl (twisting) KWekagedayrmYl (torsional buckling) b¤edaybnSMén twisting nig bending (flexural-

torsional buckling). eyIgnwgBicarNavaenAkñúgEpñkTI 4>6.



sißrPaBedaytMbn; Local Stability

ersIusþg;EdlRtUvKñanwg buckling mode minGacnwgekIteLIg)aneT RbsinebIEpñkrbs;muxkat; manlkçN³esþIgeBkEdlnwgekItman local buckling. GesßrPaBRbePTenHKWCakarekagedaytMbn; b¤ wrinkle enAtMbn;epSg²Kña. RbsinebIvaekIteLIg muxkat;KμanRbsiT§PaBeBj)anyUr hIyGgát;nwg)ak;. muxkat;rUbragGkSr I nig H Edlmansøab b¤RTnugesþIgnwggayrg)atuPUtenH ehIyeKKYrEteCogvagkñúg kareRbIR)as;va. RbsinebImindUecñaHeT ersIusþg;sgát;Edl[eday AISC Equation E2-2 nig E2-3 RtUvEtkat;bnßy. karvas;EvgnUvPaBgayrgnUv)atuPUtenHKWKNnapleFobTTwgelIkRmas; (width-

thickness ratio) rbs;Epñkénmuxkat;nImYy². EpñkBIrRbePTRtUv)anBicarNa ³ unstiffened element EdlRCugmYytambeNþayTisedAbnÞúkminRtUv)an support, nig stiffened element EdlRCugTaMg sgçagrbs;vaRtUv)an support.

témøkMNt;rbs; width-thickness ratio RtUv)an[enAkñúg AISC B5, “Local Buckling” Edl rUbragrbs;muxkat;RtUv)ancat;cMNat;fñak;Ca compact, noncompact b¤ slender GaRs½yeTAtamtémø rbs;pleFob. sRmab;Epñkrgkarsgát;es μI dUcCaGgát;rgkmøaMgsgát;tamG½kS ersIusþg;RtUv)ankat;bnßy RbsinebIrUbragman slender element. Width-thickness ratio RtUv)an[eQ μaHsMKal;CaTU eTAfa λ . GaRs½yeTAnwgEpñkrbs;muxkat; λ GacCapleFob tb / b¤ wth / EdlnwgRtUv)anbgðajenA TIenH. RbsinebI λ FMCagtémøkMNt; rλ rUbragKW slender ehIyeKrkviFIedIm,IkarBar local buckling. ¬sRmab;rUbrag compact nig uncompact nwgRtUvykmkniyaykñúgCMBUkTI5¦ sRmab;rUbragGkSr I nig H søabrbs;vaRtUv)ancat;TukCa unstiffened element ehIyTTwgrbs;søabGacRtUv)anKitEtBak; kNþal. edayeRbI AISC notation eyIg)an³

f

f

f

f

tb

tb

tb

22/===λ

Edl fb nig ft CaTTwg nigkRmas;rbs;søab. lImItx<s;KW

yr f

250=λ

RTnugrbs;rUbragGkSr I nig H Ca stiffened element ehIy stiffened width KWCacm¶aycenøaH root rbs;søab. Width-thickness parameter KW



wth

=λ

Edl h Cacm¶aycenøaH root rbs;søab ehIy wt CaTTwgsøab. lImItx<s;bMputKW

yr f

665=λ

témørbs;pleFob ff tb 2/ nig wth / RtUv)anerobcMdak;enAkñúg dimension and properties tables in

Part 1 of the manual. Stiffened element nig unstiffened element rbs;rUbragmuxkat;CaeRcInRtUv)anbgðajenAkñúg rUbTI 4>9. EdnkMNt; rλ Edl)anmkBI AISC B5 RtUv)an[sRmab;krNInImYy².



]TahrN_ 4>3³ Gegát;ssrenAkñúg]TahrN_ 4>2 sRmab; local buckling. dMeNaHRsay³ sRmab; 08.1360×W / mmbf 256= / mmt f 9.19= / nig

43.69.192

2562

=×

=f

f

tb

témøén ff tb 2/ k¾RtUv)andak;enAkñúg properties table. 43.68.15

250250

>= (OK)

3.25=wth ¬BI properties table¦

3.2542250

665665>==

yf (OK)

cemøIy³ Local instability minmanbBaða. eKk¾GnuBaØat[eRbIrUbragmuxkat;EdlminbMeBjtRmUvkar width-thickness ration pgEdr k¾ b:uEnþGgát;EbbenaHminRtUv)anGnuBaØat[RTbnÞúkF¶n;²dUcrUbragmuxkat;EdlbMeBjlkçxNÐeT. müa:gvij eTot design strength k¾GacRtUv)ankat;bnßyedaysarEt local buckling. dMeNIrkarTUeTAkñúgkar GegátmandUcxageRkam.

- RbsinebI width-thickness ration λ FMCag rλ eyagtam Appendix B of the

Specification nigKNnaemKuNkat;bnßy (reduction factor) Q .

- KNna cλ dUcFm μta³ EF

rKL y

c πλ =

- RbsinebI 5.1≤cQλ / yQ

cr FQF c ⎟⎠⎞

⎜⎝⎛=

2658.0 λ (AISC Eq. A-B5-15)

- RbsinebI 5.1>cQλ / yc

cr FF⎥⎥⎦

⎤

⎢⎢⎣

⎡= 2

877.0λ

(AISC Eq. A-B5-16)

- Design strength KW crgnc FAP 85.0=φ kñúgkrNICaeRcIneKGacrk rolled shape EdlbMeBjtRmUvkar width-thickness ratio dUcenHeK

mincaM)ac;eFVInUvdMeNIrénkarKNnaenHeT. enAkñúgesovePAenH eyIgBicarNaEtGgát;rgkarsgát;Edlman rλλ < bu:eNÑaH.



taragsRmab;Ggát;rgkarsgát; Tables for Compression Members

Manual mantaragEdlmanRbeyaCn_CaeRcInsRmab;karviPaK nigkarKNna. sRmab;Ggát;rg karsgát;Edl strength rbs;valubeday flexural buckling ¬RbePTEdl)anBicarNaknøgmk¦/ tarag 3-36, 3-50 nig 4 enAkñúg Numerical Value section rbs; Specification nig column load table enAkñúg part 3 rbs; Manual, “Column Design,” manRbeyaCn_CageK. tarag 3-36 [nUvtémø

crcFφ CaGnuKmn_én rKL / sRmab; MPaksiFy 25036 == . tarag 3-50 sRmab; ksiFy 50= MPa350= nig tarag 4 [ ycrc FF /φ CaGnuKmn_én cλ . ¬RKb; Manual table TaMgGs;sRmab;

ksiFy 50= MPa350= xusBItaragsRmab; MPaksiFy 25036 == edaykarpat;BN’RbepH¦. Column load table [ design strength rbs;rUbragEdleRCIserIssRmab;témøRbEvgRbsiT§PaB (effective length) CaeRcIn. tarag 3-36 nig 3-50 bBa©b;edaylImItx<s;bMput 200/ =rKL ehIy column load table rYm bBa©Últémø KL EdlRtUvKñanwg 200/ =rKL . kareRbIR)as;nUvtarag nImYy²RtUv)anbgðajenA kñúg]TahrN_xageRkam.

]TahrN_ 4>4³ KNna design strength rbs;Ggát;rgkarsgát;rbs; 7414×W EdlmanRbEvg ft20 nigmanTRm pinned renAcugsgçag edayeRbI ¬!¦ Table 3-36 ¬@¦ Table 4 nig ¬#¦ column load

table . eRbIEdk 36A . dMeNaHRsay³ Slenderness ratio:

témøGtibrma ( ) 20077.9648.2

12200.1<=

×==

yrKL

rKL (OK)

085.129000

3677.96===

ππλ

EF

rKL y

c

¬!¦ sRmab; ksiFy 36= / eyIgeRbI Table 3-36 . témørbs; crcFφ RtUv)an[sRmab;témø rKL / Kt;/ sRmab;témø rKL / TsSPaK eyIgGaceFVIkarrMkil ex,óseLIg (rounded up) b¤eFVI linear interpolation. enAkñúgesovePAenHeyIgnwgeRbI linear

interpolation sRmab;RKb;taragTaMgGs;elIkElgEtmankarbgðajR)ab;. sRmab; 77.96/ =rKL ksiFcrc 69.18=φ ( ) kipsFAFAP crcgcrgcnc 40769.188.21)( ==== φφφ



¬@¦ BI Table 4 sRmab; 085.1=cλ eyIg)an 519.0=

y

crc F

Fφ

( )( ) kipsFFFAP y

y

crcgnc 40736519.08.21 ==⎟

⎟⎠

⎞⎜⎜⎝

⎛= φφ

¬#¦ Column load table in Part 3 of the Manual [ design strength sRmab;muxkat;rUbrag W, HP,

pipe, tube, double-angle, WT nig single-angle. témøenAkñúgtaragsRmab;rUbragsIuemRTI (W, HP,

pipe nig tube)RtUv)anKNnaedayeRbI radius of gyrationsRmab;rUbragnImYy². sRmab;]TahrN_ enH 0.1=k dUcenH ( ) ftKL 20200.1 == sRmab; 7414×W / Edk 36A nig ftKL 20= eyIgTTYl)an kipsPnc 407=φ . témøEdl)anBI Table 3-36, 3-50 nig 4 KWQrelI flexural buckling nig AISC Equation E2-

2 nig E2-3. dUcenH local stability RtUv)ansnμt; ehIy width-thickness ratio nwgminFMCagtémø kMNt;eLIy. Design strength enAkñúg column load table )anKitbBa¢ÚlenAkarkat;bnßycaM)ac; enAeBlEdl width-thickness ratio FMCagtémøkMNt;.

4>4> karKNnamuxkat; (Design)

kareRCIserIsnUv rolled shape EdlmanlkçN³esdækic© edIm,ITb;nwgbnÞúksgát;Edl[man lkçN³samBaØCamYynwgkareRbIR)as; column load tables. emIltaragCamYynwg effective length

ehIyrMkiltamTisedk rhUtdl;eyIgrkeXIjnUv design strength EdleyIgcg;)an ¬b¤mantémøFMCag bnþicbnþÜc¦. kñúgkrNIxøH eyIgRtUvbnþrkrhUtdl;eyIgGacrk)anrUbragEdlmanTm¶n;RsalCageK. CaTU eTArUbrag (W, WT, etc) RtUv)aneKeFVIkarsMercmuneK. CaerOy² TMhM nigrUbragrbs;muxkat; RtUv)andwgmun edaytRmUvkarsßabtükm μ nigtRmUvkardéTeTot. dUcEdl)anbgðajBIxagedIm RKb;témø EdlmanenAkñúgtaragRtUvKñanwg slenderness ratio tUcCagb¤esμ Inwg 200 . rUbragGt;sIuemRTI (structural tees and the single and double-angles) RtUvkarnUvkarBicarNaBiessEdlnwgmanbk



RsayenAkñúgEpñk 4>6. ]TahrN_ 4>5³ Ggát;rgkarsgát;RTnUv service dead load kNkips 734165 = nig service live load

kNkips 2380535 = . Ggát;enHmanRbEvg mmft 792526 = ehIymanTRm pinned sgçag. eRbIEdk 36A nigerIsrUbrag 14W .

dMeNaHRsay³ KNnabnÞúkemKuN (factored load)³ kipsPu 10545356.11652.1 =×+×= b¤ kN4689 dUcenH required design strength kipsPnc 1054=φ BI column load table sRmab; ftKL 26= / 17614×W man design strength kipsPnc 1150=φ cemøIy³ eRbI 17614×W . ]TahrN_ 4>6³ eRCIserIsrUbrag W EdlmanTm¶n;RsalCageKbMputEdlGacRTbnÞúksgát;emKuN

kNkipsPu 845190 == . RbEvgRbsiT§PaBKW mft 731524 = . eRbIEdk ASTM A572 Grade 50. dMeNaHRsay³ viFId¾smrmüenATIenHKWdMbUgeyIgerIsrUbragEdlRsalCageKenAkñúg nominal size nI mYy² ehIybnÞab;mkeTIberIsrUbragEdlRsalCageKelIrUbragTaMgGs;. CeRmIsmandUcxageRkam³ 4W / 5W nig 6W ³ K μanrUbragNamYyenAkñúgtaragEdlGacyk)an 8W ³ 588×W / kipsPnc 194=φ 10W ³ 4910×W / kipsPnc 239=φ 12W ³ 5312×W / kipsPnc 247=φ 14W ³ 6114×W / kipsPnc 276=φ cMNaMfa load capacity minsmamaRtnwgTm¶n;eT ¬b¤RkLaépÞmuxkat;eT¦. eTaHbICa 588×W man design strength tUcCageKkñúgcMeNamCeRmIsTaMgbYn EtvamanTm¶n;F¶n;CageKbnÞab; 6114×W . cemøIy³ eRbI 4910×W . sRmab;rUbragEdlKμanenAkñúg column load table, eKRtUveRbI trial-and-error approach. dMeNIrkarTUeTAKWsn μt;rUbrag bnÞab;mkKNna design strength rbs;va. RbsinebIersIusþg;tUceBk ¬K μansuvtßiPaB¦ b¤FMeBk ¬K μanlkçN³esd©kic©¦ eKRtUveFVIkarsakl,gepSgeTot. viFIsaRsþkñúgkareFVI trial selection mandUcxageRkam³



!> snμt;témøsRmab; critical buckling stress crF . karBinitü AISC equation E2-2 nig E2-

3 bgðajfatémø crF GtibrmatamRTwsþICa yield stress yF . @> BItRmUvkarKW unc PP ≥φ / yk ucrgc PFA ≥φ enaH

crc

ug F

PAφ

≥

#> eRCIserIsrUbragEdlRtUvKñanwgRkLaépÞcaM)ac;. $> KNna crF nig ncPφ sRmab;rUbragsakl,g. %> eFVIkarEktRmUveLIgvijRbsinebIcaM)ac;. RbsinebI design strength mantémøEk,rtémøRtUvkar

TMhMEdlmanenAkñúgtaragbnÞab;GacRtUv)ansakl,g. RbsinebImindUecñaHeT eFVIkarKNna eLIgvijTaMgRsug. eRbItémø crF EdlrkeXIjsRmab;témøsakl,gCatémøsRmab;CMhan TI !>.

^> RtYtBinitü local stability ¬RtYtBinitü width-thickness ration). EktRmUveLIgvijRbsin ebIcaM)ac;.

]TahrN_ 4>7³ eRCIserIsrUbrag 460W rbs;Edk 36A EdlGacRTbnÞúkemKuN (factored load)

kN4688 . RbEvgRbsiT§PaBKW mm7925 . dMeNaHRsay³ sakl,g kNFcr 5.165= ¬BIrPaKbIén yF ¦³

Required 233

10325.335.16585.0

104688 mF

PAcrc

ug

−⋅=×⋅

==φ

sakl,g 8.2460×W

2323 10325.331039.36 mmAg−− ⋅>⋅=

2008.1119.70

7925

min<==

rKL (OK)

5.1258.1200000

2508.111<===

ππλ

EF

rKL y

c eRbI AISC Equation E2-2

( )( ) ( ) MPaFF ycr c 9.128250658.0658.022 258.1 ==⎟

⎠⎞

⎜⎝⎛= λ

kNkNFAP crgnc 46883987109.1281039.3685.085.0 33 <=⋅×⋅×== −φ (N.G)



sakl,g MPaFcr 9.128= ¬témøEdleTIbnwg)anBIkarKNnasRmab; 8.2460×W ¦ Required 23

310787.42

9.12885.0104688 m

FPA

crc

ug

−⋅=×⋅

==φ

sakl,g 41.3460×W 2323 10787.421039.44 mmAg

−− ⋅>⋅= 2005.109

4.727925

min<==

rKL (OK)

5.1232.1200000

2505.109<===

ππλ

EF

rKL y


( )( ) ( ) MPaFF ycr c 45.132250658.0658.022 232.1 ==⎟

⎠⎞

⎜⎝⎛= λ

kNkNFAP crgnc 46885.49971045.1321039.4485.085.0 33 >=⋅×⋅×== −φ (O.K)

edaysarrUbragenHminmanenAkñúg column load table dUcenHeKRtUvkarRtYtBinitü width-thickness ration

8.15250

2508.22

=<=f

ft

b (O.K)

2.42250

6658.13 =<=wth (O.K)

cemøIy³ eRbIEdk 41.3460×W RbsinebIeKeRbI table 3-36 b¤ table 3-50 témøsakl,grbs; crcFφ manlkçN³gayRsYlkñúg kareRbIenAkñúgsmIkar Required

crc

ug F

PAφ

=

4>5> esckþIbEnßmsRmab;RbEvgRbsiT§PaB (More on Effective Length)

enAkñúgEpñk 4>2 “column theory” )anENnaMBIRbEvgRbsiT§PaB. RKb;gGát;rgkarsgát;TaMg RtUv)anKitCaTRm pinned edayminKitBIlkçxNÐcugTRmBitR)akd EdlnegeFVI[RbEvgRbsiT§PaB KL mantémøxusBIRbEvgBitR)akd. CamYynwgkarEkERbenH load capacity rbs;Ggát;rgkarsgát;Ca GnuKmn_Etnwg slenderness parameter cλ . enAeBlEdleKsÁal;lkçN³rbs;smÖar³ vaCaGnuKmn_eTA



nwg slenderness ration KL .

RbsinebIGgát;rgkarsgát;manTRmepSgKñaenAelIG½kSemrbs;va enaHvanwgmanRbEvgRbsiT§PaB epSgKñaenAelIG½kSTaMgBIr. enAkñúgrUbTI 4>10 W -shape RtUv)aneRbICassr ehIyenAEpñkxagelIva RtUv)anBRgwgedayGgát;edkenAelITisTaMgBIrEdlEkgKña. Ggát;TaMgenHkarBarkarrMkilrbs;ssrRKb; TisedA EtkarlMGitrbs;ssrminRtUv)anbgðajEdlGnuBaØat[karviltictYcekItman. eRkamlkç- xNÐenH Ggát;GacnwgRtUv)anKitCaTRm pinned enAEpñkxagelI. sRmab;mUlehtudUcKña tMNedIm,I RTTRmenAxageRkamk¾GacKitCatMN pinned Edr. CaTUeTA eKBi)aknwgTTYl lkçxNÐ rigid b¤ fixed Nas; luHRtaEteKdak;lkçxNÐBiess. tMNFmμta CaTUeTAxiteTArktMN hinge b¤ pinned . enARtg; Bak;kNþalkm<s;ssrRtUv)anBRgwgEttamTismYy. tMNkarBarEtkarrMkil EtvaminTb;karvileT. kar BRgwgenHkarBarkarrMkiltamG½kSexSayrbs;muxkat; b:uEnþmin)anTb;karrMkilTisxøaMgeT. dUc)anbgðaj enAkñúgrUbTI 4>10 RbsinebIGgát;ekagtamG½kSxøaMg RbEvgRbsiT§PaBrbs;vaKW m9.7 b:uEnþkarekagtam TisexSayGacekagkñúgrUbrag second buckling mode RtUvKñanwgRbEvgRbsiT§PaB m95.3 . eday



sarersIusþg;rbs;vaRcassmamaRteTAnwgkaerén slenderness ratio ssrnwgekagkñúgTisedA Edlman slenderness ration FMCageK dUcenHeKRtUveRbobeFob xx rLK / CamYynwg yy rLK / . enAkñúgrUbTI 4>10 pleFob xr/7900 RtUv)aneRbobeFobCamYynwg yr/3950 ¬Edl xr nig yr KitCa mm ¦ ehIy pleFobEdlmantémøFMCageKRtUv)aneRbIsRmab;kMNt; nominal axial compressive strength nP . ]TahrN_4>8³ Edk 95.0300×W manRbEvg m2.7 RtUv)anRTedayTRm pinned sgçag ehIyTb;tamTis exSayRtg;cMNucmYyPaKbI dUcbgðajkñúgrUbTI 4>11. eRbIEdk 36A kMNt; design

compressive strength . dMeNaHRsay³

7.531.134

7200==

x

xr

LK

3.317.76

2400==

y

yr

LK

xx rLK / mantémøFMCag dUcenHvamanlkçN³lub. BI table 3-36 CamYynwg 7.53/ =rKL

MPaksiFcrc 3.181895.629.2629.26 =×==φ

( ) kNFAP crcgnc 6.2233103.1811032.12 33 =⋅×⋅== −φφ cemøIy³ Design strength kN6.2233=



Design strength Edl[enAkñúg column load table KWQrelIRbEvgRbsiT§PaBtamG½kS y . dMeNIrkarsRmab;eRbIR)as;taragenHCamYynwg LK x GaceFVIeTA)anedaydwgBIedImehtuEdleKTTYl)an témøenAkñúgtaragenH. edaycab;epþImCamYynwgtémø KL eKnwgTTYl)an ncPφ edaydMeNIrkarRsedog KñanwgdMeNIrkarxageRkam³ - KL RtUv)anEckeday yr edIm,ITTYl)an yrKL / .

- KNna slenderness parameter EF

ry

y

KLc πλ =

- KNna crF - KNna design strength crgnc FAP 85.0=φ dUcenHersIusþg;Edl)anerobCataragKWQrelItémørbs; KL Edlesμ Inwg LK y . RbsinebIlT§PaBRT RTg;eFobnwgTisedA x eKGaceRbItaragedayCMnYs

yx

xrrLKKL

/=

enaHbnÞúkEdlenAkñúgtaragnwgQrelI

x

x

y

yxx

y rLK

rrrLK

rKL

==)//(

pleFob y

xrr RtUv)an[enAkñúg column load table sRmab;rUbragnImYy².

]TahrN_ 4>9³ Ggát;rgkarsgát;dUcbgðajenAkñúgrUbTI 4>12 manTRm pinned sgçagehIyenA RtUv)anTb;tamTisenABak;kNþalkm<s;ssr. Service load KW Kips400 EdlbnÞúkefr nigbnÞúkGefr mantémøes μ IKña. eRCIserIs W-Shape EdlmanTm¶n;RsalCageK. dMeNaHRsay³ Factored load kipsPu 5602006.12002.1 =×+×== edaysnμt;faTisedAexSaylub ehIyBinitüemIlkñúg column load table CamYynwg feetKL 9= . cab;epþImCamYynwgrUbragtUcCageK dMbUgeyIgrk)anrUbrag 7710×W CamYynwg design strength

kips632 . RtYtBinitüG½kSxøaMg

ftftrrLK

yx

x 940.1073.1

18/

>==



LK x manlkçN³lubsRmab;rUbragenH emIltaragCamYy feetKL 4.10= . 7710×W enAEtCarUbragRsalCageKsRmab; 10W CamYynwg design strength kips612 ¬eRkayeBleFVI interpolation¦.

bnþGegátelI 7212×W ³ ftft

rrLK

yx

x 93.1075.1

18/

>==

LK x enAEtlub ehIyman design strength kips592 . kMNt;rUbragEdkRsalCageKsRmab; 14W . rUbragEdlRsalCageKKW 7414×W EtvaF¶n;CagrUbrag Edl)anrkBIelIkmun. cemøIy³ eRbIEdk 7212×W

RKb;eBlTaMgGs;EdlGaceFVIeTA)an GñkKNnaKYrEtbEnßmTRmsRmab;TisedAexSayrbs;ssr. RbsinebImindUcenaHeT Ggát;nwgKμanRbsiT§PaB³ vamanersIusþg;FMEtmYyTis. enAeBl LKx mantémø xusKñaBI LK y enaH LK y nwglub elIkElgEt yx rr / tUcCag LKLK yx / . enAeBlpleFobTaMgBIr es μ IKña ssrnwgmanersIusþg;esμIKñakñúgTisedATaMgBIr. sRmab; W-shape enAkñúg column load table

yx rr / sßitenAcenøaH 6.1 nig 8.1 elIkElgsRmab;rUbragEdlRsalCagxøH.

]TahrN_ 4>10³ ssrEdlbgðajenAkñúgrUbTI 4>13 RTnUv factored axial load Kips840 . eRbIEdk

36A ehIyeRCIserIs W-Shape.



dMeNaHRsay³ ftLKx 20= nigtémøGtibrmarbs; ftLK y 8= RbEvgRbsiT§PaB LKx manlkçN³lubenAeBlEdl

LKrrLK

yyx

x >/

b¤k¾enAeBlEdl LK

rrLK

yyx

x >/

( )LKrrLK yy

xx ⎟

⎟⎠

⎞⎜⎜⎝

⎛>

kñúgkrNIenH 5.2

820

==LkLK

y

x b¤ LKLk yx 5.2=

edaysar LKx mantémøFMCag LK y q¶ay enaH LKx RbEhlCanwglub. mUlehtuKWfatémø yx rr / EdlmanenAkñúgtaragPaKeRcInmantémøtUcCag 5.2 dUcenH LKLk yx 5.2= TMngCanwgFMCag

( ) LKrr yyx / . sakl,g 7.1/ =yx rr ³ LK

rrLK

yyx

x >== 76.117.1

20/

rMkillT§pl[eTACa ftKL 12= ehIyBinitüemIlenAkñúg column load table. sakl,g 11210×W ¬ kipsPnc 865=φ ¦³ témøBitR)akd ftft

rrLK

yx

x 125.1174.1

20/

<==

kipsPnc 840>φ EdlRtUvkar ¬edayeFVI interpolation kipsPnc 876=φ RtYtBinitü 10612×W ft

rrLK

yx

x 4.1176.1

20/

==

sRmab; ftKL 12= ftkipsPnc 840853 >=φ (OK)

GegátrUbrag 14W . sRmab; 7.1/ =yx rr ¬pleFobRbEhlsRmab;RKb;krNIEdlGacekItman¦ ftLKft

rrLK

yyx

x 876.117.1

20/

=>==

sRmab; ftKL 12= / 10914×W EdlmanlT§PaBRTRTg; kips905 CarUbragEdlRsalCagsRmab;



14W . RbEvg ft12 CatémøEdlmanlkçN³snSMsMécénRbEvgRbsiT§PaBBitR)akd rUbragenHKWRKb; RKan;. cemøIy³ eRbI 10612×W ¬RsalCageKkñúgcMeNambIrUbragEdl)ansikSa¦



sRmab;ssrdac;edayELk (isolated column) EdlminEmnCaEpñkrbs;eRKagCab; (continuous frame), Table C-C2.1 enAkñúg Commentary to the specification manlkçN³RKb; RKan;CaTUeTA. EtsRmab;eRKagrwg (rigid frame) enAkñúgrUbTI 4>14. ssrenAkñúgeRKagenHminman lkçN³ÉkraCü EtvaCaEpñkrbs;rcnasm<n§½Cab;. elIkElgsRmab;ssrEdlenACan;eRkamssrRtUv)an Tb;enAcugsgçagrbs;va edayFñwmnwgssrdéTeTot. eRKagenHk¾Ca unbraced frame mann½yfaeRKag GacmanbMlas;TItamTisedk ehIyssrTaMgGs;rgnUv sidesway. RbsinebIeKeRbI Table C-C2.1

sRmab;eRKagenH ssrCan;eRkameKmanlkçxNÐRbhak;RbEhlnwglkçxNÐ (f) ehIytémørbs; 0=K GacRtUv)aneRbI. sRmab;ssrEdldUcssr AB témørbs; 2.1=K EdlRtUvKñanwglkçxNÐ (c) Gac RtUv)aneRCIserIs. EtdMeNIrkarEdlsmRsbCaghñwg KWKitGMBIkRmiténkarTb;Edlpþl;[edaytMN rbs;Ggát;. karTb;nwgkarvilEdlpþl;[edayFñwm b¤rtenAxagcugssrCaGnuKmn_eTAnwg rotational

stiffness rbs;Ggát;EdlRbsBVKñaenARtg;cMNucenaH. Rotational stiffness rbs;Ggát;CasmamaRteTA nwg LEI / / Edl I Ca moment of inertia rbs;muxkat;eFobnwgG½kSénkarBt;. Gaylord nig Stallmeyer (1992) )anbgðajfaemKuNRbEvgRbsiT§PaB K GaRs½ynwgpleFobrbs; column

stiffness elI girder stiffness enAxagcugrbs;Ggát;nImYy² EdlGacsMEdgCa

∑∑

∑∑ ==

gg

cc

ggg

cccLILI

LIELIEG

//

// ¬$>&¦

Edl =∑ ccc LIE / plbUk stiffness rbs;ssrTaMgGs;EdlenAcugrbs;ssrEdlBicarNa =∑ ggg LIE / plbUk stiffness rbs;rtTaMgGs;EdlenAcugrbs;ssrEdlBicarNa === EEE gc m:UDuleGLasÞicrbs;eRKOgbgÁúMEdk RbsinebIssrEdlRsavxøaMg (very slender column) RtUv)anP¢ab;eTAnwgrtEdlmanmuxkat;FM enaHrtnwgkarBarkarvilrbs;ssry:agmanRbsiT§PaB. cugrbs;ssrmanlkçN³ approximately

fixed enaH K nwgmantémøtUc. lkçxNÐenHRtUvKñanwgtémøtUcbMputrbs; G Edl[edaysmikar $>&. b:uEnþ cugrbs;ssrmaM (stiff column) EdlP¢ab;eTAnwg flexible beam Gacnwgpþl;karvileday esrIdl;ssr EdlRtUvKñanwglkçxNÐTRm pinned Edl[témø G nig K FM. TMnak;TMngrvag G nig K RtUv)andak;enAkñúg Jackson-Mooreland Alignment Chart

(Johnston, 1976) EdlRtUv)anpliteLIgvijenAkñúg Figure C-C2.2 enAkñúg Commentary . edIm,I



TTYl)antémø K BIr nomogram mYykñúgcMeNamTaMgBIr dMbUgKNnatémø G enAcugnImYy²rbs;ssr eday[mYyCa AG nigmYyeTotCa BG . P¢ab; AG nig BG edaybnÞat;Rtg; ehIyGantémø K enAelIbnÞat;kNþal. emKuNRbsiT§PaBEdlTTYl)anCatémøEdleFobTAnwgG½kSénkarBt; EdlCaG½kS EkgeTAnwgbøg;rbs;eRKag. karviPaKdac;edayELkGaceFVIeLIgsRmab;karekagEdleFobnwgG½kSmYy eTot. CaFm μta beam-to-column connection enAkñúgTisedAenHnwgminbBa¢Únm:Um:g; ¬ sidesway

RtUv)ankarBareday bracing ¦ ehIy K Gacnwgykesμ I 0.1 . ]TahrN_ 4>11³ eRKagrwgEdlbgðajenAkñúgrUbTI 4>15 CaeRKag unbraced frame . Ggát;nImYy² RtUv)andak;eday[RTnugrbs;vasßitenAkñúgbøg;rbs;eRKag. kMNt;emKuNRbEvgRbsiT§PaB xK sRmab;ssr AB nig BC .

dMeNaHRsay³ ssr AB ³ sRmab;tMN A

95.09.231

2205.5/7626/5606.3/4456.3/347

//

==++

==∑∑

gg

ccLILIG

sRmab;tMN B 95.0

9.2313.220

5.5/7626/5606.4/4456.3/445

//

==++

==∑∑

gg

ccLILIG

BI alignment chart sRmab; sidesway uninhibited CamYynwg 95.0=AG nig 95.0=BG / 3.1=K



sRmab;ssr AB . ssr BC sRmab;tMN B KNnadUcmun

95.0=G sRmab;tMN C Rtg;TRm pinned . sßanPaBrbs;vamanlkçN³dUceTAnwgssrEdlmaMxøaMgP¢ab;eTAnwg infinity flexible girder Edlrtman stiffness es μ IsUnü. dUcenHpleFobPaBrwgRkajrbs;ssr (column stiffness) elIPaBrwgRkajrbs;rt (girder stiffness) mantémøesμ IGnnþsRmab;snøak;Kμan kkiteBjelj (perfectly frictionless hinge). lkçxNÐcugenHGaceFVIeTA)ansRmab;karsμanenAkñúgkarGnuvtþ dUcenH eyIgGacyk 10=G sRmab; tMNenH. BI alignment chart CamYynwg 95.0=AG nig 10=BG / 85.1=K sRmab;ssr BC . dUcEdl)anKUsbgðajenAkñúg]TahrN_4>11 sRmab;TRm pinned G KYrRtUv)anykesμ Inwg

0.10 sRmab; TRm fixed G KYrRtUv)anykes μInwg 0.1 . lkçxNÐTRm fixed RtUvKñanwgrtEdlrwgmaMxøaMg (infinitely stiff girder) nig flexible column EdlRtUvKñanwgtémøtamRTwsþI 0=G . kñúgkareRbIR)as; alignment chart enAkñúg Commentary )anENnaM[eRbI 0.1=G edaysarEteKBi)annwgTTYl)anTRm fixed eBjelj.

Unbraced frame manlT§PaBTb;nUvkmøaMgxagedaysartMNEdlTb;nwgm:Um:g;rbs;va. Ca erOy²eRKagbEnßmedayRbB½n§BRgwgtamrUbragepSg² eRKagEbbenHRtUv)aneKehAfa braced frame. karTb;kmøaMgxagbEnßmGaceFVIeLIgkñúgTRmg;Ca diagonal bracing dUcbgðajenAkñúgrUbTI 4>16 b¤ rigid

shear wall. kñúgkrNIepSgeTot ssrRtUv)anTb;eday panel b¤ bay sRmab;km<s;TaMgmUlrbs;eRKag. TRmenHbegáItCa cantilever structure EdlTb;nwgbMlas;TItamTisedk ehIyk¾pþl;nUvTRmtamTisedk sRmab;ElVgdéTeTot. GaRs½yeTAnwgTMhMrbs;eRKOgbgÁúM ElVgeRcInCagmYyGacRtUv)anBRgwg. ssr EdlCaGgát;rbs; braced frame RtUv)ankarBarBI sidesway nigmankarTb;karvilenAxagcugrbs;vaxøH. dUcenH vaCaRbePTGgát;sßitenAkúñgcenøaHkrNI (a) nig (d) enAkñúg Table C-C2.1 rbs; Commentary ehIy K sßitenAcenøaH 5.0 nig 0.1 . dUcenH 0.1 CatémøEdltUcsRmab;Ggát; én braced frame

ehIyCatémøEdl AISC C2.1 ENnaM[eRbI elIkElgEtmankarviPaKNamYyeFVIeLIg. karviPaKGaceFVI



eTA)anedayeRbI alignment chart sRmab; braced frame . kareRbI nomogram nwgpþl;lT§-plCa effective length factor EdltUcCag 1.0 bnþicbnþÜc ehIyeKnwgTTYl)ankarsnSMsMécxøH *. CamYynwg design aid xøH eKeRbI alignment chart kñúglkçxNÐEdleKbegáItvaeLIg. lkçxNÐ TaMgenHmanenAkñúg Section C2 of the Commentary to the Specification ehIyminRtUv)anerobrab; enATIenHeT. RKb;lkçxNÐTaMgGs;nwgRtUv)anbMeBjesÞIrEtTaMgGs;CaTUeTA RbsinebIdUcenaHeT PaBxus KñaenaHCaEpñkmYyKYr[RbugRbytñ½. lkçxNÐmYyEdlminRtUv)anbMeBjCaTUeTAenaH KWtRmUvkarEdlfa RKb;karRbRBwtþeTArbs;Ggát;sßitkñúglkçN³eGLasÞic. RbsinebI slenderness parameter cλ tUcCag

5.1 ssrnwgekageday inelastic ehIyemKuNRbEvgRbsiT§PaBEdlTTYl)anBI alignment chart nwg mantémøtUcEmnETn. ssrPaKeRcInsßitenAkñúgRkumenH. dMeNIrkargayRsYlkñúgkarkMNt; K sRmab; inelastic column GnuBaØat[eRbI alignment chart (Yura, 1971 and Dique, 1973). edIm,IbkRsay

* RbsinebIeRKagRtUv)anBRgwgTb;nwg sidesway tMN beam-to-column minRtUvkar moment resisting ehIyRbBn§½BRgwgGac RtUv)anKNnaedIm,ITb;nUvRKb; sidesway tendency . b:uEnþRbsinebItMNminEmnCa moment resisting vanwgminmanPaBCab; rvagssr nigrt ehIyeKminGaceRbI alignment chart . sRmab; braced frame RbePTenH xK KYrRtUvykes μ Inwg 0.1 .



dMeNIrkarenH eyIgcab;epþImCamYynwg critical buckling load sRmab; inelastic column Edl[eday smIkar $>^ b. edayEckvanwgRkLaépÞmuxkat;eKTTYl)an buckling stress³

( )22

/ rKL

EF t

crπ

=

Rotational stiffness rbs;ssrenAkñúgkrNIenHCasmamaRtnwg cct LIE / ehIytémøEdlsmRsb rbs; G sRmab;eRbIenAkñúg alignment chart KW elasticinelastic /

/G

EE

LEILIE

G t

gg

cct ==∑∑

eday tE tUcCag E enaH inelasticG nwgtUcCag elasticG ehIy effective length factor K nwgRtUv)an kat;bnßy CalT§pleKTTYl)ankarKNnamYyEdlmanlkçN³esdækic©Cag. edIm,IkMNt; EEt / Edl eK[eQ μaHfa emKuNkat;bnßyPaBrwgRkaj (stiffness reduction factor SRF)/ BicarNaTMnak;TMng xageRkamsRmab;ssrEdlmanTRmcug pinned ³

( )( ) E

E

rLE

rLEF

F tt

cr

cr == 22

22

elastic)(

inelastic)(

//

//

π

π ¬$>*¦

AISC eRbItémøRbhak;RbEhlsRmab;Epñk inelastic én column strength curve dUcenHsmIkar $>* CatémøRbhak;RbEhlenAeBlEdl AISC Equation E2-2 nig E2-3 RtUv)aneRbIsRmab; crF . Rbsin ebI eyIg[

AP

APF cucr

crφ/

≈= enAeBlEdl elastic)(inelastic)( / crcr FF CaGnuKmn_én ( )AP cu φ/ . ]TahrN_ sRmab;

( ) MPaAP cu 180/ =φ nig MPaFy 250= ( )250658.0658.0180

22inelastic)( cc ycr FMPaF λλ ==≈

785.02 =cλ MPaFF y

ccr 3.279250

785.0877.0877.0

2elastic)( ===λ

dUcenHemKuNkat;bnßyPaBrwgRkajKW SRF 644.0

3.279180

elastic)(

inelastic)( ===cr

crF

F



edaysar cφ efr enaH SRF k¾CaGnuKmn_én APu / . témørbs; SRF EdlCaGnuKmn_én APu / RtUv)an[enAkúñg Table 3-1 in Part 3 of the Manual. ]TahrN_ 4>12³ rUb 4>17 bgðajBI rigid unbraced frame. Ggát;TaMgGs;RtUv)andak;edayeFVIy:ag Na[karBt; eFobnwgG½kSxøaMg. TRmxagRtUv)andak;enAtMNnImYy²edaytMNFm μtaEdlBRgwgkñúgTis edAEkgeTAnwg eRKag. kMNt;emKuNRbEvgRbsiT§PaBedayeFobnwgG½kSnImYy²sRmab;Ggát; AB . bnÞúktamG½kSemKuNenAelIGgát;enHKW kips180 ehIyeKeRbIEdk 36A . dMeNaHRsay³ KNnaemKuNeGLasÞicrbs; G

sRmab;tMN A / ( )( ) 52.1

35.917.14

18/6.8820/6.8812/170

//

==+

=∑∑

gg

ccLILI

sRmab;tMN B ( )( )

( ) 35.10.213.28

18/19020/19012/1702

//

==+

=∑∑

gg

ccLILI

BI alignment chart sRmab; unbraced frames, 43.1=xK / edayQrelI elastic behavior dUcenH ( )( ) 5512.0

2900036

19.4121243.1

=⋅

==ππ

λEF

rLK y

x

xc

edaysar cλ tUcCag 5.1 enaHeKRtUveRbIemKuN K inelastic Edl[ ksi

APu 5.18

71.9180

== BI Table 3-1in Part 3 of the Manual emKuNkat;bnßyPaBrwgRkaj SRF 83.0= sRmab;tMN A 26.152.183.0 =×=×= elasticinelastic GSRFG sRmab;tMN B 12.135.183.0 =×=×= elasticinelastic GSRFG cemøIy³ BI alignment chart 37.1=xK . edaysarlkçxNÐTRmFm μtasRmab;eRKag enaH yK esμ Inwg 1.



RbsinebIcugssrCaTRm fixed (G=1.0) b¤ pinned (G=10.0) témørbs; G minRtUv)anKuNnwg SRF eT. 4>6>karekagedayrmYl nigedayBt;-rmYl (Torsional and Flexural-Torsional Buckling)

enAeBlEdlGgát;rgkarsgát;edaybnÞúkcMG½kS køayCaKμansßirPaB¬minEmn locally unstable¦ vaGacekagkñúgrUbragmYykñúgcMeNamrUbragbI dUcbgðajenAkñúgrUbTI 4>18. !> karekagedaykarBt; (flexural buckling) eyIg)anBicarNakarekagRbePTenHtaMgBImunrhUtmk

dl;eBlenH. vaCaPaBdabEdlekIteLIgedaykarBt; (bending or flexure) CMuvijG½kSEdlRtUv nwgpleFobPaBrwgRkaj (slenderness ratio) FMCageK ¬rUbTI 4>18 a¦. CaTUeTAvaCa minor

principle axis EdlmankaMniclPaB (radius of gyration) tUcCageK. Ggát;rgkarsgát;Edlman muxkat;RKb;rUbragGac)ak;tamTRmg;enH.

@> karekagedayrmYl (torsional buckling) kar)ak; (failure) edayRbePTenHKWbNþaledaykarmYl (twisting) tamG½kSbeNþayrbs;Ggát;. vaGacekIteLIgEtCamYynwgGgát;EdlmanlkçN³Rsav xøaMg ehIymanmuxkat;sIuemRTIDub (double symmetrical cross section) ¬rUbTI 4>18 b¦. Standard hot-rolled shapes mingaynwgrgnUvkarekagedayrmYlenHNas; b:uEnþGgát; built-up BI



bnÞHesþIggayeRKaH nigKYreFVIkarGegát. rUbragExVgbgðajnUvPaBgayrgeRKaHBiesssRmab;RbePT énkarekagenH. rUbragenHGac)anmkBIkarpÁúMBIbnÞHdUcbgðajenAkñúgrUb b¤ built-up BImMubYnTl;xñgKña.

#> karekagedaykarBt;-rmYl (flexural-torsional buckling) kar)ak;RbePTenHbegáIteLIgedaybnSM

énkarekagedaykarBt; nigkarekagedayrmYl. Ggát;ekag nigrmYlkñúgeBlEtmYy¬rUbTI4>18 c¦. karekagRbePTenHGacekIteLIgEtCamYymuxkat;EdlmanrUbragminsIuemRTI TaMgrUbragEdlman G½kSsIuemRTImYyTis dUcCa channel, structural tee, double-angle shape nig equal-leg sigle

angles nigrUbragEdlK μanG½kSsIuemRTI dUcCa unequal-leg single angle. AISC Specification tRmUvnUvkarviPaKBI torsional b¤ flexural-torsional buckling enAeBl smrmü. Section E3 of the Specification erobrab;BIGgát; double angle nig tee-shaped ehIy Appendix E3 pþl;nUvviFITUeTAEdlGaceRbIsRmab;RKb;rUbragminsIuemRTI. dMbUgeyIgerobrab;BIviFIEdlmanenAkñúg Appendix E3. vaQrenAelIkareRbIR)as; slenderness

parameter eλ CMnYs[ cλ . eyIgTTYl eλ dUcxageRkam. BI Euler buckling stress/



( )2

2

/ rKLEFe

π=

Slenderness ratio GacsresrCa

eFE

rKL 2π

=

RbsinebI eF RtUv)ankMNt;Ca elastic buckling stress EdlRtUvnwgrUbragénkar)ak;Edllub eTaHeday flexural, torsional b¤ flexural-torsional enaH slenderness ratio EdlRtUvKñaKW

ee FE

rKL 2π

=⎟⎠⎞

⎜⎝⎛

ehIy slenderness parameter EdlRtUvKñaKW

( )e

yeyyee F

F

E

rKLFEFrKL

=== 2

2)/(/

ππλ

dMeNIrkarKNnamandUcxageRkam³ !> kNt; eF sRmab; torsional elastic buckling b¤ flexural-torsional elastic buckling BIsmIkar

Edl[enAkñúg Appendix E3. @> KNna effective slenderness parameter, eλ . #> KNna critical stress crF BIsmIkarFmμta (AISC Equations E2-2 and E2-3) b:uEnþeRbI eλ CMnYs

[ cλ . bnÞab;mk design strength KW crgcnc FAP φφ =

Edl 85.0=cφ dUcKñasRmab; flexural buckling. smIkarsRmab; eF Edl[enAkñúg AISC Appendix E3KWQrelI well-established theory

Edlmankñúg Theory of Elastic Stabality (Timoshenko and Gere, 1961). elIkElgsRmab;kar pøas;bþÚrxøHenAkñúg notation vamansmIkardUcKñaenAkñúgesovePAenaH edayK μankarsRmYl. sRmab; doubly symmetrical shapes (torsional buckling)/

( ) yxz

we II

GJLK

ECF

+⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

12

2π (AISC Equation A-E3-5)

sRmab; singly symmetrical shape (flexural-torsional buckling)/



( ) ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−−

+= 2

411

2 ezey

ezeyezeye

FF

HFFH

FFF (AISC Equation A-E3-6)

sRmab;rUbragEdlK μanG½kSsIuemRTI (flexural-torsional buckling)/

( )( )( ) ( )( )( ) 0/

/)(22

22

=−−

−−−−−

ooexee

ooeyeeezeeyeexe

ryFFF

rxFFFFFFFFF (AISC Equation A-E3-7)

smIkarcugeRkayCasmIkardWeRkTI3 dUcenHrbs; eF KWtUcNas;. CasMNagl¥ PaBcaM)ac;kñúgkaredaH RsaysmIkarenHKWticbMput edaysareKkMreRbIrUbragminsIuemRTICaGgát;rgkarsgát;Nas;. GgÁEdl min)ankMNt;BImunEdleRbIenAkñúgsmIkarTaMgbIenHRtUv)ankMNt;dUcteTA³ =wC warping constant

=zK emKuNRbEvgRbsiT§PaBsRmab;karekagedayrmYl EdlQrelIbrimaNénkarTb;cug RbqaMgnwgkarrmYltamG½kSbeNþay.

=G shear modulus

=J torsional constant ¬es μ IeTAnwg polar moment of inertia sRmab;Etmuxkat;mUl¦

( )22

/ xxex

rLKEF π

= (AISC Equation A-E3-10)

( )22

/ yyey

rLKEF π

= (AISC Equation A-E3-11)

Edl y CaG½kSsIuemRTIsRmab; singly symmetric shapes.

( ) 22

2 1

oz

wez

rAGJ

LK

ECF⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

π (AISC Equation A-E3-12)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +−= 2

221

o

oo

r

yxH (AISC Equation A-E3-9)

Edl ox nig oy CakUGredaenén shear center rbs;muxkat;edayeFobnwgTIRbCMuTm¶n;. Shear

center CacMNucenAelImuxkat;EdlbnÞúkeFVI[Ggát;ekagedayminrmYl. Shear center RtUv)anniyay lMGitenAkñúgCMBUk 5.

AII

yxr yxooo

+++= 222 (AISC Equation A-E3-8)

eKGacrktémøefrEdleRbIenAkñúgsmIkarTaMgbIsRmab; eF enAkñúgtarag torsion properties nig flexural-torsional properties enAkñúg part 1 of the Manual . sRmab; W, M, S nig HP shapes,



J nig wC RtUv)an[. eK[témø J / wC / or nig H RtUv)an[sRmab; channel, single angle nig structural tee. taragsRmab; double angle [témø or nig H ¬ J nig wC esμ InwgBIrdgén témøEdl[sRmab; single angle¦.

dUc)anbgðajBIxagelI eKkRmnwgviPaKkarekagedayrmYlsRmab;muxkat;sIuemRTIDub. dUcKña eKkRm eRbIrUbragKμanG½kSsIuemRTICaGgát;rgkarsgát; ehIyeKkMrnwgviPaK flexural-tensional buckling én Ggát;RbePTenHEdr RbsinebIman eKcaM)ac;RtUvEtviPaKva. sRmab;ehtuplTaMgenH eyIgkMNt;kar BicarNaelIrUbrag flexural-torsional buckling CamYynwgG½kSsIuemRTImYy. elIsBIenH double angle

EdlCa built-up shape CaRbePTrUbragEdleKniymeRbIeRcIn. sRmab; singly symmetrical shape, flexural-torsional buckling stress eF TTYl)anBI

AISC Equation A-E3-6. enAkñúgsmIkarenH y RtUv)ankMNt;CaG½kSsIuemRTI ¬edayminKitBITisedA rbs;Ggát;¦ehIy flexural-torsional buckling RtUv)anKitEttamG½kSmYyenH ¬flexural buckling

tamTisenHnwgminekItman¦. G½kS x RbQmEtnwg flexural buckling. dUcenH sRmab; singly

symmetrical shape eKGacmanersIusþg;BIrKW flexural-torsional buckling tamG½kS y ¬G½kSsIuemRTI¦ b¤ flexural buckling eFobG½kS x . edIm,IkMNt;mYyNamanlkçN³lub KNnaersIusþg;EdlRtUvnwg G½kSnImYy² ehIyeRbItémøNaEdltUcCag. ]TahrN_ 4>13³ KNna design compressive strength rbs; 5.805.13 ×WT . RbEvgRbsiT§PaB tamG½kS x KW feet25 inches6 RbEvgRbsiT§PaBtamG½kS y KW feet20 ehIyRbEvgRbsiT§PaBtam G½kS z KW feet20 . eRbIEdk 36A . dMeNaHRsay³ KNna design compressive strength sRmab;G½kS x ³

( ) 27.7796.3125.25

==x

xr

LK

5.18666.029000

3627.77<===

ππλ

EF

rKL y


( ) ( ) ( ) ksiFF ycr c 29.2636658.0658.022 8666.0 === λ

( )( ) kipsFAP crgcnc 53029.267.2385.0 === φφ



KNna flexural-torsional buckling strength CMuvijG½kS y

( )( ) ksi

rLKEF

yyey 17.52

)07.74(29000

/ 2

2

2

2===

ππ

( ) 22

2 1

oz

wez

rAGJ

LK

ECF⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

π

( )( )( )

( )( )

ksi7.10767.57.23

131.7112001220

7.422900022

2=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

×=

π ksiFF ezey 9.1597.10717.52 =+=+

( ) ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−−

+= 2

411

2 exey

ezeyezeye

FF

HFFH

FFF

( )( )( )( )

( )ksi81.45

9.159813.07.10717.52411

813.029.159

2 =⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

8865.081.45

36===

e

ye F

Fλ

edaysartémøenHtUcCag 5.1 eRbI AISC Equation E2-2 CamYynwg eλ CMnYs[ cλ ³ ( )( ) ( ) ksiFF ycr e 91.2536658.0658.0

22 8865.0 ==⎟⎠⎞

⎜⎝⎛= λ

( )( ) kipsFAP crgcnc 52291.257.2385.0 ===φφ (controls) cemøIy³ Design strength kips522=

cMNaMfa enAeBlEdl crF nig eF RtUv)anKNna karKNnasRmab; flexural buckling CMuvij G½kS x nig flexural-torsional buckling CMuvijG½kS y manlkçN³dUcKña. dUcenHbnÞab;BI crF nig eF RtUv)anKNna TaMg cλ nig eλ GacRtUv)anKNna ehIytémøEdltUcCagRtUv)aneRbIedIm,IKNna strength . kareFVIEbbenHedIm,Ikat;bnßykarcaM)ac;kñúgkarKNna strength sRmab;G½kSTaMgBIr.

dMeNIrkarviPaK flexural-torsional buckling elI double-angle nig tee Edl[enAkñúg AISC

Section E3 CakarEksRmYldMeNIrkarviPaKEdl[enAkñúg AISC Appendix E3. vak¾mankarEkERb kMNt;cMNaMxøHdUcCa³ BI eF eTACa crftF / eyF eTACa cryF nig ezF eTACa crzF . kugRtaMg cryF RtUv)anrkBI AISC E2 nigQrelI flexural buckling eFobG½kS y .

edIm,ITTYl)an crzF eyIgGacecalG½kSTImYyrbs; AISC Equation A-E3-12 enaH



2o

crzrA

GJF =

karlubecalenHGacGnuBaØat)an BIeRBaHsRmab; double-angle nig tee GgÁTImYymantémøtUc Gacecal)anebIeFobnwgGgÁTIBIr.

Flexural buckling stress cryF RtUv)anKNnaCamYynwgsmIkarFmμtarbs; AISC Chapter E

edayeRbI rKL / EdlRtUvKñanwgG½kS y ¬G½kSsIuemRTI¦. bnÞab;mkeTot nominal strength GacRtUv)anKNnadUcxageRkam crftgn FAP =

Edl ( ) ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ += 2

411

2 crzcry

crzcrycrzcrycrft

FF

HFFH

FFF (AISC Equation E3-1)

RKb;GgÁTaMgGs;Edl)anmkBI Appendix E3 rkSadEdl. dMeNIrkarenH RtUv)aneRbIsRmab;Et double-angle nig tee eRBaHvapþl;nUvcemøIysuRkitCagkareRbIdMeNIrkarEdl[enAkñúg Appendix E3. ]TahrN_ 4>14³ KNna design strength rbs;rUbragenAkñúg]TahrN_TI 4>13 edayeRbIsmIkarrbs; AISC Equation E3. dMeNaHRsay³ BI]TahrN_ 4>13 flexural buckling strength sRmab;G½kS x KW kips530 ehIy

07.74/ =yy rLK . BI AISC E2-4, slenderness parameter KW 5.18307.0

290003607.74

<===ππ

λEF

rKL y

c BI AISC Equation E2-2, ( )( ) ( ) ksiFFF ycrycr c 97.2636658.0658.0

22 8307.0 ==⎟⎠⎞

⎜⎝⎛== λ

BI AISC E3,

( )( )

ksirA

GJFo

crz 5.10767.57.23

31.71120022 ===

ksiFF crzcry 5.1345.10797.26 =+=+

( ) ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ += 2

411

2 crzcry

crzcrycrzcrycrft

FF

HFFH

FFF



( )( )( )( )

( )ksi48.25

5.134813.05.10797.26411

813.025.134

2 =⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

( )( ) 51348.257.2385.0 === crftgcnc FAP φφ (Control)

cemøIy³ Design strength kips513=

lT§plenAkñúg]TahrN_ 4>13 nig 4>14 bgðajBIkMhuskñúgkareRbIR)as; Appendix E3

sRmab; rUbragenHmanlkçN³minsnSMsMéc. viFIsaRsþEdleRbIenAkñúg]TahrN_ 4>14 EdlQrelI AISC Specification E3 EtgEtRtUv)aneRbIsRmab; double angle nig tee. b:uEnþkñúgkarGnuvtþ ersIusþg; rbs; double angle nig tee PaKeRcInGacrk)anenAkñúg column load table. taragTaMgenaH KWQrelI viFIsaRsþEdlesñIeLIgeday AISC E3 ehIyk¾GaceRbIedIm,IepÞógpÞal;lT§plrbs;]TahrN_ 4>14. taragpþl;nUvtémø design strength BI EdlmYyCa flexural buckling eFobG½kS x nigmYyeTotCa flexural-torsional buckling eFobG½kS y .

taragTaMgenaHk¾pþl;pgEdrsRmab;Ggát;rgkarsgát; single-angle. Design strength Edl [edayminQrelIRTwsþI flexural-torsional buckling RtUv)an[enAkñúg specification dac;edayELk sRmab; single-angle member enAkñúg Part 6 of the Manual, Specification and Codes.

4>7> Built-up Member

RbsinebIeKsÁal;lkçN³muxkat; (cross-sectional properties)rbs;Ggát;rgkarsgát; built-up karviPaKrbs;vamanlkçN³RsedogKñasRmab;Ggát;rgkarsgát;epSgeTot RbsinebIEpñkpÁúMrbs;muxkat;t P¢ab;)anl¥. AISC E4 mankarlMGitCaeRcInEdlTak;TgeTAnwgkartP¢ab;enH CamYynwgtRmUvkardac; edayELksRmab;Ggát;EdlpÁúMeday rolled shape mYy b¤eRcIn nigGgát;EdlpÁúMeday plate b¤bnSMén plate nig Edkrag (shape). munnwgBicarNaBIbBaðatP¢ab; eyIgnwgrMlwkBIkarKNnalkçN³muxkat;rbs; rUbrag built-up. Design strength rbs;Ggát;rgkarsgát; built-up CaGnuKmn_eTAnwg slenderness parameter

cλ . dUcenHeKRtUvkMNt;G½kSem nigkaMniclPaBEdlRtUvKñanwgG½kSTaMgenaH. sRmab;muxkat; homogenous G½kSemRtYtsIunwgG½kSTIRbCMuTm¶n;. viFIsaRsþkñúgkarKNnaRtUv)anbgðajenAkñúg]TahrN_ 4>15. EpñkpÁúMrbs;muxkat;RtUv)ansnμt;fatP¢ab;)anl¥.



]TahrN_ 4>15³ ssrEdlbgðajenAkñúgrUbTI 4>19 RtUv)anplitedaykarpSarEdkbnÞH ""4 83× BIelI

søabrbs;Edk 3518×W . EdkpÁúMTaMgBIrCaEdk 36A . RbEvgRbsiT§PaBeFobG½kSTaMgBIrKW feet15 . edaysnμt;EdkpÁúMTaMgBIrRtUv)antP¢ab;edayeFVIy:agNa[Ggát;manRbsiT§PaBeBj ehIyKNna design

strength edayQrelI flexural buckling.

dMeNaHRsay³ CamYynwgkarbEnßmEdkBIelI rUbragmanlkçN³minsIuemRTIbnþic b:uEnþ\T§iBl flexural-

torsionalRtUv)anecal. G½kSsIuemRTIbBaÄrCaG½kSemmYyEdleKminRtUvkarKNna. eKnwgrkG½kSemedkedayeRbI

principle of moment³ plbUkm:Um:g;RkLaépÞrbs;FatupSMnImYy²eFobnwgG½kSNamYy ¬enAkñúg]Ta-hrN_enH G½kSedksßitenAEpñkxagelIrbs; plateRtUv)aneRbI¦ RtUvEtes μ Inwgm:Um:g;RkLaépÞsrub. eyIgeRbItarag 4>1 edIm,IsRmYldl;karKNna.

tarag 4>1 Component A y Ay Plate 1.500 0.1875 0.2812 W 10.3 9.225 95.02 ∑ 11.8 95.30

inAAyy 076.8

8.1130.95

===∑∑

CamYynwgTItaMgrbs;G½kSTIRbCMuTm¶n;edkEdl)anKNnaxagelI eyIgGacKNnam:Um:g;niclPaB eFobnwgG½kSenHedayeRbI parallel-axis theorem³

2AdII += Edl =I m:Um:g;niclPaBeFobG½kSTIRbCMuTm¶n;rbs;RkLaépÞpSM =A RkLaépÞrbs;EpñkpSM =I m:Um:g;niclPaBeFobG½kSRsbeTAnwgG½kSTIRbCMuTm¶n;rbs;RkLaépÞpSM



=d cm¶ayEkgrvagG½kSBIr karcUlrYmBIRkLaépÞpSMnImYy²RtUv)anKNna nigRtUv)anbUkedIm,ITTYl)anm:Um:g;niclaPaBrbs; composite area. tarag 4>2 CataragEdlbEnßmBIelItarag 4>1 edayrYmbBa©ÚlkarKNnaenH. sRmab;G½kSQr ( )( ) 43 30.173.15483

121 iny =+= ¬ controle¦

inAI

r yy 211.1

8.1130.17

=== tarag 4>2

( ) 5.1667.129000

36211.1

1215>===

ππλ

EF

rKL y

c

( )

( ) ksiFF yc

cr 36.1136667.1877.0877.0

22 =⎥⎥⎦

⎤

⎢⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

λ

( )( ) kipsFAP crgcnc 11436.118.1185.0 === φφ cemøIy³ Design strength kips114= . tRmUvkarkartP¢ab;sRmab; Built-up Members EdlpSMeLIgeday Rolled Shapes rUbrag built-up EdleKniymCageKKWrUbragEdlpÁúMeLIgeday rolled shap EdleK[eQ μaH fa double-angle shape. Ggát;RbePTenHnwgRtUv)aneRbIedIm,IbgðajBItRmUvkarsRmab;Ggát; built-up Rb ePTenH. rUbTI 4>20 bgðajGgát;rgkarsgát;rbs; truss EdlP¢ab;eTAnwg gusset plate enAxagcugnImYy ²rbs;va. edIm,IrkSa back-to-back seperation rbs; angle tambeNþayRbEvg fillers nig spacers EdlmankRmas;es μ Inwg gusset plate RtUv)andak;enA angles edayKMlates μ I²Kña. KMlatRtUvEtmantémø tUcRKb;RKan;edIm,IeFVI[ built-up member enHeFVIkarCalkçN³EtmYy. RbsinebIGgát;ekageFobG½kS x ¬flexural buckling¦ eRKOgP¢ab; (connector) minrgnUvbnÞúkKNnaNamYyeT ehIybBaðaénkartP¢ab; KWsamBaØedayrkSaTItaMgrbs;Ggát;TaMgBIr. edImI,Fanafa built-up member eFVIkarCalkçN³EtmYy

Component A y Ay I d 2AdI + Plate 1.500 0.1875 0.2812 0.01758 7.889 93.37` W 10.3 9.225 95.02 510 1.149 523.6 ∑ 11.8 95.30 617.0= xI



AISC tRmUvfa stiffness rbs;FatupSMnImYy²minRtUvFMCagbIPaKbYnén stiffness rbs; built-up

member eT.

rKL

ra

i 43

≤

Edl =a KMlatrbs;eRKOgP¢ab; =ir kaMniclPaBGb,brmarbs;FatupÁúM =rKL / maximum slenderness ratio rbs; built-up member

RbsinebIGgátekageFobG½kSsIuemeRTI ¬EdlvargnUv flexural-torsional buckling eFobG½kS

y ¦ eRKOgP¢ab;rgnUvkmøaMgkat;. lkçxNÐenHGacRtUv)anemIleXIjedayBicarNa planks BIrEdleRbICa Fñwm RtUv)anbgðajenAkñúgrUbTI 4>21. RbsinebI plank minRtUv)anP¢ab; vanwgrGiltamépÞb:H enAeBl EdlvargbnÞúk ehIyvanwgeFVIkarCaFñwmBIrdac;edayELkBIKña. enAeBlEdlvaRtUv)anP¢ab;edayb‘ULúg ¬b¤eRKOgP¢ab;epSgeTotdUcCa EdkeKal¦ plank TaMgBIrnwgeFVIkarEtmYy ehIyersIusþg;Tb;nwgkarrGil nwgbegáItCakmøaMgkat;enAkñúgb‘ULúg. kareFVIkarEbbenHekItmanenAkñúg double-angle shape enAeBl karekageFobnwgG½kS y . RbsinebIFñwm plank RtUv)andak;eday[karekagekItmaneFobnwgG½kSepSg eTot ¬G½kS b ¦ enaH plank TaMgBIrnwgekagkñúglkçN³dUcKña ehIyK μankarrGil nigKμankmøaMgkat;. kareFVIkarenHmanlkçN³RsedogKñanwgkarekageFobG½kS x rbs; double-angle shape . enAeBlEdl eRKOgP¢ab;rgnUvkmøaMgkat; eKRtUvkar modified slenderness ratio EdlmantémøFMCagtémøBitR)akd.



ASIC E4 BicarNaeRKOgP¢ab;BIrRbePT³ ¬!¦ snug-tight bolt nig ¬@¦ pSar b¤ fully tightned

bolt . karbriyaylMGitBIkartP¢ab;manenAkñúgCMBUkTI7. Column load table sRmab; double-angle KWQrelIkarpSar b¤ fully tightened bolt. sRmab;krNIenH³

( )2

2

22

182.0 ⎟⎟

⎠

⎞⎜⎜⎝

⎛

++⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

ibom ra

rKL

rKL

αα (AISC Equation E4-2)

Edl ( ) =orKL / original unmodified slenderness ratio ( ) =mrKL / modified slenderness ratio

=ibr kaMniclPaBrbs;FatupSMeFobG½kSRsbeTAG½kSénkarekagrbs;Ggát; =α separation ratio

ibrh

2=

=h cm¶ayrvagTIRbCMuTm¶n;rbs;FatupSM ¬EkgeTAnwgG½kSénkarekagrbs;Ggát;¦ enAeBlEdleRKOgP¢ab;Ca snug-tight bolts

22

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

ibom ra

rKL

rKL (AISC Equation E4-1)

Column load table sRmab; double-angle shape bgðajBIcMnYneRKOgP¢ab;caM)ac;sRmab; flexural-torsional buckling strength Edl[tamG½kS y . cMnYneRKOgP¢ab;sRmab; flexural buckling

strength tamG½kS x RtUv)ankMNt;tamPaBcaM)ac;Edlfa slenderness rbs; angle mYyminRtUvFMCagbI PaKbYnén slenderness rbs; double-angle shape TaMgmUleT. ]TahrN_ 4>16³ KNna design strengthrbs;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI 4>22. Edl rag angle BI 2

135 ×× RtUv)andak;eday[eCIgEvgTl;xñgKña ehIyXøatBIKña inch83 . RbEvg

RbsiT§PaB feetKL 16= nigman fully tightened intermediate connectors cMnYn 3. eRbIEdk 36A .



dMeNaHRsay³ KNna flexural buckling strength sRmab;G½kS x

( ) 8.12059.11216

==xr

KL

5.1355.129000

368.120<===

ππλ

EF

rKL y


( ) ( )( ) ( ) ksiFF ycr c 69.1636658.0658.022 355.1 === λ

( )( ) kipsFAP crgcnc 10669.165.785.0 === φφ sRmab;G½kS y 6.153

25.112(16

==yr

KL

edIm,IkMNt; flexuaral-torsional buckling strength sRmab;G½kS y eRbI modified slenderness ratio

edayQrelIKMlatrbs;eRKOgP¢ab;. KMlatrbs;eRKOgP¢ab;KW ( ) ina 48

41216

== bnÞab;mk ( ) 2.1156.15375.007.74

648.048

=<===zi ra

ra (OK)

inrr yib 829.0== ( ) inh 875.1

8375.02 =+=

( ) 131.1829.02

875.12

===ibr

hα BI AISC Equation E4-2, modified slenderness ration KW

( )2

2

22

182.0 ⎟⎟

⎠

⎞⎜⎜⎝

⎛

++⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

ibom ra

rKL

rKL

αα

( ) ( )( )[ ] 5.158

829.048

313.11131.182.06.153

2

2

22 =⎟

⎠⎞

⎜⎝⎛

++=

témøenHRtUv)aneRbICMnYs[ yrKL / sRmab;KNna cryF 5.1778.1

29000365.158

>===ππ

λEF

rKL y

c



eRbI AISC Equation E2-3

( )( ) ksiFF y

ccry 987.936

778.1877.0877.0

22 =⎥⎥⎦

⎤

⎢⎢⎣

⎡=

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

λ

( )( )

ksirA

GJFo

crz 4.15152.25.7

322.021120022 =

×==

ksiFF crzcry 4.1614.151987.9 =+=+

( ) ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ += 2

411

2 crzcry

crzcrycrzcrycrft

FF

HFFH

FFF

( )( )( )( )

( )ksi748.9

4.161645.04.151987.9411

645.024.161

2 =⎥⎥⎦

⎤

⎢⎢⎣

⎡−−= ( )( ) kipsFAP crftgcnc 1.62748.950.785.0 === φφ (control)

cMNaMfa lT§plenAkñúg]TahrN_enHmantémøRsedogKñanwgtémøEdl[enAkñúg column load table cemøIy³ Design strength KW kips62 ]TahrN_ 4>17³ KNnaGgát;rgkarsgát;EbEvg feet14 edIm,IRTbnÞúkemKuN kips50 . eRbIEdkrUbrag double angle EdlmaneCIgxøITl;xñgKña nigmanKMlatBIKña inch8

3 . Ggát;RtUv)anTl;BRgwgenARtg; Bak;kNþalRbEvgedIm,ITb;nwgkarekageFobG½kS x ¬G½kSEdlRsbeTAnwgeCIgEvg¦. kMNt;cMnYneRKOg P¢ab;enAkNþalEdlRtUvkar ¬EdkEdlBRgwgenABak;kNþalRbEvgRtUv)anpþl;eRKOgP¢ab;mYy¦. eRbIEdk

36A . dMeNaHRsay³ BI column load table eRCiserIs 4

12

1 332 ××L EdlmanTm¶n; ftlb /8.10 . smtßPaBrbs;muxkat;enHKW kips51 edayQrelIkarekageFobG½kS y CamYynwgRbEvgRbsiT§PaB

feet14 . ¬ersIusþg;EdlRtUvKñanwg flexural buckling eFobG½kS x KW kips60 EdlQrelIRbEvg RbsiT§PaB feet7 ¦. karekageFobG½kS y eFVI[eRKOgP¢ab;rgkmøaMgkat; dUcenHcMnYneRKOgP¢ab;RKb;RKan; RtUv)andak; edIm,ITb;Tl;nwgkmøaMgenH. taragbgðajfa vaRtUvkareRKOgP¢ab;cMnYn 3. cemøIy³ eRbI 4

12

1 332 ××L CamYynwgeRKOgP¢ab;cMnYn 3sRmab;RbEvg feet14 .



tRmUvkarcaM)ac;énkartP¢ab;sRmab; built-up member EdlpSMeLIgeday plate b¤ both plate

CamYynwg shapes

enAeBlEdl built-up member EdlpSMeLIgeday rolled shapes BIr b¤eRcInedaymanKMlat dac;BIKña plate RtUv)aneRbIedIm,ItP¢ab; shape. AISC E4 mankarlMGitCaeRcInGMBItRmUvkarcaM)ac; sRmab;kartP¢ab; nigTMhMrbs; plate . tRmUvkarcaM)ac;énkartP¢ab;RtUv)an[bEnßmsRmab; built-up

compression member d¾éTeTotEdlpSMeLIgeday plate b¤ plate CamYynwg shape .


T.Chhay 120 Beams

V. Fñwm Beams

5>1> esckþIepþIm (Introduction) FñwmCaGgát;rbs;eRKOgbgÁúMEdlRTbnÞúkTTwg dUcenHehIy)aneFVI[vargnUvkarBt; (flexural or

bending). RbsinebImanvtþmanbnÞúktamG½kSkñúgbrimaNmYyFMKYrsm vanwgRtUv)aneKehAvafa beam-

column ¬EdlnwgRtUvbkRsayenAkñúgCMBUkTI6¦. enAkñúgGgát;eRKOgbgÁúMxøHEdlmanvtþman axial load kñúgtémøtictYc Et\T§iBld¾sþÜcesþIgenHRtUv)aneKecalenAkñúgkarGnuvtþCaeRcIn ehIyeK)ancat;TukvaCa beam. CaTUeTAFñwmRtUv)aneKdak;kñúgTisedk nigrgnUvbnÞúkbBaÄr EtvamincaM)ac;EtkñúgkrNIEbbenHeT. Ggát;eRKOgbgÁúMEdlRtUv)aneKcat;TukCa beam RbsinebIvargnUvbnÞúky:agNaEdleFVI[vaekag(bending). rUbragmuxkat; (cross-sectional shape)EdlRtUv)aneKeRbICaTUeTArYmman W-, S- nig M-shapes. eBlxøH chanel shape k¾RtUv)aneRbIdUcCaFñwmEdlpSMeLIgBIEdkbnÞH kñúgTRmg; I-, H- b¤ box shape. Doubly symmetric shape dUcCa standard rolled W-, M- nig S-shape CarUbragEdlman RbsiT§PaBCaeK.

CaTUeTA rUbragEdl)anBIkarpSMrbs;EdkbnÞHRtUv)aneKKitCa plate girder b:uEnþ AISC Speci-

fication EbgEck beam BI plate girder edayQrelIpleFobTTwgelIkRmas; (width-thickness ratio)

rbs;RTnug. rUbTI 5>1 bgðajTaMg hot-rolled shape nig built-up shapeCamYynwgTMhMEdlRtUv eRbIsRmab; width-thickness ratios. Rbsin

yw Fth 2555≤ ¬xñat IS¦

yw Fth 970≤ ¬xñat US¦

Ggát;eRKOgbgÁúMRtUv)aneKcat;TukCa beam edayminKitfavaCa rolled shape b¤Ca built-up. EpñkenH RtUv)anerobrab;enAkñúg chapter F of the Specification, “Beams and Other Flexural Members” ehIyvak¾CaRbFanbTEdlRtUvykmkniyayenAkñúgCMBUkenH. RbsinebI


Fñwm 121 T.Chhay

yw Fth 2555> ¬xñat IS¦

yw Fth 970≤ ¬xñat US¦

enaHGgát;eRKOgbgÁúMRtUv)aneKcat;TukCa plate girder nwgRtUv)anerobrab;enAkñúg Chapter G of the

specification, “Plate Girders”. enAkñúgesovePAenHeyIgnwgniyayBI plate girder kñúgCMBUkTI 10. edaysarEt slenderness rbs;RTnug plate girder RtUvkarBicarNaBiessenABIelI nigBIeRkamEdl caM)ac;sRmab;Fñwm. RKb; standard hot-rolled shape EdlGacrk)anenAkñúg Manual KWsßitenAkñúgRbePT beams. Built-up shape PaKeRcInRtUv)ancat;cMNat;fñak;Ca plate girder b:uEnþ built-up shape xøHRtUv)ancat; TukCaFñwmedaykarkMNt;rbs; AISC. sRmab; beams/ TMnak;TMngeKalrvag\T§iBlbnÞúk (load effects) nig strength KW

nbu MM φ≤ Edl =uM bnSMénm:Um:g;emKuNEdlFMCageK =bφ emKuNersIusþg;sRmab;Fñwm 9.0= =nM nominal moment strength Design strength, nbMφ enAeBlxøHRtUv)aneKehAfa design moment. 5>2> kugRtaMgBt; nigm:Um:g;)øasÞic (Bending Stress and the Plastic Moment) edIm,IGackMNt; nominal design strength nM dMbUgeyIgRtUvBinitüemIlkarRbRBwtþeTA (behavior) rbs;Fñwmtamry³énkardak;bnÞúkRKb;lkçxNÐ taMgBIbnÞúktUcrhUtdl;bnÞúkEdlGaceFVIeday Fñwm)ak;. BicarNaFñwmEdlbgðajenAkñúgrUbTI 5>2 a EdlRtUv)andak;edayeFVIy:agNa[vaekageFobnwg G½kSem ¬G½kS xx − sRmab; I- nig H-shape¦. sRmab; linear elastic material nigkMhUcRTg;RTaytUc karBRgaykugRtaMgBt;RtUv)anbgðajenAkñúg rUbTI 5>2 b CamYynwgkugRtaMgEdlRtUv)ansnμt;faBRgay es μ ItamTTwgrbs;Fñwm. ¬kmøaMgkat;RtUv)anBicarNaedayELkenAkñúgEpñkTI 5>7¦. BI elementary

mechanics of materials/ kugRtaMgRtg;cMNucNamYyGackMNt;)anBI flexural formula³

xb I

Myf = ¬%>!¦

Edl M CamU:m:g;Bt;enAelImuxkat;EdlBicarNa/ y Cacm¶ayEkgBIbøg;NWt ¬neutral plane) eTAcMNuc Edlcg;dwg nig xI Cam:Um:g;niclPaBénmuxkat;EdleFobnwgG½kSNWt. sRmab; homogeneous


T.Chhay 122 Beams

material G½kSNWtRtYtsIuKñanwgG½kSTIRbCMuTm¶n;. smIkar %>! KWQrenAelIkarsnμt;fa karBRgay strain manlkçN³CabnÞat;BIelIdl;eRkam Edlmüa:geToteyIgGacsnμt;fa muxkat;Edlrab (plane) munrgkar Bt;enArkSarabdEdleRkaykarBt;. el;IsBIenH muxkat;FñwmRtUvEtmanG½kSsIuemRTIbBaÄr ehIybnÞúkRtUv EtsßitenAkñúgbøg;EdlmanG½kSsIemRTIenaH. FñwmEdlminbMeBjtamklçxNÐTaMgenH RtUv)anBicarNaenA kñúgEpñkTI 5>13. kugRtaMgGtibrmanwgekItenAsrésEpñkxageRkAbMput Edl y mantémøGtibrma. dUcenH vamantémøGtibrmaBIrKW kugRtaMgsgát;GtibrmarnAsrésEpñkxagelIbMput nigkugRtaMgTaj GtibrmaenAsrésEpñkxageRkambMput. RbsinebIG½kSNWtCaG½kSsIuemRTIkugRtaMgTaMg BIrenHnwgmantémø es μ IKña.

sRmab;kugRtaMgGtibrma smIkar %>! GacsresrkñúgTRmg;

xxx SM

cIM

IMcf ===

/max ¬%>@¦

Edl c CacMNayEdkBIG½kSNWteTAsrésrEpñkxageRkAbMput ehIy xS Cam:UDulmuxkat;eGLasÞicénmux kat; (elastic section modulus) . sRmab;RKb;rUbragmuxkat; section modulus mantémøefr. sRmab; mux kat;minsIuemRTI xS nwgmantémøBIr³ mYysRmab;srésEpñkxagelIbMput nigmYyeTotsRmab;srés EpñkxageRkambMput. témørbs; xS sRmab; standard rolled shape RtUv)andak;kñúg dimension and

properties table enAkñúg Manual.


Fñwm 123 T.Chhay

smIkar %>! nig %>@ mantémøeTA)ankñúgkrNIbnÞúktUclμmEdlsmÖar³enAEtsßitenAkñúg linear

elastic range. sRmab;eRKOgbgÁúMEdk vamann½yfakugRtaMg maxf minRtUvFMCag yf ehIymann½yfa m:Um:g;minRtUvFMCag xyy SFM = Edl yM Cam:Um:g;Bt;EdleFVI[FñwmeTAdl;cMNuc yielding.

enAkñúgrUbTI 5>3 FñwmTRmsamBaØCamYynwgbnÞúkcMcMNucenAkNþalElVgRtUv)anbgðajnUvkardak; bnÞúktamdMNak;kalCabnþbnÞab;. enAeBl yielding cab;epþIm karBRgaykugRtaMgenAelImuxkat;Elg


T.Chhay 124 Beams

manlkçN³CabnÞat; ehIy yielding nwgrIkralBIsrésEpñkxageRkAeTAG½kSNWt. kñúgeBlCamYyKña tMbn;Edlrg yield nwglatsn§wgtambeNþayFñwmBIG½kSkNþalrbs;FñwmEdlm:Um:g;Bt;mantémøesμ Inwg

yM enATItaMgCaeRcIn. tMbn;Edlrg yield enHRtUv)angðajedayépÞBN’ex μAenAkñúgrUbTI 5>3 c nig d. enAkñúgrUbTI 5>2 b yielding eTIbnwgcab;epþIm. enAkñúgrUbTI 5>2 c yielding )anrIkralcUleTAkñúgRTnug ehIyenAkñúgrUbTI 5>2 b muxkat;TaMgmUl)an yield. eKRtUvkarm:Um:g;bEnßmkñúgtémøCamFüm vaes μ IRb Ehl %12 én yield moment edIm,InaMFñwmBIdMNak;kal (b) eTAdMNak;kal (d) sRmab; W-shape . enAeBleKeTAdl;dMNak;kal (d) RbsinebIenAEtbEnßmbnÞúkeTotFñwmnwg)ak; enAeBlEdlFatuTaMgGs; rbs;muxkat;)aneTAdl; yield plateau rbs; stress-strain curve ehIy unrestrict plastic flow nwg ekIteLIg. Plastic hing RtUv)aneLIgRtg;G½kSrbs;Fñwm ehIysnøak;enHCamYynwgsnøak;BitR)akdenA xagcugrbs;FñwmbegáIt)anCa unstable machanism . kñúgeBl plastic collapse, mechanism motion RtUv)anbgðajenAkñúgrUbTI 5>4. Structural analysis EdlQrelIkarBicarNa collapse mechanism RtUv)aneKehAfa plastic analysis. karENnaMBI plastic analysis nig design RtUv)anerobrab;enAkñúg Appendix A kñugesovePAenH.

lT§PaBm:Um:g;)aøsÞic EdlCam:Um:g;EdlRtUvkaredIm,IbegáItsnøak;)aøsÞic GacRtUv)anKNnay:ag gayRsYlBIkarBicarNakarBRgaykugRtaMgRtUvKña. enAkñúgrUbTI 5>5 ers‘ultg;kugRtaMgsgát; nigkug RtaMgTajRtUv)anbgðaj Edl cA CaRkLaépÞmuxkat;Edlrgkarsgát; nig tA CaRkLaépÞmuxkat;Edl rgkarTaj. RkLaépÞTaMgenHCaRkLaépÞEdlenABIxagelI nigBIxageRkamG½kSNWt)aøsÞic (plastic

neutral axis) EdlmincaM)ac;dUcKñanwgG½kSNWteGLasÞic. BIsßanPaBlMnwgrbs;kmøaMg eyIg)an TC = ytyc FAFA = tc AA =


Fñwm 125 T.Chhay

dUcenHG½kSNWt)aøsÞicEckmuxkat;CaBIcMENkesμ IKña. sRmab;rUbragEdlsIemRTIeFobnwgG½kSénkarBt; G½kSNWteGLasÞic nigG½kSNWt)aøsÞicKWdUcKña. m:Um:g;)aøsÞic pM Ca resisting couple EdlbegáIteLIg edaykmøaMgBIres μ IKña nigmanTisedApÞúyKña b¤ ( ) ( ) ZFaAFaAFaAFM yytycyp =⎟

⎠⎞

⎜⎝⎛===

2

Edl =A RkLaépÞmuxkat;srub =a cm¶ayrvagG½kSNWtrbs;RkLaépÞBak;kNþalTaMgBIr =⎟

⎠⎞

⎜⎝⎛= aAZ

2m:UDulmuxkat;)aøsÞic (plastic section modulus)

]TahrN_ 5>1³ CamYynwg built-up shape EdlbgðajenAkñúgrUbTI 5>6 cUrkMNt; ¬k¦ elastic section

modulus S nig yielding moment yM nig ¬x¦ plastic section modulus Z nig plastic moment

pM . karekageFobnwgG½kS x ehIyEdkEdleRbIKW 572A Grade 50 .

dMeNaHRsay³ ¬k¦ edaysarvamanlkçN³sIuemRTI enaH elastic neutral axis ¬G½kS x ¦ sßitenABak;kNþalmuxkat;

¬TItaMgrbs;TIRbCMuTm¶n;¦. m:Um:g;niclPaBrbs;muxkat;GacRtUvkMNt;)anedayeRbIRTwsþIbTG½kS Rsb (parallel axis theorem) ehIylT§plénkarKNnaRtUv)ansegçbenAkñúgtarag 5>1. tarag 5>1


T.Chhay 126 Beams

Component I A d 2AdI + Flange 260417 5000 162.5 132291667 Flange 260417 5000 162.5 132291667 Web 28125000 - - 28125000 Sum 292.71×106

Elastic section modulus KW

( )36

661067.1

1751071.292

2/300251071.292 mm

cIS ⋅=

⋅=

+⋅

==

Yield moment KW mkNSFM yy .15.57667.1345 =×==

cemøIy³ 361067.1 mmS ⋅= nig mkNM y .15.576= ¬x¦ edaysarrUbragenHmanlkçN³sIuemRTIeFobnwgG½kS x / enaHG½kSenHEckmuxkat;CaBIrcMEnkesμ IKña

ehIyG½kSenHk¾Ca plastic neutral axis Edr. TIRbCMuTm¶n;rbs;épÞBak;kNþalxagelIRtUv)an kMNt;edayeRbI principle of moment. Kitm:Um:;g;eFobG½kSNWténmuxkat;TaMgmUl ¬rUbTI 5>6¦ ehIykarKNnaRtUv)anerobCatarag 5>2.

tarag 5>2 Component A y Ay Flange 5000 162.5 812500Web 1875 75 140625Sum 6875 953125

mmAAyy 64.138

6875953125

===∑∑

rUbTI 5>7 bgðajfaédXñas;m:Um:g;rbs;m:Um:g;KUrEdlekItmanenAxagkñúgKW ( ) mmya 28.27764.13822 ===


Fñwm 127 T.Chhay

ehIy plastic section modulus KW 3610906.128.2776875

2mmaAZ ⋅=×=⎟

⎠⎞

⎜⎝⎛=

Plastic moment KW mkNZFM yp .6.657906.1345 =×==

cemøIy³ 3610906.1 mmZ ⋅= nig mkNM p .6.657= ]TahrN_ 5>2³ KNna plastic moment, pM sRmab; 6010×W rbs;Edk 36A . dMeNaHRsay³ BI dimensions and properties tables enAkñúg Part1 of the Manual

26.17 inA = inA 8.8

26.17

2==

TIRbCMuTm¶n;sRmab;RkLaépÞBak;kNþalGacrk)anBIkñúgtaragsRmab; WT-shapes EdlRtUv)an kat;ecjBI W-shapes. rUbragEdlRtUvKñarbs;vaKW 305×WT ehIycm¶ayBIépÞxageRkAbMputrbs;søab eTATIRbCMuTm¶n;KW in884.0 dUcbgðajenAkñúgrUbTI 5>8.

( ) ( ) inda 452.8884.0222.10884.02 =−=−= ( ) 338.74452.88.8

2inaAZ ==⎟

⎠⎞

⎜⎝⎛=

lT§plEdlTTYl)anenHmantémøRbhak;RbEhlnwgtémøEdl[enAkñúg dimensions and properties

tables ¬PaBxusKñabNþalmkBIkarKitcMnYnxÞg;eRkayex,ós¦ cemøIy³ ( ) kipsftkipsinZFM yp −=−=== 223.267838.7436

5>3> lMnwg (Stability)


T.Chhay 128 Beams

RbsinebIFñwmGacrkSalMnwgrbs;va)anrhUtdl;vasßitkñúglkçxNÐ)aøsÞiceBjelj enaH nominal

moment strength RtUv)aneKKitfamantémøesμ Inwg plastic moment capacity Edl pn MM =

pÞúymkvij pn MM < . dUckrNIssrEdr PaBKμanlMnwgGacmann½yCalkçN³srub b¤Gacmann½yCalkçN³edaytMbn;. karekagrbs;Ggát;RtUv)anbgðajenAkñúgrUbTI 5>9 a. enAeBlFñwmekag tMbn;rgkarsgát; ¬EpñkxagelI G½kSNWt¦ manlkçN³ nigkareFVIkarRsedognwgssr ehIyvanwg buckle RbsinebIEpñkrbs;muxkat;man lkçN³RsavRKb;RKan;. EtvamindUcssr edaysartMbn;rgkarsgát;rb;muxkat;RtUv)anTb;edayEpñkEdl rgkarTaj ehIyPaBdabmkxageRkA (flexural buckling) RtUv)anbegáIteLIgeday twisting (torsion). karbegáItnUvPaBKμanlMnwgenHRtUv)aneKehAfa lateral-torsional buckling (LTB). eKGacbgáar Lateral-torsional buckling )aneday lateral bracing tMbn;rgkarsgát; CaBiesssøabEdlrgkar sgát;CamYynwgcenøaHRKb;RKan;. karBRgwgenHRtUv)anbgðajlkçN³nimitþsBaØaenAkñúgrUbTI 5>9 b. dUcGVI EdleyIg)aneXIj moment strength GaRs½yeTAnwgRbEvgEpñkEdlmin)anBRgwgEdlCacm¶ayrvag cMNucénTRmxag (lateral support) . eTaHbICaFñwmGacTTYlm:Um:g;RKb;RKan;edIm,IeFVI[vaeTAdl;lkçxNÐ)aøsÞiceBjelj vak¾RtUv GaRs½yfaetIva)anrkSa cross-sectional integrity b¤Gt;. vanwg)at;bg; integrity RbsinebIEpñkrgkar sgát;NamYyrbs;muxkat; buckle. RbePT buckling GacCa compression flange buckling Edl eKehAfa flange local buckling (FLB) b¤ buckling énEpñkrgkarsgát;rbs;RTnug EdleKehAfa web

local buckle (WLB). dUcEdl)anerobrab;enAkñúgCMBUk 4 RbePT local buckling epSgeTotekIteLIg edayGaRs½ynwg width-thickness ratio rbs;Epñkrgkarsgát;rbs;muxkat;.


Fñwm 129 T.Chhay

rUbTI 5>10 bgðajBI\T§iBlrbs; local and lateral-torsional buckling. FñwmR)aMdac;eday ELkRtUv)anbgðajenAkñúgRkaPicénbnÞúk-PaBdab. ExSekagTI ! CaExSekagbnÞúk-PaBdabrbs;FñwmEdl K μanlMnwg ¬edayviFINak¾eday¦ ehIy)at;bg;lT§PaBRTbnÞúkrbs;vamuneBlvaeTAdl; first yield ¬rUbTI 5>3 b¦. ExSekag @ nig # RtUvKñanwgFñwmEdlGacRTbnÞúkedayqøgkat; first yield bu:Enþmin)anyUrRKb; RKan;edIm,IbegáItsnøak;)aøsÞic nigTTYl)an plastic collapse. RbsinebIvaGaceTAdl; plastic collapse

enaHExSekagbnÞúk-PaBdabnwgmanlkçN³dUcExSekag $ b¤ %. ExSekag $ sRmab;krNIm:Um:g;esμ IenA eBjRbEvgFñwmTaMgmUl ehIyExSekag % sRmab;FñwmEdlrgm:Um:g;ERbRbYl (moment gradient) . eKGacTTYl)ankarKNnaRbkbedaysuvtßiPaBCamYynwgFñwmEdlRtUvKñanwgExSekagNamYyénExSekag TaMgenH b:uEnþExSekag ! nig @ bgðajBIkareRbIsmÖar³edayKμanlk μN³RbsiT§PaB.

5>4> cMNat;fñak;rbs;rUbrag (Classification of Shapes) AISC cat;cMNat;fñak;rUbragmuxkat;Ca compact, noncompact b¤ slender GaRs½ynwgtémø rbs; width-thickness ratios. sRmab; I- nig H-shapes pleFobsRmab;søab (unstiffened element)

KW ff tb 2/ ehIypleFobsRmab;RTnug (stiffened element) KW wth / . eKGacrk)an karcat;cMNat; fñak;rbs;muxkat;enAkñúg Section B5 of the specification, “Local Buckling” in Table B5.1. vanwg RtUv)ansegçbdUcxageRkam. edayyk =λ width-thickness ratio =pλ upper limit for compact category

=rλ upper limit for noncompact category

enaH RbsinebI pλλ ≤ ehIysøabP¢ab;eTAnwgRTnugCab;K μandac; enaHrUbragmanlkçN³ compact.


T.Chhay 130 Beams

RbsinebI rp λλλ ≤< enaHrUbragmanlkçN³ uncompact. RbsinebI rλλ > enaHrUbragmanlkçN³ slender. cMNat;fñak;RtUvQrelI width-thickness ratio rbs;muxkat;EdlmantémøFMCag. ]TahrN_ RbsinebI RTnugCa compact ehIysøabCa noncompact enaHrUbragRtUv)ancat;cMNat;fñak;Ca noncompact . tarag 5>3 RtUv)andkRsg;ecjBI AISC Table B5.1 nigman width-thickness ratio sRmab;muxkat; hot-rolled I- nig H-shape. tarag 5>3 Width-thickness parameters*

pλ rλ Element λ IS US IS US Flange

f

ft

b2

yF

170 yF

65 69

370−yF

10

141−yF

Web wth

yF1680

yF640

yF2550

yF970

* sRmab; hot-rolled I- nig H-shape rgkarBt; 5>5> Bending Strength of Compact Shapes FñwmGac)ak;edayvaTTYlm:Um:g; pM ehIyvakøayCa)aøsÞiceBjelj b¤k¾vaGac)ak;eday !> lateral-torsional buckling (LTB), eday elastically b¤ inelastically @> flange local buckling (FLB), eday elastically b¤ inelastically #> web local buckling (WLB), eday elastically b¤ inelastically

RbsinebIkugRtaMgBt;Gtibrma (maximum bending stress) tUcCagEdnsmamaRt (proportional limit) enAeBlEdl buckling ekIteLIg failure enHRtUv)aneKehAfa elastic. RbsinebI minGBa©wgenH vaCa inelastic. ¬sUmemIlkarbkRsayEdlTak;TgenAkñúgEpñk 4>2 rbs;emeronTI 4 .¦

edIm,IgayRsYl CadMbUgeyIgcat;cMNat;fñak;FñwmCa compact, noncompact b¤ slender. kar erobrab;enAkñúgEpñkenHGnuvtþcMeBaHFñwmBIrRbePT³ ¬!¦ hot-rolled I-nig H-shape ekageFobG½kSxøaMg ehIyEdlbnÞúkenAkñúgbøg;énG½kSexSay ehIy ¬2¦ channels ekageFobG½kSxøaMg ehIybnÞúkdak;tam shear center b¤k¾RtUv)anTb;RbqaMgnwgkarrmYl. ¬ Shear center CacMNucenAelImuxkat; EdltamcMNuc enHbnÞúkTTwgRtUv)ankat;tam RbsinebIFñwmekagedayKμankarrmYl.¦ vanwgekItmancMeBaH I-nig H-


Fñwm 131 T.Chhay

Shapes. eKminBicarNaGMBI Hybrid beam ¬Edlsøab nigRTnugrbs;vamanersIusþg;epSgKña¦eT ehIy smIkar AISC xøHnwgRtUv)anEkERbbnþicbnþÜcedIm,IeqøIytbeTAnwgkarkMNt;enH edayeKCMnYs yfF nig

ywF EdlCa yield strength rbs;søab nigRTnugeday yF . eyIgcab;epþImCamYynwg compact shape EdlRtUv)ankMNt;CarUbragEdlRTnugrbs;vaRtUv)an

P¢ab;eTAsøabCab;\tdac; ehIyEdlbMeBjnUvtRmUvkar width-thickness ratio xageRkamsRmab;søab nig RTnug³

yf

f

Ftb 1702

≤ nig yw Ft

h 1680≤ ¬xñatCa IS ¦

yf

f

Ftb 652

≤ nig yw Ft

h 640≤ ¬xñatCa IS ¦

sRmab;RKb; standard hot-rolled shape Edl)anrayeQ μaHenAkñúg Manual )aneKarBlkçxNÐxag elI dUcenHeKRtUvkarBinitüEtpleFobsøabb:ueNÑaH. rUbragPaKeRcInk¾bMeBjtRmUvkarrbs;søabEdr dUcenH vaRtUv)ancat;cMNat;fñak;Ca compact. RbsinebIFñwmCa compact ehIymanTRmxagCab; b¤ unbraced length xøI enaH nominal moment strength, nM Ca plastic moment capacity eBjrbs; rUbrag pM . sRmab;Ggát;EdlminmanTRmxagRKb;RKan; moment resistance RtUv)ankMNt;eday lateral-torsional buckling strength EdlmanlkçN³Ca elastic b¤ inelastic . RbePTTImYy (laterally supported compact beam) CakrNIEdlFm μta nigsamBaØCageK. AISC F1.1 [ nominal strength Ca pn MM = (AISC Equation F1.1) Edl yyp MZFM 5.1≤= témøkMNt;eday yM5.1 sRmab; pM KWedIm,IkarBarbnÞúkEdleFVIkarelIslb; nigRtUv)anbMeBj enAeBlEdl SFZF yy 5.1≤ b¤ 5.1≤

SZ

sRmab; I- nig H-shape ekageFobG½kSxøaMg enaH SZ / EtgEttUcCag 5.1 Canic©. ¬b:uEnþsRmab; I- nig H-shape ekageFobG½kSexSay enaH SZ / nwgminEdltUcCag 5.1 eT.¦ ]TahrN_ 5>3³ FñwmEdlbgðajenAkñúgrUbTI 5>11 CaEdl 36A EdlmanrUbrag 3116×W . vaRTkM ralxNÐebtugGarem:Edlpþl;nUv continuous lateral support dl;søabrgkarsgát;. Service dead


T.Chhay 132 Beams

loadKW ftlb /450 . bnÞúkenHRtUv)andak;BIelIFñwm vaminRtUv)anKItbBa©ÚlbnÞúkpÞal;rbs;FñwmeT. Service

live load KW ftlb /550 . etIFñwmenHman moment strength RKb;RKan;b¤eT?

dMeNaHRsay³ Service dead load srub edayrYmbBa©ÚlTaMgTm¶n;rbs;FñwmKW ftlbwD /48131450 =+= sRmab;FñwmTRmsamBaØrgbnÞúkBRgayes μ I m:Um:g;Bt;GtibrmaekItmanenAkNþalElVgesμ Inwg 2

max 81 wLM =

Edl w CabnÞúkEdlmanxñatkmøaMgelIÉktþaRbEvg ehIy L CaRbEvgElVg. enaH kipsftwLM D −=

×== 11.54

830481.0

81 2

2

kipsftM L −=×

= 88.618

3055.0 2

edaysar dead load tUcCag live load min)an 8 dg enaHbnSMbnÞúk A4-2 nwgmantémøFMCageK³ kipsftMMM LDu −=×+×=+= 16488.616.111.542.16.12.1 müa:gvijeTot bnÞúkGacRtUv)anKitemKuNmun ftkipswww LDu /457.1550.06.1431.02.16.12.1 =×+×=+= kipsftLwM uu −=

×== 164

830457.1

81 2

2 RtYtBinitü compactness ³ 3.6

2=

f

ft

b ¬BI Part 1 of the Manual ¦

3.68.1036

6565>==

yF dUcenH søabCa compact .

yw Ft

h 640< ¬sRmab;RKb;rUbragenAkñúg Manual ¦

dUcenH 3116×W Ca compact sRmab;Edk 36A . edaysarFñwmCa compact ehIymanTRmxag ( ) kipsftkipsinZFMM xypn −=−==== 16219440.5436


Fñwm 133 T.Chhay

RtYtBinitüsRmab; yp MM 5.1≤ ³ 5.115.1

2.4754

<==x

xSZ (OK)

( ) kipsftkipsftM nb −<−== 16414616290.0φ (NG)

cemøIy³ Design moment tUcCagm:Um:g;emKuN dUcenH 3116×W minRKb;RKan;. eTaHbICakarRtYtBinitüsRmab; yp MM 5.1≤ RtUv)aneFVIenAkñúg]TahrN_xagelI b:uEnþvamin caM)ac;sRmab; I- nig H-shape ekageFobG½kSxøaMg ehIyvaminRtUv)aneFVIdEdl²enAkñúgesobePAenHeT.

Strength moment rbs; compact shape CaGnuKmn_nwg unbraced length, bL EdlRtUv)ankM Nt;Cacm¶ayrvagcMNucénTRmxag b¤karBRgwg. enAkñúgesovePAenH bgðajcMNucénTRmxageday “X”

dUcbgðajenAkñúgrUbTI 5>12. TMnak;TMngrvag nominal strength nM nig unbraced length RtUv)an bgðajenAkñúgrUbTI 5>13 . RbsinebI unbraced length minFMCag pL FñwmRtUv)anBicarNamanTRm xageBj ehIy pn MM = . RbsinebI bL FMCag pL b:uEnþtUcCag b¤esμ I)a:ra:Em:Rt rL enaHersIusþg;nwg QrelI inelastic LTB . RbsinebI bL FMCag rL enaHersIusþg;nwgQrelI elastic LTB .


T.Chhay 134 Beams

eKGacrksmIkarsRmab; theorical elastic lateral-torsional buckling strength enAkñúg

Theory of Elastic Stability (Timoshenko and Gere, 1961) nigCamYykarpøas;bþÚrnimitþsBaØaxøH smIkarenHmanragdUcxageRkam³

wyb

yb

n CILEGJEI

LM

2

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ππ ¬%>#¦

Edl =bL unbraced length =G shear modulus MPa77225= b¤ ksi11200= sRmab;eRKOgbgÁúMEdk =J torsional constant =wC warping constant ( 6mm )

RbsinebIm:Um:g;enAeBlEdl lateral-torsional buckling ekIteLIgFMCagm:Um:g;EdlRtUvKñanwg first yield

enaH strength QrenAelI inelastic behavior. m:Um:g;EdlRtUvKñanwg first yield KW xLr SFM = (AISC Equation F1-7) Edl LF CatémøEdltUcCageKkñúgcMeNam )( ryf FF − nig ywF . enAkñúgsmIkarenH yield stress enA kñúgsøabRtUv)ankat;bnßyeday rF kugRtaMgEdlenAsl; (residual stress) . sRmab; nonhybrid

member, yymyf FFF == ehIy LF EtgEtes μ Inwg ry FF − . teTAmuxeTotenAkñúgCMBUkenH eyIg CMnYs LF eday ry FF − . Ca]TahrN_ eyIgsresr AISC Equation E1-7 Ca ( ) xryr SFFM −= (AISC Equation F1-7)


Fñwm 135 T.Chhay

EdlkugRtaMgEdlenAsl; MPaksiFr 6910 == sRmab; rolled-shapes nig MPaksiFr 1145.16 == sRmab; welded built-up shapes. dUcbgðajenAkñúgrUbTI 5>13 RBMEdnrvag elastic behavior nig inelastic behavior KW unbraced length rL Edltémørbs; rL RtUv)anTTYlBIsmIkar %># enAeBl Edl nM RtUv)andak;[esμ I rM . eKTTYl)ansmIkarxageRkam³ ( ) ( )22

1 11 ryry

yr FFX

FFXr

L −++−

= (AISC Equation F1-6)

Edl

2

2

1

4

2

⎟⎠⎞

⎜⎝⎛=

=

GJS

IC

X

EGJAS

X

x

y

w

x

π

(AISC Equation F1-8 and F1-9)

dUckrNIssrEdr inelastic behavior rbs;FñwmmanlkçN³s μ úKsμajCag elastic behavior CaTUeTAeK eRcIneRbIrUbmnþEdl)anmkBIkarBiesaF (empirical formulas). CamYynwgkarEktRmUvd¾tictYc AISC

)an[eRbIsmIkarxageRkam³

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

pbrppn LL

LLMMMM ¬%>$¦

Edl y

yp F

rL

790= ¬xñat IS¦

y

yp F

rL

300= ¬xñat US¦ (AISC Equation F1-4)

Nominal bending strength rbs; compact beam RtUv)anbgðajedaysmIkar %># nig %>$ rgnUv upper limit pM sRmab; inelastic beam RbsinebIm:Um;g;EdlGnuvtþBRgayesμ IelI unbraced length

bL . RbsinebIdUcenaHeT vaman moment gradient ehIysmIkar %># nig %>$ RtUv)anEksRmYl edayemKuN bC . emKuNenHRtUv)an[eday AISC F1.2 kñúgTRmg;

CBAb MMMM

MC

3435.25.12

max

max+++

= (AISC Equation F1-3)

Edl =maxM témødac;xatrbs;m:Um:g;GtibrmaenAkñúg unbraced length (including the end points) =AM témødac;xatrbs;m:Um:g;enAcMNucmYyPaKbYnén unbraced length

=BM témødac;xatrbs;m:Um:g;enAcMNucBak;kNþalén unbraced length

=CM témødac;xatrbs;m:Um:g;enAcMNucbIPaKbYnén unbraced length

enAeBlm:Um:g;Bt;BRgayesμ I témø bC es μ Inwg


T.Chhay 136 Beams

0.13435.2

5.12=

+++=

MMMMMCb

]TahrN_ 5>4³ kMNt; bC sRmab;FñwmTRmsamBaØRTbnÞúkBRgayes μ ICamYyEtnwgkarTb;xagenAxagcug b:ueNÑaH. dMeNaHRsay³ edaysarlkçN³suIemRTI m:Um:g;GtibrmasßitenAkNþalElVg dUcenH 2

max 81 wLMM B ==

dUcKña edaysarlkçN³sIuemRTI m:Um:g;enAcMNucmYyPaKbIes μ Im:Um:g;enAcMNucbIPaKbYn. BIrUbTI 5>14 2

2

323

3282

8442wLwLwLLwLLwLMM CA =−=⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛==

( ) 14.1)32/3(3)8/1(4)32/3(3)8/1(5.2

8/15.123435.2

5.12

max

max =+++

=+++

=CBA

b MMMMM

C cemøIy³ 14.1=bC

rUbTI 5>15 bgðajBItémørbs; bC sRmab;krNIFm μtaCaeRcInénkardak;bnÞúk nigTRmxag. sRmab; unbraced cantilever beams, AISC kMNt;témø 0.1=bC . témø 0.1 CatémøtUc

¬edayminKitBIrrUbragrbs;Fñwm nigkardak;bnÞúk¦ b:uEnþkñúgkrNIxøHvaCatémøEdltUcEmnETn. karkMNt; TaMgGs;én nominal moment strength sRmab; compact shapes GacRtUv)ansegçbdUcxageRkam³

sRmab; pb LL ≤ / ypn MMM 5.1≤= (AISC Equation F1-1)


Fñwm 137 T.Chhay

sRmab; rbp LLL ≤< /

( ) ppr

pbrppbn M

LLLL

MMMCM ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−= (AISC Equation F1-2)

sRmab; rp LL > / pcrn MMM ≤= (AISC Equation F1-12)

Edl wyb

yb

bcr CILEGJEI

LCM

2

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ππ (AISC Equation F1-13)

( )22

211

/21

/2

ybyb

xb

rLXX

rLXSC

+=

témøefr 1X nig 2X RtUv)ankMNt;BImun ehIyRtUv)anrayCataragenAkñúg dimensions and

properties tables in the Manual.


T.Chhay 138 Beams

\T§iBlrbs; bC eTAelI nominal strength RtUv)anbgðajenAkñúgrUbTI5>16. eTaHbICa strength

smamaRtedaypÞal;eTAnwg bC k¾eday EtRkaPicenH)anbgðajy:agc,as;BIsar³sMxan;rbs; upper limit

pM edayminKitBIsar³sMxan;rbs;smIkarEdlRtUveRbIsRmab; nM . ]TahrN_ 5>4³ kMNt; design strength nbMφ sRmab; 6814×W rbs;Edk 242A Edl³ k> TRmxagCab; x> unbraced length ft20= / 0.1=bC K> unbraced length ft20= / 75.1=bC

dMeNaHRsay³ k> BI Part 1 of the Manual / 6814×W KWsßitenAkñúg shape group 2 /dUcenHvaGacman yield stress

ksiFy 50= / kMNt;faetIrUbragenHCa compact, noncompact b¤ slender.

50650.7

2<=

f

ft

b

rUbragenHKW compact dUcenH kipsftkipsinZFMM xypn −=−==== 2.479.5750)115(50

cemøIy³ ( ) kipsftM nb −== 4312.4799.0φ x> ftLb 20= nig 0.1=bC . KNna pL nig rL ³


Fñwm 139 T.Chhay

ftinF

rL

y

yp 7.8.4.104

5046.2300300

==×

==

BI torsion properties tables in Part 1 of the Manual, 402.3 inJ = nig 65380inCw = eTaHbICa 1X nig 2X RtUv)anerobCataragenAkñúg dimensions and properties table in part 1 of

the Manual eyIgnwgKNnavaenATIenHsRmab;bgðaj ( )( )( ) ksiEGJA

SX

x3021

22002.31120029000

10321 ===ππ

222

2 001649.002.311200

103121

538044 −=⎟⎠⎞

⎜⎝⎛

×⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛= ksi

GJS

ICX x

y

w

22

1 )(11)( ry

ry

yr FFX

FFXr

L −++−

=

( ) ( ) ftin 40.268.3161050001649.011)1050(

302146.2 2 ==−++−

=

edaysar rbp LLL << strength QrelI inelastic LTB nig ( ) ( )( ) kipsftSFFM xryr −=

−=−= 3.343

121031050

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

pbrppbn LL

LLMMMCM

( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−−

−−=7.84.26

7.8203.3432.4792.4790.1

cemøIy³ ( ) kipsftM nb −== 3534.39290.0φ K> ftLb 20= nig 75.1=bC . Design strength sRmab; 75.1=bC KWes μ Inwg 75.1 dgén Design

strength sRmab; 0.1=bC . dUcenH ( ) kipsftMkipsftM pn −=>−== 2.4797.6864.39275.1

Nominal strength minGacFMCag pM / dUcenHeRbI nominal strength kipsftM n −= 2.479 cemøIy³ ( ) kipsftM nb −== 4312.47990.0φ Part 4 of the Manual of Steel Construction, “Beam and Girder Design,” mantaragmanRbeyaCn_ CaeRcInsRmab;viPaK nigKNnaFñwm. Ca]TahrN_ Load Factor Design Selection Table raynUvrUbrag


T.Chhay 140 Beams

EdleRbICaTUeTAsRmab;Fñwm EdlRtUv)anerobCalMdab;én xZ . edaysar xyp ZFM = rUbragk¾RtUv)an erobCalMdab;én design moment pbMφ . témøefrdéTeTotEdlmanRbeyaCn_k¾RtUv)anerobCatarag EdlrYmman pL nig rL ¬EdlCaEpñkmYyEdlKYr[FujRTan;kñúgkarKNna¦. Plastic Analysis

enAkñúgkrNICaeRcIn m:Um:g;emKuNGtibrma uM nwgRtUv)anTTYlBI elastic structural analysis

edayeRbIbnÞúkemKuN. eRkamlkçxNÐc,as;las; ersIusþg;EdlcaM)ac; (required strength) sRmab;rcna sm½<n§EdlminGackMNt;edaysþaTic (statically inderteminate structure) RtUv)anrkedayeRbI plastic

analysis. AISC GnuBaØat[eRbI plastic analysis RbsinebIrUbrag compact nigRbsinebI pdb LL ≤

Edl ( )y

ypd r

FMML 21 /1520024800+

= ¬xñat SI ¦ (AISC Equation F1-17)

=1M m:Um:g;EdltUcCageKkñúgcMeNamm:Um:g;cugTaMgBIrsRmab; unbraced segment =2M m:Um:g;EdlFMCageKkñúgcMeNamm:Um:g;cugTaMgBIrsRmab; unbraced segment pleFob 21 / MM viC¢manenAeBlEdlm:Um:g;begáIt reverse curvature enAkñúg unbraced

segment. enAeBlenH bL Ca unbraced length EdlenACab;nwgsnøak;)aøsÞicEdlCaEpñkmYyén failure

mechanism. b:uEnþRbsinebIeKeRbI plastic analysis, nominal moment strength nM EdlenACab;nwg snøak;cugeRkayEdlminenAEk,rsnøak;)aøsÞicRtUv)anKNnatamviFIdUcKñasRmab;FñwmEdlviPaKedayviFIeGLasÞic ehIyvaRtUvEttUcCag pM . 5>6> Bending Strength of Noncompact Shapes dUckarkt;cMNaMBImun standard W-, M-, nig S-shapes PaKeRcInCa compact sRmab; =yF

MPa250 nig MPaFy 350= . cMnYntictYcb:ueNÑaHCa noncompact edaysar width-thickness ratio rbs;søab b:uEnþK μanrUbragmYyNaCa slender eT. edaysarmUlehtuTaMgenH AISC Specification edaH Rsay noncompact nig slender flexural member enAkñúg]bsm<n§½ (Appendix F). enAkñúgesovePA enH eyIgnwgBicarNa slender flexural member enAkñúgCMBUkTI10.


Fñwm 141 T.Chhay

CaTUeTA FñwmGac)ak;eday lateral-torsional buckling, flange local buckling b¤ web local

buckling. RKb;RbePTénkar)ak;GacsßitenAkñúgEdneGLasÞic b¤ inelastic range. RTnugrbs;RKb; rolled shapes enAkñúg Manual Ca compact dUcenH noncompact shapes CaRbFanbTsRmab;Etsßan PaBkMNt; (limit states) én lateral-torsional buckling nig flange local buckling. ersIusþg;EdlRtUv nwgsßanPaBkMNt;TaMgBIrRtUv)anKNna ehIyeKyktémøEdltUcCageK. BI AISC Appendix F CamYy

f

ft

b2

=λ

RbsinebI rp λλλ ≤< / enaHsøabCa noncompact ehIy buckling Ca inelastic eyIgnwgTTYl)an

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

prppn MMMM

λλλλ (AISC Equation A-F1-3)

Edl y

p F170

=λ ¬sRmab; IS ¦ y

p F65

=λ ¬sRmab; US ¦

ry

r FF −=

370λ ¬sRmab; IS ¦ ry

r FF −=

141λ ¬sRmab; US ¦

( ) xryr SFFM −= =rF kugRtaMgEdlenAesssl; ksiMPa 1069 == sRmab; rolled shapes ¬GgÁenHRtUv)an kMNt;sRmab; nonhybrid beam¦ ]TahrN_ 5>6³ FñwmTRmsamBaØmYymanRbEvg feet40 RtUv)anTb;xagenAxagcugrbs;va ehIyvargnUv service load dUcxageRkam³ Dead load ftlb /400= ¬edayrYmbBa©ÚlTaMgTm¶n;Fñwm¦ Live load ftlb /1000= RbsinebIeKeRbI AISC A572 Grade 50 etI 9014×W RKb;RKan;b¤Gt;? dMeNaHRsay³ bnÞúkemKuN nigm:Um:g;emKuNKW ftkipswww LDu /08.2)00.1(6.1)40.0(2.16.12.1 =+=+= ( ) kipsftLwM uu −=== 0.416

84008.2

81 2

2 kMNt;lkçN³rUbragmuxkat; ¬faetICa compact, noncompact b¤ slender¦³


T.Chhay 142 Beams

2.102

==f

ft

bλ

19.950

6565===

yp F

λ

3.221050

141141=

−=

−=

ryr FF

λ

eday rp λλλ << dUcenHrUbragenHKW noncompact. RtYtBinitülT§PaBRTRTg;edayQrelIsßanPaB kMNt;rbs; flange local buckling³ ( ) kipsftZFM xyp −=== 2.654

1215750

( ) ( ) kipsftSFFM xryr −=−=−= 7.476121431050

( ) ( ) kipsftMMMMpr

prppn −=⎟

⎠⎞

⎜⎝⎛

−−

−−=⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−= 5.640

19.93.2219.92.107.4762.6544.652

λλλλ

Design strength EdlQrenAelI FLBdUcenH ( ) kipsftM nb −== 5765.6409.0φ

RtYtBinitülT§PaBRTRTg;EdlQrelIsßanPaBkMNt;rbs; lateral-torsional buckling. BI Load

Factor Design Selection Table³ ftLp 15= nig ftLr 4.38= rb LftL >= 40 dUcenHvanwg)ak;edayeGLasÞic LTB. BI Part 1 of the Manual/ 4362inI y = 406.4 inJ = 616000inCw = sRmab;FñwmTRmsamBaØRTbnÞúkBRgayesμ ICamYynwgTRmxagenAxagcugsgçag 14.1=bC AISC Equation F1-13[

pwyb

yb

bn MCILEGJEI

LCM ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

2ππ


Fñwm 143 T.Chhay

( ) ( )( )( ) ( )( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎠⎞

⎜⎝⎛

××

+= 160003621240

2900006.411200362290001240

14.12ππ

( ) kipsftkipsin −=−== 0.515.6180541214.1 kipsftkipsftM p −>−= 0.5152.654 edaysar 5.6400.515 < dUcenH LTB lub ehIy ( ) kipsftMkipsftM unb −=>−== 4164640.51590.0φ (OK)/ cemøIy³ eday nbu MM φ< enaHFñwmman moment strength RKb;RKan;. lkçN³kMNt;rbs; noncompact shapes RtUv)ansRmYleday Load Factor Design Selection

Table. Noncompact shapes RtUv)ankMNt;sMKal;eday footnote farUbragCa noncompact sRmab; ksiMPaFy 36250 == b¤ ksiMPaFy 50350 == . Noncompact shapes k¾RtUv)anerobcMenAkñúg

taragedaylkçN³xusEbøkKñadUcxageRkam³ !> sRmab; noncompact shapes témøEdlmanenAkñúgtaragrbs; pbMφ CatémøBitR)akd

rbs; design strength EdlQrelI flange local buckling. enAkñúg]TahrN_TI 5>6 eyIg)an KNnatémøenHes μ Inwg kipsft −576 b:uEnþtémøRtwmRtUvenAkñúgtarag pbMφ KW

( ) kipsft −= 5892.65490.0 @> témø pL enAkñúgtaragCatémørbs; unbraced length Edl nominal strength EdlQr elI

inelastic lateral torsional buckling es μ Inwg nominal strength EdlQrelI flange local

buckling dUcenH nominal strength sRmab; unbraced length GtibrmaGacRtUv)an KitCaersIusþg;EdlQrelI web local buckling. ¬rMlwkfa pL sRmab; compact shapes Ca unbraced length GtibrmaEdl nominal strength GacRtUv)anKites μ Inwg plastic

moment¦. sRmab;rUbragenAkñúg]TahrN_5>6 karKNna nominal strength EdlQrelI FLB eTAersIusþg;EdlQrelI inelastic LTB (AISC Equation F1-2) CamYynwg

0.1=bC ³

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

pbrppn LL

LLMMMM ¬%>%¦


T.Chhay 144 Beams

témørbs; rM nig rL RtUv)anTTYlBI]TahrN_ 5>6 ehIynwgminRtUv)anpøas;bþÚr. b:uEnþ témørbs; pL RtUvEt)anKNnaBI AISC Equation F1-4³ ( ) .08.13.0.157

5070.3300300

ftinF

rL

y

yp ====

CMnYstémøxagelIkñúgsmIkar %>% eyIgTTYl)an ( ) ⎟

⎠⎞

⎜⎝⎛

−−

−−=08.134.38

08.137.4762.6542.6545.640 bL

.0.15 ftLb =

enHCatémøbBa©ÚlkñúgtaragCa pL sRmab; 9014×=W CamYynwg ksiFy 50= . cMNaMfa

y

yp F

rL

300=

GaceRbIsRmab; noncompact shapes. RbsinebIeFVIEbbenH lT§plEdlTTYl)anenAkñúg smIkarsRmab; inelastic LTB EdlRtUv)aneRbIenAeBl bL minmantémøFMRKb;RKan; enaH ersIusþg;EdlQrelI FLB nwglub.

5>7> Summary of Moment Strength viFIsaRsþkñúgkarKNna nominal moment strength sRmab; I- nig H-shaped sections Edl ekageFobnwgG½kS x nwgRtUv)ansegçbenATIenH. GgÁTaMgGs;EdlmanenAkñúgsmIkarxageRkamRtUv)an kMNt;rYcehIyBImun ehIyelxsmIkarrbs; AISC minRtUv)anbgðajenATIenHeT. karsegçbenHsRmab;Et compact shapes nig noncompact shapes Etb:ueNÑaH ¬minmansRmab; slender shapes eT¦. !> kMNt;faetIrUbrag compact b¤Gt; @> RbsinebIrUbrag compact, RtYtBinitüsRmab; lateral-torsional buckling dUcxageRkam³ RbsinebI pb LL ≤ vaminEmn LTB ehIy pn MM = RbsinebI rbp LLL ≤< / vaman inelastic LTB ehIy

( ) ppr

pbrppbn M

LLLL

MMMCM ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

RbsinebI rb bL > / vaman elastic LTB ehIy


Fñwm 145 T.Chhay

pwyb

yb

bn MCILEGJEI

LCM ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

2ππ

#> RbsinebIrUbrag noncompact edaysarsøab/ RTnug b¤TaMgBIr enaH nominal strength nwgCa témøtUcCageKénersIusþg;EdlRtUvKñanwg flange local buckling, web local buckling nig lateral-torsional buckling.

k> Flange local buckling³ RbsinebI pλλ ≤ vaminman FLB. RbsinebI rp λλλ ≤< søabCa noncompact, ehIy

( ) ppr

prppn MMMMM ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

λλλλ

x> Web local buckling³ RbsinebI pλλ ≤ vaminman WLB. RbsinebI rp λλλ ≤< RTnugCa noncompact, ehIy

( ) ppr

prppn MMMMM ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

λλλλ

K> Lateral-torsional buckling³ RbsinebI pb LL ≤ vaminman LTB.

RbsinebI rbp LLL ≤< / vaman inelastic LTB ehIy

( ) ppr

pbrppbn M

LLLL

MMMCM ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

RbsinebI rb bL > / vaman elastic LTB ehIy

pwyb

yb

bn MCILEGJEI

LCM ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

2ππ

5>8> ersIusþg;kmøaMgkat;TTwg (Shear Strength) ersIusþg;kmøaMgkat;rbs;FñwmRtUvEtRKb;RKan;edIm,IbMeBjTMnak;TMng

nvu VV φ≤


T.Chhay 146 Beams

Edl =uV kmøaMgkat;TTwgGtibrmaEdll)anBIkarbnSMbnÞúkemKuNFMCageK =vφ emKuNersIusþg;sRmab;kmøaMgkat;TTwg 9.0= =nV nominal shear strength/

BicarNaFñwmsamBaØenAkñúgrUbTI 5>17. enAcm¶ay x BITRmxageqVgnigsßitenAelIG½kSNWtrbs; muxkat; sßanPaBrbs;kugRtaMgRtUv)anbgðajenAkñúgrUbTI 5>17 d . edaysarFatuenHsßitenAelIG½kS NWt vaminrgnUvkugRtaMgBt;eT. BI elementary mechanics of materials/ kugRtaMgkmøaMgkat;TTwg (shearing stess) KW

IbVQfv = ¬%>^¦

Edl =vf kugRtaMgkmøaMgkat;TTwgbBaÄr nigedkenARtg;cMNucEdleyIgBicarNa =V kmøaMgkat;TTwgbBaÄrenARtg;muxkat;EdlBicarNa

=Q m:Um:g;RkLaépÞTImYyeFobG½kSNWt rvagcMNucEdlBicarNanwgEpñkxagelIb¤EpñkxageRkam rbs;muxkat;


Fñwm 147 T.Chhay

=I m:Um:g;niclPaBeFobnwgG½kSNWt =b TTwgrbs;muxkat;enAcMNucEdlBicarNa

smIkar %>^ KWQrelIkarsnμt;fakugRtaMgmantémøefreBjelITTwg b dUcenHvapþl;témøsuRkit sRmab;Et b mantémøtUc. sRmab;muxkat;ctuekaNEkgEdlmankm<s; d nigTTwg b témølMeGog sRmab; 2/ =bd KWRbEhl %3 . sRmab; 1/ =bd témølMeGogKW %12 nigsRmab; 4/1/ =bd témølMeGogKW %100 (Higdon, Ohlsen, and Stiles, 1960). sRmab;mUlehtuenH smIkar %>^ min GacGnuvtþ)ansRmab;søabrbs; W-shape dUcKñasRmab;RTnugrbs;va.

rUbTI 5>18 bgðajBIkarBRgaykugRtaMgkmøaMgkat;sRmab; W-shape. ExSdac;CakugRtaMgmFüm

wAV / EdlBRgayenAkñúgRTnug ehIytémøenHminxusKñaBIkugRtaMgGtibrmaenAkñúgRTnugeRcIneT. eyIg eXIjc,as;ehIyfa RTnugnwg yield y:agyUrmunnwgsøabcab;epþIm yield. edaysarbBaðaenH yielding

rbs;RTnugsMEdgnUvsßanPaBlImItkMNt;mYy. edayyk shear yield stress esμ Inwg %60 én tensile

yield stress eyIgGacsresrsmIkarsRmab;kugRtaMgenAkñúgRTnugenAeBl)ak;Ca y

w

nv F

AVf 60.0==

Edl =wA RkLaépÞmuxkat;rbs;RTnug. dUcenH nominal strength EdlRtUvKñanwgsßanPaBkMNt;enHKW wyn AFV 6.0= ehIyvaGacCa nominal strength in shear RbsinebIRTnugminman shear buckling. RbsinebIvaekIt eLIgvanwgGaRs½ynwgpleFob width-thickness ratio wth / rbs;RTnug. pleFob wth / rbs;RTnug EdlRsavxøaMgmantémøFMNas; enaHRTnugGacnwg buckle in shear eday inelastic b¤ elastic. TMnak;TM ngrvag shear strength nig width-thickness ration manlkçN³RsedogKñanwgTMnak;TMngrvag flexural


T.Chhay 148 Beams

strength nig width-thickness ratio ¬sRmab; FLB b¤ WLB¦ nigrvag flexural strength nig unbraced length ¬sRmab; LTB¦. TMnak;TMngRtUvbgðajenAkñúgrUbTI 5>19 nigRtUv)an[enAkñúg AISC

F2.2 dUcxageRkam³ sRmab; yw Fth /418/ < ¬sRmab; US¦/ yw Fth /1100/ < ¬sRmab; IS¦ RTnugmanesßrPaB wyn AFV 6.0= (AISC Equation F2-1)

sRmab; ywy FthF /523//418 ≤< ¬sRmab; US¦/ ywy FthF /1375//1100 <≤ ¬sRmab; IS¦ enaH inelastic web buckling GacnwgekIteLIg

w

ywyn th

FAFV

/

/4186.0= ¬sRmab; US¦

w

ywyn th

FAFV

/

/11006.0= ¬sRmab; IS¦

(AISC Equation F2-1)

sRmab; 260//523 ≤< wy thF ¬sRmab; US¦/ 260//1375 <≤ wy thF ¬sRmab; IS¦ enaH sßanPaBkMNt;KW elastic web buckling

( )2/

132000

w

wn

th

AV = ¬sRmab; US¦ ( )2/

910

w

wn

th

AV = ¬sRmab; IS¦ (AISC Equation

F2-1)

Edl =wA RkLaépÞmuxkat;rbs;RTnug wdt= KitCa ¬ 2mm ¦ =d km<s;srubrbs;Fñwm =nV nominal strength ¬KitCa KN ¦

RbsinebI 260/ >wth enaHeKRtUvkar web stiffener ehIyvaRtUv)anbriyayenAkñúg Appendix

F2 ¬b¤ Appendix G sRmab; plate girder ¦. AISC Equation F2-3 KWQrelI elastic stability theory, ehIy Equation F2-2 CasmIkar Edl)anBIkarBiesaFsRmab;tMbn; inelastic Edlpþl;nUvkarpøas;bþÚrrvagsßanPaBkMNt; web yielding nig elastic web buckling. kmøaMgkat;CabBaðaEdlkRmekItmansRmab; rolled steel beams karGnuvtþTUeTAKWbnÞab;BIKNna FñwmsRmab; flexural ehIyeyIgnwgRtYtBinitümuxkat;EdlTTYl)ansRmab;kmøaMgkat;TTwg.


Fñwm 149 T.Chhay

]TahrN_ 5>7³ RtYtBinitüFñwmenAkñúg]TahrN_ 5>6 sRmab;kmøaMgkat;TTwg. dMeNaHRsay³ BI]TahrN_ 5>6/ ftkipswu /080.2= nig ftL 40= . Edk 9014×W CamYynwg

ksiFy 50= RtUv)aneRbI. sRmab;FñwmTRmsamBaØRTbnÞúkBRgayesμ I kmøaMgkat;GtibrmaekItmanenA elITRm ehIyes μ InwgkmøaMgRbtikmμ kips

LwV u

u 6.412

)40(080.22

=== BI dimensions and properties tables in Part 1 of the Manual, web width-thickness ratio rbs;

9014×W KW 9.25=

wth

11.5950

418418==

yF

edaysar yw Fth /418/ < enaHersIusþg;RtUv)anRKb;RKgeday shear yielding rbs;RTnug ( ) ( )( )( ) kipsdtFAFV wywyn 1.18544.002.14506.06.06.0 ==== ( ) kipskipsVnv 6.411671.18590.0 >==φ (OK)

cemøIy³ Shear design strength FMCagkmøaMgkat;emKuN dUcenHFñwmmanlkçN³RKb;RKan;.


T.Chhay 150 Beams

témø nvVφ EdlRtUv)anerobCataragenAkñúg factored uniform load table enAkñúg part 4 of

the Manual dUcnHkarKNnarbs;vaminmanRbeyaCn_sRmab; standard hot-rolled shapes. , Block Shear

Block shear Edl)anBicarNasRmab;tMNenAkñúgGgát;rgkarTaj k¾GacekItmanenAkñúgRbePT xøH rbs;tMNenAkñúgFñwmEdr. edIm,IsRmYlkñúgkartP¢ab;BIFñwmmYyeTAFñwmmYyeTot eday[nIv:UsøabxagelI es μ IKña enaHRbEvgd¾xøIrbs;søabxagelIrbs;FñwmmYyRtUvEtkat;ecj b¤ coped. RbsinebI coped beam

RtUv)antP¢ab;edayb‘ULúgdUckñúgrUbTI 5>20 kMNt; ABC cg;rEhkecj. bnÞúkEdlGnuvtþenAkñúgkrNI enHnwgCaRbtikm μbBaÄrrbs;Fñwm dUcenHkmøaMgkat;nwgekItenAtamExS AB ehIynwgekItmankmøaMgTaj tam BC . dUcenH block shear strength nwgCatémøEdlkMNt;rbs;Rbtikmμ.

eyIg)anerobrab;BIkarKNna block shear strength enAkñúgCMBUkTI3rYcehIy b:uEnþeyIgnwgrMlwk vaeLIgvijenATIenH. kar)ak;GacekIteLIgedaybnSMén shear yielding nig tendion fracture b¤eday shear fracture nig tension yielding. AISC J4.3, “Block Shear Rupture Strength,” [smIkar BIrsRmab; block shear design strength³

[ ]ntugvyn AFAFR += 6.0φφ (AISC Equation J4.3a) [ ]gtynvun AFAFR += 6.0φφ (AISC Equation J4.3b)

Edl 75.0=φ =gvA gross area rgkmøaMgkat; ¬enAkñúgrUbTI 5>20 RbEvg AB KuNnwgkRmas;RTnug¦ =nvA net area rgkmøaMgkat;

=gtA gross area rgkmøaMgTaj ¬enAkñúgrUbTI 5>20 RbEvg BC KuNnwgkRmas;RTnug¦ =ntA net area rgkmøaMgTaj

smIkarEdlmanlT§plFMCagKWCasmIkarEdlmantY fracture FMCag.


Fñwm 151 T.Chhay

]TahrN_ 5>8³ kMNt;RbtikmμemKuNGtibrma EdlQrelI block shearEdlGacRTFñwmdUcbgðajkñúg rUbTI 5>21. dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaBKW .8/78/14/3 in=+ . gross nig net shear areas KW

( ) ( ) 2.300.3300.0113332 intA wgv ==+++= ( ) 2.381.2300.0

875.311 inAnv =⎟⎠⎞

⎜⎝⎛ ×−=

gross nig net tension areas KW ( ) 2.375.0300.025.125.1 intA wgt === ( ) 2.2438.0300.0

875.025.1 inAnt =⎟⎠⎞

⎜⎝⎛ ×−=

AISC Equation J4.3a [ [ ] ( )( ) ( )[ ] kipsAFAFR ntugvyn 1.642438.0583.3366.075.06.0 =+=+=φφ

AISC Equation J4.3b [ [ ] ( )( ) ( )[ ] kipsAFAFR gtynvun 3.723750.036381.2586.075.06.0 =+=+= φφ tY fracture enAkñúg AISC Equation J4.3b mantémøFMCag ¬Edl 82.86>14.14¦ dUcenHsmIkarenH mantémøFMCag. cemøIy³ RbtikmμemKuNGtibrmaEdlQrelI block shear=72.3kips.


T.Chhay 152 Beams

5>9> PaBdab (Deflection) bEnßmBIelIsuvtßiPaB eRKOgbgÁúMRtUvEt serviceable . eRKOgbgÁúMEdlman serviceable CaeRKOg bgÁúMEdleFVIkar)anl¥ minbNþal[GñkEdleRbIR)as;vamanGarm μN_favaKμansuvtßiPaB. sRmab;Fñwm edIm,I TTYl)an serviceable eKRtUvkMNt;bMlas;TIbBaÄr b¤PaBdab. PaBdabFMCaTUeTAekItmancMeBaH flexible

beam EdlGacmanbBaðaCamYynwgrMjr½. PaBdabGacbgábBaðaeTAdl;Ggát;déTeTotEdlP¢ab; eTAnwgva edaybNþal[mankMhUcRTg;RTaytUc. elIsBIenH GñkeRbIR)as;sMNg;nwgeXIjPaB GviC¢manedaysar PaBdabFM ehIyeFVIkarsnidæanxusfasMNg;KμansuvtßiPaB. sRmab;krNITUeTArbs;FñwmTRmsamBaØEdlRTbnÞúkBRgayesμ IdUckúñrUbTI 5>22 PaBdabbBaÄr GtibrmaKW³

EIwL4

3845

=Δ eKGacrk)anrUbmnþPaBdabsRmab;FñwmeRcInRbePT niglkçxNÐdak;bnÞúkenAkñúg Part 4, “Beam

and Girder Design,”of the Manual. sRmab;sßanPaBminFmμtaeKGaceRbI standard analytical

method dUcCa method of virtual work CaedIm. PaBdabCa serviceability limit state minEmnCa sßanPaBkMNt;sRmab;ersIusþg;eT dUcenHCaTUeTAPaBdabRtUv)ankMNt;CamYy service loads. karkMNt;d¾smrmüsRmab;PaBdabGtibrmaGaRs½yeTAnwgtYnaTIrbs;Fñwm nwgkarRbmaNBIPaB xUcxatEdlekItBIPaBdab. AISC Specification pþl;nUvkarENnaMtictYcEdlmanEcgenAkñúg Chapter

L, “Serviceability Design Consideration,” faeKRtUvEtRtYtBinitüPaBdab. eKGacrk)ankarkMNt; d¾smrmüsRmab;PaBdabBI governing building code. témøxageRkamCaPaBdabGnuBaØatGtibrma srub ¬service dead load bUknwg service live load¦.


Fñwm 153 T.Chhay

Plastered construction: 360L

Unplastered floor construction: 240L

Unplastered roof construction: 180

L Edl L CaRbEvgElVg.

eBlxøHeKcaM)ac;eRbIkarkMNt;PaBdabCatémøelx CagkareRbIPaBdabCatémøRbPaK. eBlxøH karkMNt;RtUv)anKitcMeBaHPaBdabEdlbNþalEtBI live load, edaysarCaerOy² dead load

deflection RtUv)ankarBarkñúgeBlsagsg;. ]TahrN_ 5>9³ RtYtBinitüPaBdab;rbs;FñwmEdlbgðajenAkñúg rUbTI 5>23. PaBdabGtibrmasrub GnuBaØatKW

240L .

dMeNaHRsay³ PaBdabGtibrmasrubGnuBaØat mmL 38240

9100240

=== Total service load mkN /3.1583.7 =+= Maximum total deflection mmmm

EIwL 382.32

1021210238491003.155

3845

65

44<=

⋅×⋅×

××== (OK)

cemøIy³ FñwmbMeBjlkçxNÐPaBdab


T.Chhay 154 Beams

Ponding CaPaBdabmYyEdlb:HBal;dl;suvtßiPaBrbs;eRKOgbgÁúM. vaeRKaHfñak;bMputsRmab; RbB½n§kRmalxNÐrabesμ IGaceFVI[TwkePøógdk;. RbsinebIRbB½n§bgðÚrTwksÞHkñúgGMLúgeBlePøógTm¶n;rbs; Twk Edldk;elIkRmaleFVI[kRmaldab EdlvabegáIt)anCaGagsRmab;sþúkTwkkan;EteRcIn. RbsinebIkrNI enHekIteLIg\tQb;Qr enaHeRKOgbgÁúMGacnwg)ak;. AISC specificationtRmUvfaRbB½n§ dMbUlRtUvEtmanPaBrwgRkajRKb;RKan;edIm,IkarBar ponding, elIsBIenH vaerobrab;BIkarkMNt;m:Um:g; niclPaB nig)a:ra:Em:RtdéTeTotenAkñúg Section K2, “Ponding”. 5>10> karKNnamuxkat; (Design) karKNnamuxkat;FñwmtRmUvkareRCIserIsrUbragmuxkat;EdlmanersIusþg;RKb;RKan; nigbMeBj tRmUvkar serviceability. enAeBleyIgKitBIersIusþg; flexure EtgEtmaneRKaHfñak;CagkmøaMgkat; dUc enHkarGnuvtþTUeTAKWeKKNnamuxkat;sRmab; flexure rYcehIyRtYtBinitükmøaMgkat;tameRkay. viFI saRsþkñúg karKNnamuxkat;RtUv)anerobrab;xageRkam³

!> kMNt;m:Um:g;emKuN/ uM . vadUcKñanwg required design strength, nbMφ . Tm¶n;rbs;Fñwm CaEpñkrbs; desd load b:uEnþvaminRtUv)andwgenARtg;cMNucenH. eKGacsn μt;témøenH b¤k¾eK ecalvasin bnÞab;mkeKnwgRtYtBinitüvaeLIgvijeRkayeBleKeRCIseIsrUbragehIy.

@> eRCIserIsrUbragEdlbMeBjnUvtRmUvkarersIusþg;enH. eKGacGnuvtþtamviFImYykñúgcMeNamviFI BIrxageRkam³

k> eRkayeBlsnμt;rUbragEdk KNna design strength rYcehIyeRbobeFobvaCamYy nwgm:Um:g;emKuN. epÞogpÞat;eLIgvijRbsinebIcaM)ac;. eKGaceRCIserIsrUbragsn μt; y:aggayRsYlEtenAkñúgsßanPaBkMNt;mYycMnYn ¬]TahrN_ 5>10¦.

x> eRbI beam design charts in Part 4 of the Manual. eKcUlcitþviFIenH ehIyva RtUv)anBnül;enAkñúg]TahrN_ 5>10 xageRkam.

#> RtYtBinitü shear strength. $> RtYtBinitüPaBdab.


Fñwm 155 T.Chhay

]TahrN_ 5>10³ eRCIserIs standardhot-rolled shape of A36 sRmab;FñwmEdlbgðajenAkñúg rUbTI 5>24. FñwmenHmanTRmxagCab; ehIyRtUv)anRT uniform service live load ftkips /5 . PaBdab GtibrmaGnuBaØatsRmab;bnÞúkGefrKW 360/L .

dMeNaHRsay³ snμt;Tm¶n;Fñwmesμ I ftlb /100 .

( ) ( ) ftkipswww LDu /120.800.56.110.02.16.12.1 =+=+= ( )

nbuu MrequiredkipsftLwM φ=−=== 5.91383012.8

81 2

2 snμt;farUbrag compact. sRmab;rUbrag compact ehIymanTRmxagCab;

yxpn FZMM == BI unb MM ≥φ / uxyb MZF ≥φ ( )

( )3.3.338

3690.0125.913 in

FM

Zyb

ux ==≥

φ

CaFm μta Load Factor Design Selection Table erob rolled shapes EdlRtUv)aneRbICaFñwmeday témø plastic section modulus fycuH. elIsBIenH RtUv)andak;CaRkumedayrUbragenAxagelIeKenAkñúg Rkum ¬GkSrRkas;¦ rUbragEdlRsalCageKEdlman section modulus RKb;RKan;edIm,IbMeBj section

modulus EdlfycuHenAkñúgRkum. kñúg]TahrN_enH rUbragEdlmantémøEk,rnwg section modulus

requirement KW 11427×W CamYynwg 3.343inZ x = b:uEnþrUbragEdlRsalCageKKW 10830×W Ca mYynwg 3.343inZ x = . edaysar section modulusminsmamaRtedaypÞal;nwgRkLaépÞ karEdlman section modulus FMCamYynwgRkLaépÞtUc dUcenHTm¶n;k¾GacRsaleTAtamRkLaépÞ. sakl,g 10830×W . rUbrag compact dUcEdl)ansnμt; ¬noncompact shapesRtUv)ankM Nt;cMNaMenAkñúgtarag¦ dUcenH pn MM = dUcEdl)ansnμt;.


T.Chhay 156 Beams

Tm¶n;rbs;vaF¶n;Cagkarsnμt;bnþic dUcenHeKRtUvKNna required strength eLIgvij eTaHbICa 10830×W manlT§PaBRTRTg;FMCaglT§PaBRTRTg;tRmUvkaredayrUbragsnμt;k¾eday EtvaPaKeRcIn

EtgEtmanlT§PaBRTRTg;FMCaglT§PaBRTRTg;tRmUvkaredayrUbragsnμt;. ( ) ( ) ftkipswu /130.800.56.108.12.1 =+= ( ) kipsftMu −== 6.914

830130.8 2

BI Load Factor Design Selection Table, kipsftkipsftMM nbpb −>−== 6.914934φφ (OK)

CMnYs[kareRCIserIsrUbragEdlQrelI required section modulus, eKGaceRbI design strength

pbMφ edaysarvasmamaRtedaypÞal;nwg xZ ehIyvak¾RtUv)anrayenAkñúgtarag. bnÞab;mkeTot epÞógpÞat;kmøaMgkat; ( ) kips

LwV u

u 1222

3013.82

=== BI factored uniform load tables / kipskipsVnv 122316 >=φ (OK)

cugeRkaybMput epÞógpÞat;PaBdab. PaBdabGtibrmaGnuBaØatsRmab;bnÞúkGefrKW 360/L .1

3601230

360inL

=×

=

( )( )( ) .1.703.0447029000

123012/00.5384

5384

5 44inin

EILw

x

L <=×

==Δ (OK)

cemøIy³ eRbI 10830×W . dff Beam Design Charts eKmanRkaPic nigtaragCaeRcInsRmab;visVkrEdlGnuvtþ ehIyRkaPic nigtaragCMnYyTaMgenHCYy sRmYly:ageRcIndl;dMeNIrkarKNnamuxkat;. vaRtUv)aneKeRbIy:agTUlMTUlayenAkñúg design office b:uEnþvisVkrRtUvEteRbIvaedayRbytñ½. enAkñúgesovePAenHmin)anENnaMnUvRkaPic nigtaragTaMgGs;enaH lMGitGs;eT b:uEnþRkaPic nigtaragxøHmansar³sMxan;kñúgkarENnaM CaBiessKW ExSekag design moment

versus unbraced length Edl[enAkñúg Part 4 of the Manual.


Fñwm 157 T.Chhay

ExSekagenHRtUv)anbgðajenAkñúgrUbTI 5>25 EdlbgðajBIRkaPic design moment nbMφ Ca GnuKmn_én unbraced length bL sRmab; particular compact shape. eKGacsg;RkaPicEbbenH sRmab;muxkat;epSg²CamYynwgtémøCak;lak;én yF nig bC edayeRbIsmIkarsmRsbsRmab; moment strength.

Manual chart rYmmanRKYsarénExSekagsRmab; rolled shapes CaeRcIn. ExSekagTaMgenHRtUv )anbegáIteLIgCamYy 0.1=bC . sRmab;ExSekagepSgeTotrbs; bC KuN design moment Edl)an BItarageday bC . RtUvcaMfa nbMφ minGacFMCag pbMφ ¬b¤ sRmab; noncompact shapes nbMφ QrelI local buckling¦. beRmIbRmas;rbs;RkaPicRtUv)anbgðajbgðajenAkñúgrUbTI 5>26 Edl ExS ekagEbbenHBIrRtUv)anbgðaj. cMNucNak¾edayenAelIRkaPicenH dUcCacMNucCYbKñaénExSdac;BIrbgðaj BI design moment nig unbraced length. RbsinebIm:Um:g;Ca required moment capacity enaH ExS ekagEdlenABI elIcMNucenaHRtUvKñanwgFñwmEdlman moment capacity FMCag. ExSekagEdlenAxag sþaMKW sRmab;FñwmEdl man required moment capacity Cak;lak; eTaHbIsRmab; unbraced length FMCag k¾eday. dUcenH enA kñúgkarKNnamuxkat; RbsinebIeyIgdak; unbraced length nig required

design strength cUleTAkñúgRkaPic ExSekagenABIelI nigenABIsþaMcMNucenaH RtUvKñanwgFñwmEdlGacTTYl yk)an. RbsinebIeKKitTaMg ExSekagdac;² enaHExSekagsRmab;rUbragRsalCagsßitenABIelI nigBIxag sþaMExS ekagdac;². cMNucenAelI ExSekagEdlRtUvnwg pL RtUv)anbgðajeday solid circle ehIy rL


T.Chhay 158 Beams

RtUv)anbgðajeday open circle. eKmanExSekagBIrRbePT mYysRmab; MPaksiFy 25036 == nig mYyeTotsRmab; ksiFy 50= 350= MPa .

kñúg]TahrN_ 5>10 required design strength ¬EdlrYmbBa©ÚlTaMgTm¶n;Fñwmsn μt;¦ KW 5.913 kipsft − ehIyvaman continuous lateral support. sRmab;TRmxagCab; eKGacyk 0=bL .

BIRkaPic ksiFy 36= ExSekagRkas;TImYyenABIelI kipsft −5.913 KW 10830×W EdldUcKña nwgkareRCIserIs enAkñúg]TahrN_ 5>10. eTaHbICa 0=bL minRtUv)anbgðajenAkñúgRkaPicBiessk¾ eday k¾témøtUcbMputrbs; bL EdlbgðajKWtUcCag pL sRmab;RKb;rUbragenAelITMB½renaH.

ExSekagFñwmEdlbgðajenAkñúgrUbTI 5>25 KWsRmab; compact shape dUcenHtémørbs; nbMφ sRmab;témøtUcEdlRKb;RKan;rbs; bL KW pbMφ . dUcEdl)anerobrab;enAkñúgEpñk 5>6 RbsinebIrUb ragCa noncompact témøGtibrma nbMφ nwgQrelI flange local buckling. vaCakarBitEdl maximum unbraced length sRmab; nbMφ xagelInwgxusKñaBItémø pL EdlTTYlCamYynwg AISC

Equation F1-4. The moment strength rbs; noncompact shape RtUv)anbgðajCalkçN³RkaPic enAkñúgrUbTI 5>27 Edl maximum design strength RtUv)ankMNt;sMKal;eday nbM 'φ ehIy maximum unbraced length EdlRtUvnwg nbM 'φ xagelIRtUv)ansMKal;eday pL' .

eTaHbICaRkaPicsRmab; compact nig noncompact shapes manlkçN³RsedogKñak¾eday k¾ nbMφ nig bL RtUv)aneRbIsRmab; compact shapes Et nbM 'φ nig pL' RtUv)aneRbIsRmab;

noncompact shapes.


Fñwm 159 T.Chhay

]TahrN_ 5>11³ FñwmEdlbgðajenAkñúg rUbTI 5>28 RtUvRTbnÞúkcMcMNucGefrBIrEdlmYy²mantémø

kips20 Rtg;cMNucmYyPaKbYn. PaBdabGtibrmaminRtUvFMCag 240/L . Lateral support RtUv)an pþl;[enAcugrbs;Fñwm. eRbIEdk A572 Grade50 nigeRCIserIs rolled shape.


T.Chhay 160 Beams

dMeNaHRsay³ RbsinebIeKecalTm¶n;rbs;Fñwm enaHkMNat;FñwmcenøaHbnÞúkcMcMNucrgnUvm:Um:g;efr. maxMMMM CBA ===

ehIy 0.1=bC eTaHRbsinCaeKKitTm¶n;pÞal;rbs;Fñwmk¾eday k¾vaGacRtUv)anecaledayeFobnwgbnÞúkcMcMNuc

ehIy bC k¾enAEtmantémøes μ I 0.1 EdlGnuBaØat[eKGaceRbIRkaPicedayK μankarEkERb. edayminKitBITm¶n;FñwmbeNþaHGasnñ eyIgTTYl)an

( ) kipsftMu −=×= 192206.16 BIRkaPic CamYynwg ftLb 24= sakl,g 5315×W ³

kipsftkipsftM nb −>−= 192219φ (OK) \LÚveyIgKitBITm¶n;Fñwm ( )( ) kipsftkipsftMu −<−=×+= 21919724053.02.1

81192 2 (OK)

kmøaMgkat;TTwgKW ( ) ( )( ) kipsVu 8.32

224053.02.1206.1 =+=

BI factored uniform load tables/ kipskipsVnv 8.32112 >=φ (OK)

PaBdabGtibrmaGnuBaØatKW ( ) .2.1

2401224

240inL

== BI Beam Diagrams nig Formulas section in Part 4 of the Manual/ PaBdabGtibrma ¬enAkNþalElVg¦ sRmab;bnÞúkBIres μ IKñaEdlRtUv)andak;sIuemRTIKñaKW ( ).43

2422 aL

EIPa

−=Δ Edl =P GaMgtg;sIuetbnÞúkcMcMNuc .a =cm¶ayBITRmeTAbnÞúk =L RbEvgElVg ( ) ( ) ( )[ ]

EIEI

622 1069.13126412243

2412620 ×

=×−××

=Δ sRmab;Tm¶n;pÞal;rbs;Fñwm PaBdabGtibrmak¾sßitenAkNþalElVgEdr dUcenH


Fñwm 161 T.Chhay

( )( )EIEIEI

wL 644 1004.0122412/053.0384

5384

5 ×=

×==Δ

PaBdabsrub ( ) .2.1.114.1

425290001073.131004.01069.13 666

ininEIEI

<=×

=×

+×

=Δ (OK)

cemøIy³ eRbI 5312×W . eTaHbICaRkaPicQrelI 0.1=bC k¾eday b:uEnþeKk¾GaceRbIvay:agRsYledIm,IKNnamuxkat;enA eBlEdl bC minesIμnwg 0.1 edayEck required design strength eday bC munnwgdak;vaeTAkñúgRka Pic. ]TahrN_ 5>12 nwgbgðajBIbec©keTsenH. ]TahrN_ 5>12³ eRbIEdk 36A ehIyeRCIserIs rolled shapes sRmab;FñwmenAkñúg rUbTI 5>29. bnÞúkcM cMNucCa service live load ehIybnÞúkBRgayes μ IKW %30 CabnÞúkefr nig %70 CabnÞúkGefr. Lateral bracing RtUv)anpþl;[enAcug nigkNþalElVg. vaminmankarkMNt;sRmab;PaBdabeT.

dMeNaHRsay³ edaysnμt;Tm¶n;Fñwmes μ I ./100 ftlb enaH ( ) ./110.0330.0 ftkipswD =+=

( ) ( ) ./560.437.06.10.12.1 ftkipswL =×+= ( ) kipsPu 4.1496.1 ==

bnÞúkemKuN nigRbtikm μRtUv)anbgðajenAkñúgrUbTI 5>30. m:Um:g;EdlcaM)ac;sRmab;KNna bC ³ m:Um:g;Bt;enAcm¶ay x BIcugxageqVgKW

2280.292.612

590.492.61 xxxxxM −=⎟⎠⎞

⎜⎝⎛−= ¬sRmab; ftx 12≤ ¦


T.Chhay 162 Beams

sRmab; ftx 3= / ( ) ( ) kipsftM A −=−= 2.1653280.2392.61 2 sRmab; ftx 6= / ( ) ( ) kipsftM B −=−= 4.2896280.2692.61 2 sRmab; ftx 9= / ( ) ( ) kipsftMC −=−= 6.3729280.2992.61 2 sRmab; ftx 12= / ( ) ( ) kipsftMM u −=−== 7.41412280.21292.61 2

max

CBAb MMMM

MC

3435.25.12

max

max+++

= ( )

( ) ( ) ( ) ( ) 36.16.37234.28942.16537.4145.2

7.4145.12=

+++=

bBa©ÚleTAkñúgRkaPicCamYynwg unbraced length ftLb 12= nigm:mU:g;Bt;KW kipsft

CM

b

u −== 30536.1

7.414 sakl,g 6221×W ³

kipsftM nb −= 343φ ¬sRmab; 1=bC ¦ edaysar 36.1=bC design strength BitR)akdKW ( ) kipsftM nb −== 46634336.1φ b:uEnþ design strength minRtUvelIs pbMφ Edlesμ IRtwmEt kipsft −389 ¬TTYl)anBIRka

Pic¦ dUcenH design strength BitR)akdRtUvEtes μ Inwg kipsftMkipsftM unb −=<−= 7.414389φ (N.G.)

sRmab;rUbragsakl,gbnÞab; eyIgRtUvrMkileLIgelIeTArkExSekagCab;Rkas;bnÞab;enAelIRkaPic eyIgTTYl)an 6821×W . sRmab; ftLb 12= design strength Edl)anBIRkaPicKW

kipsft −385 sRmab; 0.1=bC . ersIusþg;sRmab; 36.1=bC KW ( ) kipsftMkipsftM pbnb −=>−== 43252438536.1 φφ

dUcenH kipsftMkipsftMM upbnb −=>−== 7.414432φφ (OK) Tm¶n;FñwmKW ftlb /68 EdltUcCagTm¶n;snμt; ftlb /100 . (OK)

kmøaMgkat;TTwgKW kipsVu 92.61=

¬lT§plBitR)akdnwgtUcCagenHbnþic edaysarTm¶n;pÞal;rbs;FñwmtUcCagbnÞúksnμt;¦ BI factored uniform load table

kipskipsVnv 92.61177 >=φ (OK)


Fñwm 163 T.Chhay

cemøIy³ eRbI 6821×W

RbsinebItRmUvkarPaBdabRKb;RKgelIkarKNnamuxkat; eKRtUvkMNt;m:Um:g;niclPaBcaM)ac;Gb,-

brma ehIyeKRtUvrkrUbragRsalCageKEdlRtUvnwgtémøenH. kargarenHRtUv)ansRmYly:ageRcIneday sar moment of inertia selection table in part 4 of the Manual. ]TahrN_ 5>13 nwgbgðajBIkar eRbIR)as;taragenH ehIynwgBnül;pgEdrBIviFIsaRsþkñúgkarKNnamuxkat;FñwmenAkñúgRbB½n§kRmalxNÐ.

]TahrN_ 5>13³ EpñkénRbB½n§eRKagkRmalRtUv)anbgðajenAkñúg rUbTI 5>31. kRmalebtugBRgwg edayEdkmankRmas; .4in RtUv)anRTeday floor beams EdlmanKMlatBIKña .7 ft . Floor beams

RtUv)anRT eday girders EdlRtUv)anbnþedayssr. ¬eBlxøH floor beamsRtUv)aneKehAfa filler

beams¦. bEnßmBIelITm¶n;rbs;rcnasm½<n§ bnÁÞúkrYmmanbnÞúkGefrBRgayesμ I psf80 nig movable

partitions EdlRtUv)anKitCabnÞúkBRgayes μ I psf20 elIépÞkRmal . PaBdabsrubGtibrmaminRtUv elIsBI 360/1 énRbEvgElVg. eRbIEdk 36A nigKNnamuxkat;rbs; floor beams. snμt;fa kRmal pþl;nUv continuous lateral support rbs; floor beams.


T.Chhay 164 Beams

dMeNaHRsay³ eRbIebtugGarem:Tm¶n;Fm μtaEdlmanTm¶n; 3/150 ftlb sRmab;KNnabnÞúkefr. Tm¶n;GacRtUv)anKitCa bnÞúk kñúgmYyÉktþaépÞedayKuNTm¶n;maDnwgkRmas;kRmalxNÐ.

Tm¶n;kRmalxNÐ psf50124150 =⎟⎠⎞

⎜⎝⎛=

snμt;faFñwmnImYy²RTnUvTTwgrgbnÞúk (tributary width) .7 ft rbs;kRmalxNÐ. kRmalxNÐ³ ( )750 ftlb /350= Partition³ ( )720 ftlb /140= Tm¶n;Fñwm³ ftlb /40= ¬)a:n;sμan¦ srub³ ftlb /530= ¬ service dead load¦ eTaHbI partition Gaccl½t)an b:uEnþ national model building codes KitvaCabnÞúkefr (BOCA,

1996; ICBO, 1997;nig SBCC, 1997). eyIgk¾KitvaCabnÞúkGefrEdrenATIenH. bnÞúkGefr³ ( ) ftlb /560780 = ehIybnÞúkemKuNsrubKW

( ) ( ) ftkipswww LDu /532.156.06.153.02.16.12.1 =+=+= kartP¢ab;kRmal-Fñwmpþl;nUv no moment restraint ehIyFñwmRtUv)anKitCaFñwmEdlRTedayTRmsamBaØ. ( ) kipsftLwM uu −=== 4.172

830532.1

81 2

2


Fñwm 165 T.Chhay

BI beam design chart CamYynwg 0=bL sakl,g 3518×W ³ kipsftkipsftMub −>−= 4.1725.179φ (OK) kmøaMgkat;TTwgKW ( ) kipsVu 98.22

2301532

=≈ BI factored uniform load tables

kipskipsVnv 98.22103 >=φ (OK)

PaBdabGtibrmaGnuBaØatKW ( ) .1

3601230

360inL

==

( )( ) ( )( ) .1.3.151029000

123056.0035.014.035.0384

5384

5 344inin

EIwL

>=+++

==Δ (N.G.) edayedaHRsaysmIkarPaBdabsRmab; required moment of inertia TTYl)an ( )( ) ( )

( )( )4

344.682

1290003841230085.15

3843845 in

EwLI

requiredrequired ==

Δ=

Moment of Inertia Selection Table RtUv)anerobcMeLIgkñúgviFIdUcKñanwg Load Factor Design

Selection Table dUcenHkareRCIserIsrUbragEdlRsalCageKCamYynwgm:Um:g;niclPaBRKb;RKan;man lkçN³samBaØ. BI xI Table sakl,g 4421×W ³ 44 .682.843 ininI x >= (OK)

kipsftkipsftM nb −>−= 4.1725.257φ (OK)

Tm¶n;rbs;rUbragenHFMCagkarsn μt;dMbUgbnþic b:uEnþTm¶n;EdlbEnßmenHminGaceRbobeFobnwg moment

capacity d¾FMenaH)aneT. kipskipsVnv 98.22141 >=φ (OK)

cemøIy³ eRbI 4421×W . 5>11> rn§RbehagenAkñúgFñwm (Holes in Beam) RbsinebIkartP¢ab;FñwmRtUv)aneFVIeLIgCamYyb‘ULúg søab b¤RTnugrbs;FñwmRtUv)anecaHRbehag b¤xYg. elIsBIenH eBlxøHRTnugFñwmRtUv)anecaHrn§FM²edIm,Irt;eRKOgbrikçaepSg²dUcCa bMBugExSePøIg GKÁisnI bMBugxül;CaedIm. eKcUlcitþecaHrn§enAelIRTnugFñwmRtg;kEnøgNaEdlmankmøaMgkat;TTwgtUc


T.Chhay 166 Beams

ehIyrn§RbehagRtUv)anecaHenAelIsøabRtg;kEnøgNaEdlmanm:Um:g;tUc. b:uEnþeKminGaceFVIEbbenH)an rhUteT dUcenHeKRtUvKitBI\T§iBlrbs;rn§Rbehag. sRmab;rn§RbehagtUc dUcsRmab;b‘ULúg \T§iBlrbs;vanwgtUc CaBiesssRmab; flexure eday mUlehtuBIr. TI1KW karkat;bnßymuxkat;tUc. TI2KW muxkat;EdlenAEk,rmin)ankat;bnßy ehIykar pøas;bþÚrmuxkat;énPaBminCab;tUcFMCag “weak link”. dUcenH AISC B10 GnuBaØat[ecalnUv\T§iBlrbslrn§RbehagenAeBlEdl fgyfnu AFAF 9.075.0 ≥ (AISC Equation B10-1)

Edl =fgA gross flange are

=fnA net flange are

RbsinebIeKminCYbnUvlkçxNÐenHeT flexural properties RtUvEtQrelIRkLaépÞsøabrgkarTajRbsiT§ PaB fn

y

ufe A

FF

A65

= (AISC Equation B10-3)

]TahrN_ 5>14³ KNna elastic section modulus EdlRtUv)ankat;bnßy xS sRmab;muxkat;Edl bgðajenAkñúgrUbTI 5>32. eKeRbIEdk 36A nigRbehagsRmab;b‘ULúgGgát;p©it .1in .

dMeNaHRsay³ ( ) 2184.681.0635.7 intbA fffg === Ggát;p©itRbehagRbsiT§PaBKW .

811

811 indh =+=

net flange area KW ( )( ) 2.362.4810.0125.12184.6 intdAA fhfgfn =−=−= ∑


Fñwm 167 T.Chhay

BI AISC Equation B10-1

( )( ) kipsAF fnu 7.189362.45875.075.0 == nig ( )( ) kipsAF fgy 4.200184.6369.09.0 == edaysar fgyfnu AFAF 9.075.0 < eyIgRtUvEtKitrn§Rbehag. edayeRbI AISC Equation B10-3

[RkLaépÞsøabRbsiT§PaB 2.856.5362.4

3658

65

65 inA

FF

A fny

ufg =⎟

⎠⎞

⎜⎝⎛==

RkLaépÞsøabenHRtUvKñanwgkarkat;bnßyeday 2.328.0856.5184.6 in=− . G½kSNWteGLasÞicsßitenA cm¶ay y BIkMBUlrbs;muxkat; ( ) ( ) .094.9

328.08.20405.047.18328.02/47.188.20 iny =

−−−

= m:Um:g;niclPaBEdlRtUv)ankat;bnßyKW ( ) ( ) 422 .114406.18094.9328.0235.9094.98.201170. inI x =−−−+=

xS sRmab;søabxagelIKW 3.126

094.91144 in

yIS x

x ===

xS sRmab;søabxageRkamKW 3.122

094.947.181144 in

ydIS x

x =−

=−

= cemøIy³ The reduced elastic section modulus sRmab;EpñkxagelIKW 3.126in nigsRmab;Epñkxag eRkamKW 3.122in .

FñwmEdlmanrn§RbehagFMenAelIRTnug RtUvkarkarKNnaBiessEdlminmanerobrab;enAkñúgesov ePAenHeT. Design of Steel and Composite Beam with Web Openings KWCakarENnaMd¾manRb eyaCn_sRmab;RbFanbTenH (Darwin, 1990).

5>12> Open-Web Steel Joists Open-web steel joists CaRbePT truss EdlplitrYcCaeRscdUcbgðajenAkñúgrUbTI 5>33. Open-web steel joists xøHEdlmanTMhMtUc eRbIr)arEdkmUlCab;sRmab;eFVICaGgát;RTnug (web


T.Chhay 168 Beams

member) ehIyvaRtUv)aneKehA bar joists. vaRtUv)aneKeRbIenAkñúgkRmal nigRbB½n§dMbUlsRmab; eRKOgbgÁúMCaeRcIn. sRmab;RbEvgElVgEdl[dUcKña open-web steel joists manTm¶n;RsalCag rolled

shapes ehIyGvtþmanrbs;RTnugtan;GnuBaØat[eKrt;RbB½n§brikçary:agRsYl. GaRs½yeTAnwgRbEvg ElVg open-web steel joist manlkçN³esdækic©Cag rolled shapes eTaHbICavaKñaeKalkarN_ENnaM sRmab;karkMNt;vak¾eday. eKGacrk open-web steel joists CamYynwgkm<s;sþg;dar niglT§PaBRTbnÞúkBIeragcRkCaeRcIn. Open-web steel joist xøHRtUv)anKNnaedIm,IeFVIkarCa floor b¤ roof joists ehIy open-web steel

joists xøHeTotRtUv)anKNnaedIm,IeFVIkarCa girder EdlRTRbtikmμEdlRbmUlpþúMBI joists. AISC

Specification min)anerobrab;BI open-web steel joists eT Etsßabn½mYyepSgeTotEdleKehAfa Steel

Joist Institute (SJI) manBiBN’naBIva. ral;kareRbIR)as; steel joists rYmTaMgkarKNna nigkarplit RtUv)ane)aHBum<pSayenAkñúg Standard Specifications, Load Tables, nig Weight Table for Steel

Joists and Joist Girders (SJI, 1994). eKGaceRCIserIs open-web steel joists CamYynwg the aid of the standard load tables (SJI,

1994) ehIytaragmYyenAkñúgcMeNamenaHRtUv)anbgðajenAkñúgrUbTI 5>34 . CamYynwgkarpSMKñarvag ElVg nig joist eKnwgTTYl)antémøbnÞúkmYyKUr. elxxagelICa total service load capacity KitCa pounds kñúgmYy foot ehIyelxenAxageRkamCa service live load kñúgmYy foot EdlnwgbegáItPaBdab es μ Inwg 360/1 énRbEvgElVg. ¬eTaHbICabnÞúkenAkñúgtaragCa service load capacities k¾eday k¾eK GaceRbItaragenHy:aggayRsYlCamYynwgviFI LRFD EdleyIgnwgbgðajenATIenH¦. elxdMbUgénelx sMKal;Cakm<s;rbs; open-web steel joist EdlKitCa .in . taragk¾[pgEdr nUvTm¶n;Rbhak;RbEhl EdlKitCa pound kñúgmYy foot énRbEvg.

eKGacrk open-web steel joists EdlRtUv)anKNnaedIm,ImannaTICa floor or roof joist ¬Edl pÞúyBImannaTICa girder¦ Ca open-web steel joist (K-series, both standard and KCS), longspan

steel joists (LH-series), nig deep longspan steel joist (DLH-series). enAeBleyIgrMkilesrIeLIg kan;Etx<s; eyIgnwgTTYl)anRbEvgElVg niglT§PaBRTbnÞúkkan;EtFM. Ca]TahrN_ 8K1 manRbEvg ElVg .8 ft niglT§PaBRTbnÞúk ./550 ftlb b:uEnþ 72DLH19 GacRTbnÞúk)an ./497 ftlb elIRbEvg .144 ft .


Fñwm 169 T.Chhay

edayelIkElg KCS joists, open-web steel joists TaMgGs;RtUv)anKNnaCa trusses EdlRT edayTRmsamBaØ CamYynwgbnÞúkBRgayes μ IenAelI top chord. kardak;bnÞúkenHeFVI[ top chord rgnUv bending k¾dUc axial compression dUcenH top chord RtUv)anKNnaCa beam-column ¬emIlCMBUk 6¦. edIm,IFananUvsißrPaBrbs; top chord eKRtUvP¢ab; the floor or roof deck kñúgviFIEbbNaedIm,IeFVI[ man continuous lateral support.


T.Chhay 170 Beams

TaMg top nig bottom chord members rbs; K-series joists RtUv)anplitedayEdkEdlman yield stress ksi50 . lT§PaBRTbnÞúkrbs; K-series joists RtUv)anepÞógpÞat;edaykarBiesaF ehIy emKuNsuvtßiPaBGb,brmaRtUv)anbgðaj[eXIjes μ Inwg 65.1 .

viFIsaRsþd¾samBaØsRmab;eRbIR)as; standard load tables CamYynwg LRFD RtUv)anENnaMeday SJI (1994) ehIyRtUv)anbgðajenATIenH kñúgTRmg;EkERbbnþicbnþÜc. BicarNa TMnak;TMngeKal LRFD smIkar @>#³

nii RQ φγ ≤∑ vaRtUv)ansresrsRmab;bnÞúkBRgayesμ IkñúgTRmg;Ca nu ww φ≤ ¬%>&¦ Edl uw CabnÞúkBRgayesμ IemKuN nig nw Ca nominal uniform load strength of the joist. Rbsin ebIeyIgeRbIpleFobmFümén nominal strength elI allowable strength es μ Inwg 65.1 * eyIgGac sresr nominal strength eday sjin ww 65.1= Edl sjiw Ca allowable strength (allowable load) Edl[enAkñúg standard load tables. Design strength KW ( ) sjisjisjin wwww 2

3485.165.19.0 ≈==φ \LÚveyIgGacsresrsmIkar %>& Ca sjiu ww 2

3≤ sRmab;eKalbMNgénkarKNna eyIgGacsresrTMnak;TMngenHCa required usji ww 3

2= ]TahrN_ 5>15³ eRbI load table Edl[enAkñúg rUbTI 5>34 eRCIserIs open-web steel joist sRmab; RbB½n§kRmal nigbnÞúkxageRkam. Joist spacing ft3=

Span length ft20=

bnÞúkKW³ kRmalxNÐkRmas; .3in * cMNaMfaemKuNsuvtßiPaBsRmab; K-series joists RtUv)ankMNt;edaykarBesaFEdleFVIeLIgedayplitkr.


Fñwm 171 T.Chhay

bnÞúkefrepSgeTot psf20= bnÞúkGefr psf50= dMeNaHRsay³ sRmab;bnÞúkefr

kRmalxNÐ³ psf5.3712350 =⎟⎠⎞

⎜⎝⎛

bnÞúkefrepSgeTot psf20= Tm¶n;rbs; joist psf3= ¬]bma¦ srub psf5.60=

( ) ftlbwD /5.18135.60 == sRmab;bnÞúkGefr psf50 ( ) ftlbwL /150350 == bnÞúkemKuNKW ( ) ( ) ftlbwww LDu '8.4571506.15.1812.16.12.1 =+=+= bMElgbnÞúkenHeTACa required service load³ required ( ) ftlbww usji /3058.457

32

32

=== rUbTI 5>34 bgðajfa joist xageRkambMeBjnUvtRmUvkarénbnÞúkxagelI³ 512K Tm¶n;RbEhl

ftlb /1.7 / 314K Tm¶n;RbEhl ftlb /6 nig 216K Tm¶n;RbEhl ftlb /5.5 . edayminman karkMNt;sRmab;km<s; dUcenHeyIgerIsnUv joist NaEdlRsalCageK. cemøIy³ eRbI 216K . 5>13> bnÞHRTFñwm nigbnÞH)atssr (Beam Bearing Plates and Column Base Plate) viFIKNnabnÞHRTssrmanlkçN³RsedogKñanwgviFIKNnabnÞHRTFñwm ehIyedaysarmUlehtu enH eyIgnwgBicarNavaCamYyKña. elIsBI karkMNt;kRmas;rbs;bnÞH)atssrtRmUv[mankarBicarNa BI flexure dUcenHvaRtUv)anelIkykmkerobrab;enATIenH EdlminEmnenAkñúgCMBUk 4. kñúgkrNITaMgBIr tYnaTIrbs;bnÞHEdkKWEbgEckbnÞúkEdlRbmUlpþúM (concentrated load) eTAsmÖar³EdlRTva. bnÞHRTFñwmmanBIrRbePTKW³ mYysRmab;bBa¢ÚnRbtikm μrbs;FñwmeTATRm dUcCaCBa¢aMgebtug nig mYyeTotsRmab;bBa¢ÚnbnÞúkeTAsøabxagelIrbs;Fñwm. dMbUg BicarNaTRmFñwmEdlbgðajenAkñúgrUbTI


T.Chhay 172 Beams

5>35 . eTaHbICaFñwmCaeRcInRtUv)antP¢ab;eTAssrb¤eTAFñwmepSgeTotk¾eday EtRbePTénTRmEdl bgðajenATIenH RtUv)aneRbICaerOy² CaBiessenARtg; bridge abutments. karKNnaBIbnÞHRTrYmman bICMhan³

!> kMNt;TMhM N EdleKGackarBar web yielding nig web crippling. @> kMNt;TMhM B EdlRkLaépÞ NB× manTMhMRKb;RKan;edIm,IkarBarsmÖar³EdlRT ¬CaTUeTAKW

ebtug¦ BIkarEbk. #> kMNt;kRmas; t EdlbnÞHRTman bending strength RKb;RKan;. karBN’naBI Web yielding and web crippling manenAkñúg Chapter K of AISC Specifica-

tion, “Strength Design Consideration”. ÉcMENk bearing strength rbs;ebtugRtUv)anniyayenA kñúg Chapter J, “Connections, Joints, and Fasteners”.

Web Yielding Web yielding KWCakarpÞúHEbkedaykarsgát; (compressive crushing) rbs;RTnugFñwmEdl bNþalBIkarGnuvtþn_kmøaMgsgát;edaypÞal;eTAsøabEdlenABIxagelI b¤BIxageRkamRTnug. kmøaMgenH GacCakmøaMgRbtikmμBITRménRbePTdUcbgðajkñúg rUbTI 5>35 b¤vaGacCabnÞúkEdlbBa¢ÚneTAsøabeday ssr b¤FñwmepSgeTot. Yielding ekIteLIgenAeBlEdlkugRtaMgsgát;enAelImuxkat;edktamry³RTnug xiteTArkcMNuc yield. enAeBlbnÞúkRtUv)anbBa¢Úntamry³bnÞHEdk web yielding RtUv)ansnμt;faekIt manenAEk,rmuxkat;EdlmanTTwg wt . enAkñúg rolled shape muxkat;enARtg;cugénBitekag (toe of the

fillet) Edlmancm¶ay k BIépÞxageRkArbs;søab ¬TMhMenHRtUv)anerobCatarag enAkñúg dimensions and

properties tables in the Manual). RbsinebIbnÞúkRtUv)ansnμt;faEbgEckxøÜnvaeday slope 5.2:1


Fñwm 173 T.Chhay

dUcbgðajenAkñúg rUbTI 5>36 RkLaépÞenARtg;TRmrgnUv yielding KW ( ) wtNk +5.2 . edayKuN RkLaépÞenHnwg yield stress [ nominal strength sRmab; web yielding enARtg;TRm³ ( ) wyn tFNkR += 5.2 (AISC Equation K1-3) The bearing length N enARtg;TRmmikKYrtUcCag k . enARtg;bnÞúkxagkñúg beNþayrbs;muxkat;rgnUv yielding KW

( ) NkNk +=+ 55.22 The nominal strength KW ( ) wyn tFNkR += 5 (AISC Equation K1-2) The design strength KW ,nRφ Edl 0.1=φ

Web Cripplimg Web crippling Ca buckling rbs;RTnugEdlbNþalBIkmøaMgsgát;EdlbBa¢Úntamry³søab. sRmab;bnÞúkxagkñúg nominal strength sRmab; web crippling KW³

w

fy

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 31135 (AISC Equation K1-4)

sRmab;bnÞúkenARtg; b¤Ek,rTRm ¬minFMCagBak;kNþalkm<s;FñwmBIcug¦ nominal strength KW³

w

fy

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 3168 sRmab; 2≤

dN (AISC Equation K1-5a)

b¤ w

fy

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+=

5.12 2.04168 sRmab; 2>

dN (AISC Equation K1-5b)

emKuNersIusþg;sRmab;sßanPaBkMNt;enHKW 75.0=φ


T.Chhay 174 Beams

Concrete Bearing Strength smÖar³EdleRbIsRmab;RTFñwmGacCa ebtug \dæ b¤smÖar³epSg²eTot b:uEnþCaTUeTAvaCaebtug. smÖar³enHRtUvEtTb;nwg bearing load EdlGnuvtþedaybnÞHEdk. The nominal bearing strength

EdlbBa¢ak;enAkñúg AISC J9 dUcKñaenAkñúg American Concrete Institute’s Building Code (ACI,

1995). RbsinebI plate RKbeBjelIépÞrbs;TRm enaH nominal strength KW 1'85.0 AfP cp = (AISC Equation J9-1)

RbsinebI plate minRKbeBjelIépÞrbs;TRmeT enaH nominal strength KW 121 /'85.0 AAAfP cp = (AISC Equation J9-2)

Edl =cf ' ersIusþg;rgkarsgát; 28éf¶rbs;ebtug =1A bearing area R =2A full area rbs;TRm RbsinebI 2A mincMCamYy 1A enaH 2A KYrmantémøFMCag 1A EdlvamanragFrNImaRtRsedog Kñanwg 1A dUcbgðajenAkñúgrUbTI 5>37. AISC tRmUv[ 2/ 12 ≤AA The design bearing strength KW pcPφ Edl 60.0=cφ . m


Fñwm 175 T.Chhay

Plate Thickness enAeBlEdlbeNþay nigTTwgrbs;bnÞHTRmRtUv)ankMNt;ehIy bearing pressure mFüm RtUv)anKitCabnÞúkBRgayes μ IeTAelI)atén plate EdlRtUv)ansn μt;RTedayTTwg k2 EdlenAkNþalFñwm nigbeNþay N dUcbgðajenAkñúgrUbTI 5>38. bnÞab;mkeTotbnÞHRtUv)anBicarNafaekageFobG½kSRsb eTAnwgElVgFñwm. dUcenH bnÞHRtUv)anKitCa cantilever EdlmanRbEvgElVg ( ) 2/2kBn −= nigTTwg N . edIm,IgayRsYl TTwg .1in RtUv)anBicarNa CamYynwgbnÞúkBRgayes μ IKitCa ./ inlb Edles μ Inwg bearing pressure EdlKitCa 2./ inlb .

BIrUbTI 5>38 m:Um:g;GtibrmaenAkñúgbnÞHKW

BNnRnn

BNRM uu

u 22

2=××=

Edl BNRu / Ca bearing pressure mFümrvagbnÞH nigebtug. sRmab;muxkat;ctuekaNEkg EdlekageFobG½kSexSay (minor axis) enaH nominal moment strength uM esμ Inwg plastic moment

capacity pM . dUcbgðajenAkñúgrUbTI 5>39 plastic moment sRmab;muxkat;ctuekaNEkg EdlmanTMhMTTwgmYyÉktþa nigkRmas; t KW

4221

2tFttFM yyp =⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛ ×=


T.Chhay 176 Beams

edaysar nbMφ RtUvEttUcCag uM unb MM ≥φ

BNnRtF u

y 249.0

22≥

y

uBNF

nRt9.0

2 2≥ b¤

y

uBNF

nRt2222.2

≥ ¬%>* / %>(¦

]TahrN_ 5>16³ KNna bearing plate edIm,IEbgEckRbtikmμrbs; 6821×W CamYynwgRbEvgElVg

.15 ft .10in KitBIG½kSeTAG½kSrbs;TRm. Service load srub EdlKitbBa©ÚlTaMgTm¶n;FñwmKW ftkips /9 EdlmanbnÞúkefr nigbnÞúkGefres μ IKña. FñwmRtUv)anRTenABIelICBa¢aMgebtugGarem:Edlman

psif c 3500' = . TaMgbnÞHEdk nigFñwmCaEdk 36A . dMeNaHRsay³ bnÞúkemKuNKW ./6.12)5.4(6.1)5.4(2.16.12.1 ftkipswww LDu =+=+= ehIyRbtikmμKW ( ) kips

LwR u

u 73.992

83.156.122

=== kMNt;RbEvgrbs; bearing N EdlcaM)ac;edIm,IkarBar web yielding. BI AISC Equation K1-3,

design strength sRmab;sßanPaBkMNt;enHKW ( ) wyn tFNkR += 5.2 sRmab; un RR ≥φ / ( )[ ]( )( ) 73.99430.036438.15.21 ≥+ N .85.2 inN ≥ eRbI AISC Equation K1-5edIm,IkMNt;témørbs; N EdlcaM)ac;edIm,IkarBar web crippling. snμt;

2.0/ ≥dN nigsakl,gTRmg;TIBIrrbs;smIkar. sRmab; un RR ≥φ /

uw

fy

f

ww R

ttF

tt

dNt ≥

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+

5.12 2.04168φ

( )( ) ( ) 73.9943.0685.036

685.043.02.0

13.214143.06875.0

5.12 ≥

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛ −+

N .27.5 inN ≥ (controls)


Fñwm 177 T.Chhay

RtYtBinitükarsnμt; 2.025.0

13.21268.5

>==dN (OK)

sakl,g .6inN = . kMNt;TMhM B BI bearing strength. karsnμt;EdlmansuvtßiPaBKWRkLaépÞeBj TaMgGs;rbs;TRmRtUv)aneRbI. ( ) ucc RAf ≥1'85.0φ ( )( ) 73.995.385.06.0 1 ≥A 2

1 87.55 inA ≥ témøGb,brmarbs;TMhM B KW .31.9

687.551 in

NAB ===

TTwgsøabrbs; 6821×W KW .270.8 in EdleFVI[bnÞHEdkFMCagsøabbnþic EdleKcg;)an. sakl,g .10inB = .

kMNt;kRmas;bnÞHEdkEdlcaM)ac; ( ) .562.3

2438.1210

22 inkBn =

−=

−=

BIsmIkar ¬%>(¦

( )( )( )( ) .14.1

36610562.373.99222.2222.2 22

inBNF

nRt

y

u ===

cemøIy³ eRbI 1061 41 ××PL .

RbsinebIFñwmminRtUv)anBRgwgxagenARtg;cMNucrgbnÞúk ¬kñúgviFIEbbNaedIm,IkarBarbMlas;TIxag rvagsøabrgkmøaMgsgát; nigsøabrgkmøaMgTaj¦ eTenaH Specification tRmUv[Gegát sidesway web

buckling (AISC K1.5). enAeBlbnÞúkGnuvtþeTAelIsøabTaMgBIr eKRtUvRtYtBinitü compression

buckling (AISC K1.6).


T.Chhay 178 Beams

Column Base Plate dUcKñanwgkarKNna beam bearing plateEdr karKNna column base plate tRmUv[mankar BicarNaBI bearing pressure eTAelIsmÖar³EdlRT nig bending rbs;bnÞHEdk. PaBxusKñad¾FMbMputKW bending enAkñúg beam bearing plate KWmYyTis b:uEnþ column base plate rgnUv bending BIrTis. elIsBIenHeTot web crippling nig web yielding minEmnCabBaðaenAkñúgkarKNna column base plate eT.

Column base plate GacRtUv)ancat;cMNat;fñak;CabnÞHFM b¤bnÞHtUc EdlbnÞHtUcmanTMhMRbhak; RbEhlTMhMssr. elIsBIenH bnÞHtUceFVIkarxusKña enAeBlvargbnÞúkRsal nigeBlvargbnÞúkF¶n;. kRmas;rbs;bnÞHFMRtUv)ankMNt;BIkarBicarNaén bending rbs;EpñkénbnÞHEdllyecjBI ssr. Bending RtUv)ansnμt;faekItmaneFobnwgG½kSenAkm<s;Bak;kNþalrbs;bnÞHEk,rRCugrbs;søab ssr. G½kSBIrRsbeTAnwgRTnugmancm¶ayBIKña fb80.0 nigG½kSBIreTotRsbeTAnwgsøabmanKMlatBIKña

d95.0 . kñúgcMeNamceRmok cantilever .1in BIrEdlsMKal;eday m nig n dUcenAkñúgrUbTI 5>40 témø EdlFMCag eKRtUv)aneRbICMnYs[ n enAkñúgsmIikar %>* edIm,IKNnakRmas;bnÞH b¤

y

uBNFP

lt9.02

≥ ¬%>!0¦


Fñwm 179 T.Chhay

Edl l CatémøFMCageKkñúgcMeNam m nig n . viFIenHsMedAdUceTAnwg cantilever method. bnÞH)attUcEdlRTTm¶n;RsalRtUv)anKNnaedayeRbI Murray-Stockwell method (Murray,

1983). enAkñúgviFIenH EpñkénbnÞúkssrEdlGnuvtþenAkñúgRBMEdnrbs;muxkat;ssr ¬BIelIRkLaépÞ db f ¦ RtUv)ansnμt;faEbgEckesμ IenAelIRkLaépÞ H-shaped dUcbgðajkñúg rUbTI 5>41. dUcenH

bearing pressure KWRbmUlpþúMenAEk,rExSRBMrbs;ssr. kRmas;bnÞHRtUv)ankMNt;BI flexural analysis

rbs;ceRmok cantilever énTTwgÉktþa nigénRbEvg c . viFIenHpþl;lT§plCasmIkar

yH

oFA

Pct9.02

≥ ¬%>!!¦

Edl dbBNPP f

uo ×=

= bnÞúkenAkñúgRkLaépÞ db f = bnÞúkenAelIRklaépÞ H-shape =HA RklaépÞ H-shape

=c TMhMEdlcaM)ac;edIm,I[kugRtaMg H

oAP esμ IeTAnwg design bearing stress rbs;smÖar³EdlRT.

cMNaMfasmIkar %>!! manTRmg;RsedogKñanwgsmIkar %>!0 edayeRbIkugRtaMg BNPu /

EdlCMnYseday Ho AP / . sRmab;bnÞHEdlRTTm¶n;F¶n; ¬RBMEdnrvagbnÞHRTTm¶n;Rsal nigbnÞHRTTm¶n;F¶n;minRtUv)ankMNt;

Cak;lak;¦/ Thornton (1990a) EdlesñIrnUvkarviPaKedayQrelIkarBt;BIrTisrbs;EpñkénbnÞHrvagRT


T.Chhay 180 Beams

nug nigsøab. dUcEdl)anbgðajenAkñúg rUbTI 5>42 kMNat;énbnÞHenHRtUv)ancat;Tukfa fixed enAnwgRT nug/ TRmsamBaØenAnwgsøab nigTMenrenARCugmYyeTot. kRmas;EdltRmUvkarKW

y

uBNFP

nt9.02

'≥

Edl fdbn41'= ¬%>!@¦

viFITaMgbIenHRtUv)anbBa©ÚlKñaeday Thornton (1990b) ehIykarsegçbmandUcxageRkam. kM

ras;bnÞHEdlcaM)ac;KW

y

uBNFP

lt9.02

≥ ¬%>!#¦

Edl )',,max( nnml λ= 1

112

≤−−

=X

Xλ

( ) pc

u

f

fP

Pbd

dbX

φ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+= 2

4

fdbn41'=

60.0=cφ =pP nominal bearing strength BI AISC Equation J9-1 b¤ J9-2.


Fñwm 181 T.Chhay

CamYynwgsmIkarxagelIenH eKmincaM)ac;kMNt;fabnÞHFM b¤tUc rgbnÞúkRsal b¤F¶n;. λ Gacyk es μ Inwg 1.0 (Thornton, 1990b). viFIenHRsedogKñaeTAnwgGVIEdl[enAkñúg Part 11 of the Manual (Volume II), “Connections

for Tension and Compression”. ]TahrN_ 5>17³ eKeRbI 4910×W CassrnwgRtUv)anRTeday concrete pierdUcbgðajkñúgrUbTI 5>43. épÞxagelIrbs; piermanTMhM .18.18 inin × . KNnabnÞH 36A sRmab;bnÞúkefr kips98 nig bnÞúkGefr

kips145 . ersIusþg;ebtugKW psif c 3000' = .

dMeNaHRsay³ bnÞúkemKuNKW ( ) ( ) kipsLDPu 6.3491456.1982.16.12.1 =+=+= KNna required bearing area upc PP ≥φ ( ) ucc PAAAf ≥121 /'85.0φ ( )( ) ( ) 6.349/1818385.06.0 11 ≥AA 2

1 .1.161 inA ≥ RtYtBinitü ( ) 241.11.161/1818/ 12 <==AA (OK) mü:ageTot bnÞHRtUvEtmanTMhMFMCagTMhMssr dUcenH ( ) 22 .1.161.8.9998.900.10 inindb f <== (OK)


T.Chhay 182 Beams

sRmab; .13inNB == . ( ) 21 .1691313 inA ==

TMhMrbs;ceRmok cantilever m nig n GacRtUv)ankMNt;BI rUbTI 5>43 b¤ indNm 76.1

248.913

295.0

=−

=−

=

.5.22

8132

8.0in

bNn f =

−=

−=

BIsmIkar %>!@ ( ) .497.21098.9

41

41' indbn f ===

edayyk 0.1=λ eKTTYl)an ( ) ( ) .5.2497.2,5.2,176max',,max innnml === BIsmIkar %>!#/ required plate thickness KW ( )

( )( )( ) .893.03613139.0

6.34925.29.02 inBNFPlt

y

u ===

cemøIy³ eRbI 13131 ××PL . 5>14> Biaxial Bending


Fñwm 183 T.Chhay

Biaxial bending ekItmanenAeBlEdlFñwmrgnUvlkçxNÐbnÞúkEdlbegáIt bending tamTaMgG½kS xøaMg (major or strong axis) nigG½kSexSay (minor or weak axis). dUckrNIbgðajenAkñúgrUbTI 5>44 EdlbnÞúkcMcMNuceTaleFVIGMeBIeTAelIG½kSbeNþayrbs;Fñwm b:uEnþeRTteFobeTAnwgG½kSeKalnImYy²rbs; muxkat;. eTaHbICakardak;bnÞúkenHmanlkçN³TUeTACagkardak;bnÞúkBIelIkmunk¾eday k¾vaenAEtCakrNI Biess edaysarbnÞúkkat;tam shear center rbs;muxkat;. The shear center KWCacMNucEdlbnÞúkeFVIGM eBIelIFñwmedaymin[FñwmrgrmYl (no twisting nor torsion). TItaMgrbs; shear center GacRtUv)an kMNt;BI elementary mechanics of materials edayKNna internal resisting torsional moment EdlbMEbkBIrMhUrkmøaMgkat;enAkñúgmuxkat;eTA external torque.

TItaMgrbs; shear center sRmab;muxkat;TUeTACaeRcInRtUv)anbgðajenAkñúg rUbTI5>45 a Edl

shear center RtUv)ansMKal;eday “o”. témørbs; oe EdlkMNt;TItaMgrbs; shear center sRmab; channel shapes RtUv)anerobcMCataragenAkñúg Manual. CaTUeTA shear center EtgEtsßitenAelIG½kS sIuemRTI dUcenH shear center nwgsßitenAelITIRbCMuTm¶n;rbs;muxkat;EdlG½kSsIuemRTITaMgBIrkat;Kña. rUbTI


T.Chhay 184 Beams

5>45 b bgðajTItaMgdabrbs;FñwmBIrepSgKña enAeBlbnÞúkGnuvtþkat;tam shear center nigminkat;tam shear center. krNITI1³ bnÞúkEdlGnuvtþkat;tam shear center RbsinebIbnÞúkeFVIGMeBIkat;tam shear center bBaðaFñwmrgnUvm:Um:g;Bt;Fm μtakñúgTisedAEkgBIr. dUcbgðajkñúg rUbTI 5>46 bnÞúkGacRtUv)anbMEbkCakMub:Usg;ctuekaNEkgkñúgTisedA x nigTisedA y EdlkMub:Usg;bnÞúknImYy²begáIt bending eFobG½kSepSgKña.

edIm,IedaHRsayCamYybnÞúkpÁÜb mundMbUgeyIgsakl,gemIl chapter H of the Specification,

“Manuals Under Combined Forces and Torsion” ¬ehIyemIleTACMBUkTI6 kñúgesovePAenH¦ sin. The Specification edaHRsaybnÞúkpÁÜbCadMbUgtamry³kareRbI interaction formulas EdlKitBIsar³sM xan;én\T§iBlbnÞúknImYy²EdlmanTMnak;TMngeTAnwgersIusþg;EdlRtUvKñanwg\T§iBlénbnÞúkenaH. ]Tahr-N_ RbsinebIman bending eFobEtnwgG½kS x / nxbux MM φ≤ b¤ 0.1≤

nxb

uxM

Mφ

Edl =uxM m:Um:g;Bt;emKuNeFobG½kS x =nxM nominal moment strength eFobG½kS x dUcKña RbsinmanEt bending eFobG½kS y enaH nybuy MM φ≤ b¤ 0.1≤

nyb

uyM

Mφ

Edl =uyM m:Um:g;Bt;emKuNeFobG½kS y


Fñwm 185 T.Chhay

=nyM nominal moment strength eFobG½kS y enAeBlmanRbePT bending TaMgBIr viFI interaction formula tRmUv[plbUkpleFobTaMgBIrtUcCag b¤esμ Inwg 0.1 Edl 0.1≤+

nyb

uy

nxb

uxM

MM

Mφφ

¬%>!$¦

tamkarBit tRmUvkarenHGnuBaØat[ designer dak;bnÞúkkñúgTisedAmYyEdlminmandak;enAelITisedA mYyeTot. AISC Section H1 bBa©ÚlpleFobsRmab;bnÞúktamG½kS nig[ interaction formulas BIr EdlmYysRmab;bnÞúktamG½kStUc nigmYyeTotsRmab;bnÞúktamG½kSFM ¬eyIgnwgsikSamUlehtusRmab; krNIenHenAkñúgCMBUk 6¦. CamYynwgm:Um:g;Bt;BIrTis ehIyKμanbnÞúktamG½kS rUbmnþsRmab;bnÞúktam G½kStUcKW 0.1

2≤++

nyb

uy

nxb

ux

n

uM

MM

MP

Pφφφ

(AISC Equation H1-1b)

RbsinebIbnÞúktamG½kS 0=uP enaHsmIkarenHRtUvKñanwgsmIkar %>!$. mkdl;cMNucenH eKminBicarNaersIusþg;rbs;muxkat; I- nig H-shaped EdlekageFobG½kS exSayeT. RbsinebIeFVIEbbenH vanwgmanlkçN³smBaØ. RKb;rUbragEdlekageFobnwgG½kSexSayrbs; vaminGac buckle kñúgTisedAepSgeToteT dUcenH lateral-torsional buckling minEmnCasßanPaBkM Nt;eT. RbsinebIrUbragmanlkçN³ compact enaH yyyypyny MZFKM 5.1≤== Edl == yyyy SFM yield moment sRmab;G½kS y . sRmab;muxkat; I- nig H-shaped Edlekag eFobG½kSexSay Ednx<s;bMput yyM5.1 nwglubCanic© ¬ yy SZ / nwgFMCag 5.1 Canic©¦. RbsinebIrUbrag Ca noncompact ersIusþg;Edl[eday AISC Equation A-F1-3 sRmab; flange local buckling b¤ web local buckling. ¬RKb; standard shapes EdlRtUv)anerobCataragenAkñúg Manual manRTnug compact dUcenHvaGacekItmanEt flange local buckling Etb:ueNÑaH.¦ ]TahrN_ 5>18³ 6821×W RtUv)aneRbICaFñwmTRmsamBaØEdlmanRbEvg feet12 . søabrgkarsgát; RtUv)andak;TRmxagEtenAxagcug. bnÞúkeFVIGMeBItamry³ shear center CamYym:Um:g;emKuN


T.Chhay 186 Beams

kipsftMux −= 200 ehIy kipsftMuy −= 25 . RbsinebIeKeRbI 36A etIFñwmenHbMeBjlkçxNÐ rbs; AISC Specification? snμt;fam:Um:g;TaMgBIrEbgEckesμ IenAelIRbEvgrbs;Fñwm. dMeNaHRsay³ eKTTYl)anTinñn½yxageRkamsRmab; 36A BI Load Factor Design Selection Table. rUbragCa compact ehIy ,5.7 ftLp = ftLr 8.22= ,432 kipsftM pb −=φ kipsftM rb −= 273φ The unbraced length ,12 ftLb = dUcenH rbp LLL << ehIysßanPaBkMNt;EdllubKWsßitenAkñúg elastic lateral-torsion buckling enaH ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

pbrppbbnxb LL

LLMMMCM φφ

( ) Pbpr

pbrbpbpbb M

LLLL

MMMC φφφφ ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

edaysarm:Um:g;Bt;BRgayesμ I/ 0.1=bC ehIy ( ) kipsftM nxb −=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−−

−−= 2.3855.78.22

5.7122734324320.1φ

müa:gvijeTot eKGacTTYl nxbMφ BI beam design charts edaysarrUbrag compact dUcenHvaK μan flange local bucklingehIy ( )( ) kipsftkipsinFZMM yybpybnyb −=−==== 88.65.6.790364.2490.0φφφ RtYtBinitü 5.155.1

7.154.24

>==y

ySZ

dUcenHeRbI ( )( ) kipsftkipsinSFMM yyyyny −=−==== 75.70.8.8477.15365.15.15.1 ( ) kipsftM nyb −== 59.6375.709.0φ BIsmIkar %>!! 0.1912.0

59.6325

2.385200

<=+=+nyb

uy

nxb

uxM

MM

Mφφ

(OK)

cemøIy³ 6821×W RKb;RKan;


Fñwm 187 T.Chhay

krNITI2³ bnÞúkEdlGnuvtþminkat;tam shear center enAeBlEdlbnÞúkGnuvtþminkat;tam shear center rbs;muxkat; lT§plKWFñwmnwgrg flexure bUk nwg torsion. RbsinebIGaceFVIeTA)an rUbragFrNImaRtrbs;eRKOgbgÁúM nigtMNrKYrRtUvEkERbedIm,IbM)at;cM Nakp©it. bBaðarbs; torsion enAkñúg rolled shapes KWs μ úKsμaj ehIyeyIgnwgedaHRsayvaCamYyviFIRb hak;RbEhl. eKGacrkkarerobrab;EdllkçN³lMGitsRmab;RbFanbT nig design aid RKb;RKan; enA kñúg Torsional Analysis of Structural Steel Members (AISC, 1997). lkçxNÐénkardak;bnÞúkEdl eFVI[ekItman torsion RtUv)anbgðajenAkñúg rUbTI 5>47 a. bnÞúkpÁÜbRtUv)andak;enAelIG½kSrbs;søab xagelI b:uEnþExSskmμrbs;vaminkat;tam shear center rbs;muxkat;eT. RbsinebIeyIgKitBIsßanPaBlM nwg eyIgGacrMkilkmøaMgeTA shear center edaybEnßm couple. dUcenHeKTTYl)anRbB½n§lMnwgEdlpSM eLIgedaykmøaMgEdl[eFVIGMeBIkat;tam shear center bUknwg twisting moment dUcEdl)anbgðaj. enAkñúg rUbTI 5>47 b eKmankMub:Usg;bnÞúkEtmYyEdlRtUvedaHRsay EtKMnitKWEtdUcKña.

rUbTI 5>48 bgðajBIviFIEdlsRmYlkñúgkaredaHRsaykrNITaMgBIrenH. enAkñúgrUbTI5>48 a eK snμt;søabxagelIpþl;nUversIusþg;srubeTAnwgkMub:Usg;bnÞúkedk. enAkñúg rUbTI5>48 b m:Um:g;rmYl (twisting

moment) RtUv)anTb;eday couple EdlpSMeLIgedaybnÞúkBIres μ IKñaeFVIGMeBIelIsøabnImYy². tamviFIRb hak;RbEhl eKGacsnμt;fasøabnImYy²Tb;nwgkmøaMgdac;edayELkBIKña. dUcenH bBaðaRtUv)ankat;bnßy


T.Chhay 188 Beams

eTACakrNIén bending rbs;rUbragBIr EdlrUbragnImYy²TTYlbnÞúktamry³ shear center. kñúgsßan PaBnImYy²Edl)anBiBN’naenAkñúg rUbTI 5>48 muxkat;EtRbEhlBak;kNþalb:ueNÑaH RtUv)anBicarNa famanRbsiT§PaBtamG½kS y dUcenH enAeBlBicarNaersIusþg;rbs;rbs;søabeTal eRbItémøEtBak; kNþalrbs; yZ sRmab;muxkat;EdlmanenAkñúgtarag. Design of Roof Perlins édrENgdMbUl (roof purlin) CaEpñkénRbB½n§dMbUlCRmal (sloping roof system) EdlrgnUvm:U m:g;Bt;BIrTis (biaxial bending) énRbePTEdleTIbnwgBN’na. sRmab; roof purlin EdlbgðajenAkñúg rUbTI 5>49 bnÞúkmanTisedAbBaÄr EtG½kSénkarBt;KWeRTt. lkçxNÐénkardak;bnÞúkenHRtUvnwgrUbTI 5>48 a. kMub:Usg;EkgeTAnwgdMbUlnwgbegáIt bending eFobG½kS x ehIykMub:Usg;RsbBt;FñwmeFobG½kS y rbs;va. RbsinebI purlin RtUv)anRTedayTRmsamBaØenAnwg trusses ( b¤ rigid frame rafter) m:Um:g; Bt;GtibrmaeFobG½kSnImYy²KW 8/2wL Edl w CakMub:Usg;rbs;bnÞúk. RbsinebIeKeRbI sag rods vanwg pþl;nUv lateral support tamG½kS x ehIynwgCaTRmsRmab;G½kS y EdltRmUv[Kit purlin CaFñwmCab;. sRmab; sag rods EdlmanKMlates μI eKGaceRbIrUbmnþsRmab;FñwmCab;enAkñúg Part 4 of the Manual.

]TahrN_ 5>19³ RbB½n§dMbUl trusses EdlbgðajenAkñúg rUbTI 5>50 EdlmanKMlatBIKña .15 ft . éd rENgRtUv)andak;enAelItMN nigenAelIcMNuckNþalrbs;Ggát;xagelI. eKdak; sag rods enAkNþal purlin nImYy². bnÞúk gravity srub EdlrYmbBa©ÚlTaMgTm¶n;édrENgsnμt;KW psf30 énépÞdMbUl CamYy


Fñwm 189 T.Chhay

nwgpleFobbnÞúkGefrelIbnÞúkefresμ Inwg 0.1 . edaysnμt;favaCalkçxNÐdak;bnÞúkeRKaHfñak; cUreRbIEdk 36A nigeRCIserIs W-shape Edlmankm<s; .6in sRmab;édrENg.

dMeNaHRsay³ sRmab;lkçxNÐbnÞúkenH bnÞúkefr bUknwg roof live load edayK μanxül; nigRBil bnSMbnÞúk (A4-3) nwgmantémøFMCageK³ ( ) ( ) psfLww rDu 42156.1152.16.12.1 =+=+ TTwgénépÞrgsMBaFEdlmanGMeBIelIédrENgKW .906.7

310

215 ft=

enaH bnÞúkelIédrENg ( ) ftlb /1.332906.742 == kMub:Usg;Ekg ( ) ftlb /1.3151.332

103

==

kMub:Usg;Rsb ( ) ftlb /0.1051.332101

==

nig ( )( ) kipsftMux −== 862.8153151.081 2

CamYynwg sag rods Edldak;enAcMNuckNþalédrENgnImYy² enaHédrENgCaFñwmCab;BIrElVgtamTis exSay. BI “Beam Diagrams and Formulas” section in Part 4 of the Manual, m:Um:g;Bt;enAelI TRmxagkñúgCamYynwgkarrgbnÞúkEtmYyElVgKW 2

161 wLM =

Edl =w bnÞúkBRgayesμ I =L RbEvgElVg ¬ElVgBIresμIKña¦ CamYynwgbnÞúkenAelIElVgTaMgBIr m:Um:g;GacTTYleday superposition³ ( ) 22

max 812

161 wLwLMM ===

dUcenH ( )( ) kipsftMuy −== 7382.02/15105.081 2


T.Chhay 190 Beams

edIm,IeRCIserIsrUbragsakl,g eRbI beam design charts nigeRCIserIsrUbragCamYynwgersIusþg;tam G½kSxøaMgFM. sRmab; unbraced length ft5.72/15 = / sakl,g 96×W . sRmab; 0.1=bC / kipsftM nxb −= 0.14φ . BI rUbTI 5>15 b 3.1=bC sRmab;lkçxNÐbbnÞúk nig lkçxNÐTRmxagénFñwmenH. dUcenH ( ) kipsftM nxb −== 20.180.1430.1φ b:uEnþ kipsftkipsftM pxb −<−= 20.188.16φ dUcenHeRbI kipsftM nxb −= 8.16φ rUbragenH compact dUcenH ( ) kipsftkipsinFZMM yybpybnyb −=−==== 644.4.73.553672.19.0φφφ b:uEnþ 5.155.1

11.172.1

>==y

ySZ

dUcenH( ) ( ) ( )( )( ) kipsftkipsinSFMM yybyybnyb −=−==== 496.4.95.5311.1365.19.05.15.1 φφφ

edaysarbnÞúkRtUv)anGnuvtþenAelIsøabxagelI eRbIlT§PaBenHEtBak;kNþaledIm,ITb;Tl;nwg\T§iBl rmYl. BIsmIkar %>!$

0.1856.02/496.4

7382.08.16

862.8<=+=+

nyb

uy

nxb

uxM

MM

Mφφ

(OK)

kmøaMgkat;TTwgKW ( ) kipsVu 363.2

2153151.0

== BI factored uniform load table³ kipskipsVnv 363.25.19 >=φ (OK) cemøIy³ eRbI 96×W . 5>15> ersIusþg;m:Um:g;Bt;rbs;rUbragepSg² (Bending Strength of Various Shape) W-, S- nig M-shapes Ca hot-rolled shapes EdleKeRbICaTUeTAsRmab;Fñwm ehIy bending

strength rbs;vaRtUv)anerobrab;BIxagedIm. b:uEnþeBlxøHeKk¾eRbIrUbragepSg²eTotCa flexural mem-

bers Edr ehIykñúgEpñkenHnwgniyaysegçbBIkarpþl;[rbs; AISC. smIkarTaMgGs;)anBI Chapter F


Fñwm 191 T.Chhay

b¤ Appendix F of the Specification. eK[ Nominal strength sRmab; compact nig noncompact

hot-rolled shapes b:uEnþminEmnsRmab; slender shapes b¤rUbragEdlpSMeLIgBIEdkbnÞHeT. kñúgEpñkenH min)anpþl;nUv]TahrN_CatémøelxeT Et]TahrN_ 6>11 bBa©ÚlnUvkarKNnaBI flexural strength

rbs; structural tee-shape. dUcEdl)anerobrab;BIxagedIm smIkarKWsRmab; nonhybrid section ( yyfyw FFF == ) nig sRmab;krNIBt;Etb:ueNÑaH ¬minmanbnÞúktamG½kSeT¦.

I. Channels A. Width-thickness parameters for flexure

1. søab

f

ftb

=λ / y

p F65

=λ nig 10

141−

=y

r Fλ ¬sRmab; US¦

f

ftb

=λ / y

p F170

=λ nig 69

370−

=y

r Fλ ¬sRmab; IS¦

2. RTnug

wth

=λ / y

p F640

=λ nig 10

970−

=y

r Fλ ¬sRmab; US¦

wth

=λ / y

p F1680

=λ nig y

r F2550

=λ ¬sRmab; IS¦

B. Bending eFobG½kSxøaMg [CamYy ¬!¦ bnÞúkGnuvtþkat;tam shear center ehIysßitenA kñúgbøg;RsbnwgRTnug b¤ ¬@¦ karTb;RbqaMgnwgkarrmYlenAcMNucbnÞúkGnuvtþ nigenARtg; TRm] ³ nM dUcKñasRmab; I-shapes ¬emIlEpñk 5>5 nig 5>6¦.

C. Bending eFobG½kSexSay³ nM dUcKñasRmab; I-shapes ¬emIlEpñk 5>14¦. II. Rectangular Structural Tubes

A. Width-thickness parameters ¬emIlrUb 5>51¦

1. søab

tb

=λ / y

p F190

=λ nig y

r F238

=λ ¬sRmab; US¦

tb

=λ / y

p F500

=λ nig y

r F625

=λ ¬sRmab; IS¦

2. RTnug


T.Chhay 192 Beams

th

=λ / y

p F640

=λ nig y

r F970

=λ ¬sRmab; US¦

th

=λ / y

p F1680

=λ nig y

r F2550

=λ ¬sRmab; IS¦

RbsinebIeKmindwgTMhMBitR)akd b nig h EdlbgðajenAkñúg rUbTI 5>51 eKGac)a:n; s μanedayykTTwgsrub b¤km<s;srubdknwgbIdgkRmas; ¬lkçN³rbs;EdkTIb RCugEdlmanenAkñúg Manual KWQrelIkaMxageRkAEdles μ Inwg t2 ¦.

B. Bending eFobG½kSxøaMg ¬bnÞúkenAkñúgbøg;sIuemRTI¦

1. rUbrag compact sRmab;rUbrag compact ersIusþg;nwgQrelIsßanPaBkMNt;én lateral-torsional

buckling (LTB). sRmab; pb LL ≤ ypn MMM 5.1≤= (AISC Equation F1-1) sRmab; rbp LLL ≤<

( ) ppr

pbrppbn M

LLLL

MMMCM ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−


sRmab; rb LL > pcrn MMM ≤= (AISC Equation F1-12) Edl

yb

bcr rL

JACM

/57000

= xñat US (AISC Equation F1-14)

yb

bcr rL

JACM/

393000= xñat IS

p

yp M

JArL

3750= xñat US (AISC Equation F1-5)


Fñwm 193 T.Chhay

p

yp M

JArL

25855= xñat IS

p

yr M

JArL


p

yr M

JArL

393000= xñat IS

xyr SFM = (AISC Equation F1-11)

2. rUbrag noncompact ³ The nominal strength es μ InwgtémøEdltUcCageKéntémø Edl)anKNnasRmab;sßanPaBkMNt; lateral torsional buckling (LTB), flange

local buckling (FLB) b¤ web local buckling (WLB). sRmab;sßanPaB nImYy² én local buckling TaMgBIr ersIusþg;RtUv)ankMNt;BIsmIkarxageRkam³

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

prppn MMMM


C. Bending eFobG½kSexSay³ vaminmansßanPaBkMNt; LTB sRmab;RKb;rUbragEdlrg karBt;eFobG½kSexSayrbs;va.

1. rUbrag compact ypn MMM 5.1≤= (AISC Equation F1-1)

2. rUbrag nonompact³ RtYtBinitü FLB nig WLB CamYynwg AISC Equation A-F-

1-3. III. Square Structural Tubes

A. Width-thickness parameters

tb

=λ / y

p F190

=λ nig y

r F238

=λ ¬sRmab; US¦

tb

=λ / y

p F500

=λ nig y

r F625

=λ ¬sRmab; IS¦ B. Nominal bending strength

vaminmansßanPaBkMNt; LTB sRmab;rUbragkaer ¬b¤ctuekaNEkgeT¦. 1. rUbrag compact

ypn MMM 5.1≤= (AISC Equation F1-1)


T.Chhay 194 Beams

2. rUbrag nonompact³ ersIusþg;RtUv)ankMNt;eday local buckling eday WLB b¤ FLB edayykmYyNaEdl nM tUcCageK.

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

prppn MMMM


IV. Solid Rectangular Bars sRmab; rectangular bars sßanPaBkMNt;EdlGacGnuvtþ)anKW LTB sRmab;G½kSBt; xøaMg local buckling minEmnCasßanPaBkMNt;sRmab;G½kSBt;xøaMg b¤k¾exSay.

A. Bending eFobG½kSxøaMg sRmab; pb LL ≤ ypn MMM 5.1≤= (AISC Equation F1-1) sRmab; rbp LLL ≤<

( ) ppr

pbrppbn M

LLLL

MMMCM ≤⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

−


sRmab; rb LL > pcrn MMM ≤= (AISC Equation F1-12) Edl

yb

bcr rL

JACM

/57000

= xñat US (AISC Equation F1-14)

yb

bcr rL

JACM/

393000= xñat IS

p

yp M

JArL


p

yp M

JArL

25855= xñat IS

p

yr M

JArL


p

yr M

JArL

393000= xñat IS

xyr SFM = (AISC Equation F1-11)

B. Bending eFobG½kSexSay³ ypn MMM 5.1≤= (AISC Equation F1-1)

V. Tees and double-anfle Shapes


Fñwm 195 T.Chhay

A. Width-thickness parameters 1. Tees

a. søab

f

ft

b2

=λ nig y

r F95

=λ eKmineRbI pλ ¬sRmab; US¦

f

ft

b2

=λ nig y

r F250

=λ eKmineRbI pλ ¬sRmab; IS¦

b. RTnug

wtd

=λ nig y

r F127


wtd

=λ nig y

r F333

=λ eKmineRbI pλ ¬sRmab; IS¦ 2. Double angles with separators, either leg

tb

=λ nig y

r F76


tb

=λ nig y

r F200


3. Double angles in continuous contact, outstanding leg

tb

=λ / y

r F95


tb

=λ / y

r F250


B. CamYybnÞúkenAkñúgbøg;sIuemRTI

⎥⎦⎤

⎢⎣⎡ ++== 21 BB

L

GJEIMM

b

ycrn

π (AISC Equation F1-15)

Edl yn MM 5.1≤ sRmab; stem rgkarTaj yn MM 0.1≤ sRmab; stem rgkarsgát;

j

ILdB y

b⎟⎟⎠

⎞⎜⎜⎝

⎛±= 3.2 (AISC Equation F1-16)

xyy SFM =


T.Chhay 196 Beams

eKeRbIsBaØabUksRmab; B enAeBlEdl stem rgkarTaj ehIysBaØadkenAeBlEdl stem rgkarsgát;enARKb;kEnøgTaMgGs;tambeNþay unbraced length.

C. Bending eFobG½kSexSay³ sRmab; nonslender shapes )( rλλ ≤ ypn MMM 5.1≤=

VI. Solid circular and square shapes ypn MMM 5.1≤=

VII. Hollow circular shapes A. Width-thickness parameters

tD

=λ / y

p F2070

=λ nig y

r F8970

=λ ¬sRmab; US¦

tD

=λ / y

p F14270

=λ nig y

r F61850

=λ ¬sRmab; IS¦

Edl D CaGgát;p©itxageRkA B. Norminal bending strength:

vaminmansßanPaBkMNt; LTB sRmab;rUbragmUl ¬b¤kaer¦. ersIusþg;RtUv)ankNt; eday local buckling. sRmab; pλλ ≤ ypn MMM 5.1≤= sRmab; rp λλλ ≤< SF

tDM yn ⎟

⎠⎞

⎜⎝⎛ +=

/600 (AISC Appendix F, Table A-F1.1)


Fñwm-ssr 197 T.Chhay

VI. Fñwm-ssr Beam-Columns

6>1> esckþIepþIm (Introduction)

enAeBlEdlGgát;eRKOgbgÁúMCaeRcInRtUv)anKitCassrrgkmøaMgtamG½kS b¤CaFñwmEdlrgEtkmøaMg Bt; (flexural loading) Fñwm nigssrCaeRcInrgnUvkmøaMgTaMgBIrKw kmøaMgBt; nigkmøaMgtamG½kS. vaCakar Bit CaBiesssRmab;eRKOgbgÁúMsþaTicminkMNt;. sUm,IEtTRm roller rbs;FñwmsamBaØGacpþl;nUvkmøaMg kkitEdlGacTb;Fñwmcl½ttambeNþay enAeBlEdlbnÞúkGnuvtþEkgnwgG½kSbeNþayrbs;Fñwm. b:uEnþkñúg krNIBiessenH CaTUeTA\T§iBlrg ¬TIBIr¦mantémøtUc ehIyGacecal)an. ssrCaeRcInRtUv)anCa Ggát;rgkmøaMgsgát;suT§CamYynwgkMrwtlMeGogEdlGacecal)an. RbsinebIssrCaGgát;sRmab;eRKOg bgÁúMmYyCan; ehIyTRmrbs;vaTaMgBIrRtUv)anKitCaTRm pinned FñwmnwgrgEt bending EdlCalT§plBI bnÞúkcMNakp©itEdleRKaHfñak;tictYc.

b:uEnþ sRmab;Ggát;eRKOgbgÁúMCaeRcIn \T§iBlTaMgBIrnwgmantémøFM EdlGgát;TaMgenaHRtUv)aneK ehAfa beam-columns. BicarNa rigid frame enAkñúgrUbTI 6>1. sRmab;lkçxNÐbnÞúkEdl[Ggát; edk AB minRtwmEtRTbnÞúkbBaÄrBRgayesμ IeT EfmTaMgCYyGgát;bBaÄredIm,ITb;nwgbnÞúkxagcMcMNuc P . Ggát; CD CakrNIEdleRKaHfñak;Cag eRBaHvaTb;;nwgbnÞúk 21 PP + edayminmanCMnYyBIGgát;bBaÄr NaeT. mUlehtuKWfa x-bracing EdlbgðajedayExSdac; karBar sidesway enACan;xageRkam. sRmab;karbgðajTisedArbs; 2P Ggát; ED nwgrgkmøaMgTaj ehIyGgát; CF nwgFUrRbsinebI bracing

element RtUv)anKNnaedIm,ITb;EtkmøaMgTaj. b:uEnþsRmab;krNIenH Ggát; CD RtUvbBa¢ÚnbnÞúk 21 PP + BI C eTA D .


T.Chhay 198 Beam-Column

Ggát;bBaÄrrbs;eRKagenHk¾RtUv)anKitCa beam-columns. enACan;xagelI Ggát; AC nig BD nigekageRkam\T§iBlrbs; 1P . elIsBIenH enARtg; A nig B m:Um:g;Bt;RtUv)anbBa¢ÚnBIGgát;edktamry³ tMNrwg. karbBa¢Únm:Um:g;enHk¾ekIteLIgenARtg; C nig D ehIyvaBitsRmab;RKb; rigid frame eTaHbI m:Um:g;TaMgenHtUcCagm:Um:g;Edl)anBIbnÞúkxagk¾eday. ssrCaeRcInenAkñúg rigid frames Ca beam-

columns ehIy\T§iBlrbs;m:Um:g;Bt;minRtUv)anecal. b:uEnþ ssrrbs;GaKarmYyCan;EdlenAdac;BIeK GacRtUv)anKitCaGgát;rgkmøaMgsgát;cMG½kS.

eBlxøH]TahrN_epSgeTotrbs; beam-columns GacCYbenAkñúg roof trusses. eTaHbICaFm μta top chord RtUv)anKitCaGgát;rgkmøaMgsgát;tamG½kSk¾eday RbsinebI purlins RtUv)andak;enAcenøaH tMN kmøaMgRbtikm μrbs;vanwgbegáItCa bending Edldac;xatRtUv)anKitkñúgkarKNna. krNIenHnwg RtUv)anerobrab;enAkñúgCMBUkenH.

6>2> smIkarGnþrkm μ (Interaction Formulas)

vismPaBrbs;smIkar @># GacRtUv)ansresrkñúgTRmg;xageRkam³ 0.1≤∑

n

iiR

Qφγ ¬^>!¦

b¤ 0.1resistance

effects load ≤

∑ RbsinebIman resistance eRcInRbePTBak;B½n§ smIkar ^>! GacRtUv)ansresrkñúgTRmg;eKal

rbs; interaction formulas. dUcEdl)anerobrab;enAkñúgCMBUk 5 Rtg;Epñkm:Um:g;Bt;BIrTis plbUkén pleFob load-to-resistance RtUv)ankMNt;RtwmmYyÉktþa. ]TahrN_ RbsinebIeKGnuvtþTaMgm:Um:g;Bt; nigkmøaMgtamG½kS interaction formulas GacsresrCa

0.1≤+nb

u

nc

uM

MP

Pφφ

¬^>@¦

Edl =uP bnÞúksgát;tamG½kSemKuN =ncPφ compressive design strength =uM m:Um:g;Bt;emKuN =nbMφ design moment sRmab;m:Um:g;Bt;BIrTis vanwgmanpleFobm:Um:g;Bt;BIr



0.1≤⎟⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

¬^>#¦

Edl x nig y sMedAelIkarBt;eFobG½kS x nigG½kS y . smIkar ^># CasmIkareKalrbs; AISC sRmab;Ggát;rgkarBt; nigrgkmøaMgtamG½kS. eK[

smIkarBIrenAkñúg Specification: mYysRmab;bnÞúkcMG½kSEdlmantémøtUc nigmYyeTotsRmab;bnÞúkcM G½kSEdlmantémøFM. RbsinebIbnÞúktamG½kSmantémøtUc tYbnÞúktamG½kSRtUv)ankat;bnßy. sRmab; bnÞúktamG½kSEdlmantémøFM tYkmøaMgBt;RtUv)ankat;bnßybnþic. tRmUvkarrbs; AISC RtUv)an[enAkñúg Chapter H, “Members Under Combined Forces and Torsion,” ehIyRtUv)ansegçbdUcxageRkam³

sRmab; 2.0≥nc

uP

Pφ

0.198

≤⎟⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(AISC Equation H1-1a)

sRmab; 2.0<nc

uP

Pφ

0.12

≤⎟⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(AISC Equation H1-1b)

]TahrN_6>1 bgðajBIkarGnuvtþn_smIkarTaMgenH. ]TahrN_6>1³ Fñwm-ssrEdlbgðajenAkñúg rUbTI6>@ manTRm pinned enAcugsgçag ehIyrgbnÞúkem KuNdUcbgðaj. karBt;KWeFobnwgG½kSxøaMg. kMNt;faetIGgát;enHbMeBjsmIkarGnþrkm μrbs; AISC

Specification b¤eT. dMeNaHRsay³ dUcEdl)anbkRsayenAkñúgEpñk 6>3 m:Um:g;EdlGnuvtþenAkñúg AISC Equations H1-1a nig b eBlxøHnwgRtUv)anbegáInedaym:Um:g;bEnßm (moment amplification). eKalbMNgén]TahrN_ enHKWbgðajBIrebobeRbIsmIkarGnþrkmμ. BI column load table ersIusþg;KNnakmøaMgsgát;tamG½kS (axial compression design

strength) rbs; 588×W CamYynwg ksiFy 50= nigRbEvgRbsiT§PaB ftLK y 17170.1 =×= KW kipsPnc 365=φ edaysarkarBt;eFobG½kSxøaMg m:Um:g;KNna (design moment) nbMφ sRmab; 0.1=bC GacTTYl



)anBI beam design chart in Part 4 of the Manual. sRmab; unbraced length ftLb 17= / kipsftM nb −= 202φ sRmab;lkçxNÐbnÞúk niglkçxNÐcugsRmab;bBaðaenH 32.1=bC ¬emIlrUbTI 5>15 c¦.

sRmab; 32.1=bC / ( ) kipsftM nb −== 26720232.1φ

b:uEnþm:Um:g;enHFMCag kipsftM pb −= 224φ ¬EdlTTYl)andUcKñaBI beam design charts¦/ dUcenH design moment RtUv)ankMNt;Rtwm pbMφ . dUcenH kipsftM nb −= 224φ m:Um:g;Bt;GtibrmaenAkNþalElVgKW ( ) kipsftMu −== 5.93

41722

kMNt;faetIsmIkarGnþrkmμmYyNalub 2.0547.0

365200

>==nc

uP

Pφ

dUcenHeRbI AISC Eq.H1-1a.

0.1919.00224

5.93985479.0

98

≤=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ Ggát;enHbMeBj AISC Specification.



6>3> m:Um:g;bEnßm (Moment Amplification) viFIBImunsRmab;karKNnaGgát;rgkarBt; nigkmøaMgtamG½kSGaceRbI)ansRmab;EtkmøaMgtamG½kS mantémøminFMeBk. vtþmanrbs;bnÞúktamG½kS ¬elIkElgenAeBlvamantémøtUc¦ begáItm:Um:g;TIBIrEdl RtUv)anKitbBa©ÚlkñúgkarKNna. rUb TI 6>3 bgðajBIFñwm-ssrCamYybnÞúktamG½kS nigbnÞúkTTwgG½kS BRgayes μ I. Rtg;cMNuc O NamYyEdlmanmanm:Um:g;Bt;EdlbegáIteLIgedaybnÞúkBRgayesμ Inwgm:Um:g; bEnßm Py EdlbegáIteLIgedaybnÞúktamG½kSeFVIGMeBIcMNakp©itBIG½kSbeNþayrbs;Ggát;. m:Um:g;TIBIr enaH mantémøkan;EtFMenAkEnøgNaEdlmanPaBdabkan;EtFM. kñúgkrNIenH Rtg;km<s;Bak;kNþalm:Um:g; srubes μ Inwg δPwL +8/2 . vaCakarBitEdl m:Um:g;bEnßmbegáItPaBdabbEnßmBIelIPaBdabEdl)anBI bnÞúkTTwgG½kS. edaysareKminGacrkPaBdabsrubedaypÞal; ¬bBaðaenHCa nonlinear¦ ehIyeday sarEteKminsÁal;PaBdab eKk¾minGacKNnam:Um:g;)anEdr.

viFIviPaKeRKOgbgÁúMFmμta (ordinary structural analysis methode) Edlminykragpøas;TImk KitRtUv)aneKKitCa viFIdWeRkTImYy (first-order method). eKeRbI Iterative numerical technique ¬EdleKehAfa viFIdWeRkTIBIr (second-order method)¦ edIm,IrkPaBdab nigm:Um:g;TIBIr b:uEnþviFIenHmin GaceRbIsRmab;karKNnaedayéd EdlvaRtUv)aneRbICaTUeTACamYynwgkm μviFIkMuBüÚT½r. Design codes

nig specifications bc©úb,nñPaKeRcIn rYmbBa©ÚlTaMg AISC Specification GnuBaØatkareRbIR)as; second-



order analysis b¤ moment amplification method. viFIenHtRmUvkarKNnam:Um:g;Bt;GtibrmaEdl)an BIlT§plBI flexural loading ¬bnÞúkTTwgG½kS b¤m:Um:g;cugGgát;¦ eday first-order analysis bnÞab;mk KuNnwgemKuNm:Um:g;bEnßm (moment amplification factor) edIm,IKitm:Um:g;TIBIr. rUbTI 6>4 bgðajGgát;TRmsamBaØCamYynwgbnÞúkcMG½kS nigPaBminRtg;dMbUg (initial out-of-

straightness). PaBdabdMbUg (initial crookedness) enHGacsMEdgeday³

Lxeyoπsin=

Edl e CabMlas;TIGtibrmadMbUg EdlekIteLIgenAkNþalElVg.

sRmab;RbB½n§kUGredaendUcEdl)anbgðaj eKGacsresrTMnak;TMngExSkMeNag-m:Um:g;

(moment-curvature relationship) dUcxageRkam³

EIM

dxyd

−=2

2

m:Um:g;Bt; M ekIteLIgedaysarcMNakp©iténkmøaMgtamG½kS uP eFobG½kSrbs;Ggát;. cMNak p©itenHpSMeLIgeday initial crookedness oy bUknwgPaBdabbEnßm y EdlekItBIkarBt;. enARtg;TI taMgNamYy m:Um:g;KW

( )yyPM ou += edayCMnYssmIkarenHeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an

⎟⎠⎞

⎜⎝⎛ +−= y

Lxe

EIP

dxyd u πsin2

2

Lx

EIePy

EIP

dxyd uu πsin2

2−=+



EdlCa ordinary, nonhomogenous differential equation. edaysarvaCasmIkardWeRkTIBIr dUcenHvamanlkçxNÐRBMEdnBIr. sRmab;lkçxNÐTRmEdlbgðaj lkçxNÐRBMEdnKW

enARtg; 0=x / 0=y nigenARtg; Lx = / 0=y enHmann½yfa PaBdabesμ IsUnüenAcugsgçag. GnuKmn_EdlbMeBjTaMgsmIkarDIepr:g;Esül nig

lkçxNÐRBMEdnKW

LxBy πsin=

Edl B Catémøefr. CMnYsvaeTAkñúgsmIkarDIepr:g;Esül eyIgTTYl)an

Lx

EIeP

LxB

EIP

LxB

Luu ππππ sinsinsin2

2−=+−

eKTTYl)antémøefr

11 2

2

2

2−

=

−

−=

−

−=

u

e

u

u

u

PP

e

LPEI

e

LEIP

EIeP

Bππ

Edl == 2

2

LEIPe

π Euler buckling load

dUcenH ( ) Lx

PPe

LxBy

ue

ππ sin1/

sin ⎥⎦

⎤⎢⎣

⎡−

==

( )yyPM ou +=

( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡−

+=Lx

PPe

LxeP

ueu

ππ sin1/

sin

m:Um:g;GtibrmaekItenARtg; 2/Lx = ³ ( ) ⎥

⎦

⎤⎢⎣

⎡−

+=1/max

ueu PP

eePM

( )( ) ⎥

⎦

⎤⎢⎣

⎡−+−

=1/

11/

ue

ueu PP

PPeP

( )⎥⎦⎤

⎢⎣

⎡−

=eu

o PPM

/11

Edl oM minEmnCam:Um:g;bEnßmGtibrma (unampliflied maximum moment). kñúgkrNIenH vaTTYl)anBI initial crookedness b:uEnþCaTUeTAvaGacCalTßplénbnÞúkTTwgG½kS b¤m:Um:g;cug. dUcenHem



KuNm:Um:g;bEnßm (moment amplification factor) KW ( )eu PP /1

1−

¬^>$¦

dUcEdl)anerobrab;mkehIy TRmg;emKuNm:Um:g;bEnßmrbs; AISC GacxusEbøkBIsmIkar ^>$ bnþic. ]TahrN_6>2³ eRbIsmIkar ^>$ edIm,IKNnaemKuNm:Um:g;bEnßmsRmab;Fñwm-ssrén]TahrN_ 6>1. dMeNaHRsay³ edaysar Euler load eP CaEpñkrbs;emKuNm:Um:g;bEnßm eKRtUvKNnavasRmab;G½kSén karBt; EdlkñúgkrNIenHKWG½kS x . eKGacsresr Euler load eP edayeRbI effective length nig slenderness ratio dUcxageRkam³

( )22

/ rKL

EAP g

eπ

=

¬emIlCMBUk 4 smIkar $>^ a¦. sRmab;G½kSénkarBt; ( )( ) 89.55

65.312170.1

===x

xr

LKr

KL

( )

( )( )( )

kipsrKL

EAP g

e 156789.55

1.1729000/ 2

2

2

2===

ππ

BIsmIkar ^>$ ( ) ( ) 15.1

1567/20011

/11

=−

=− eu PP

EdlbgðajkarekIneLIg %15 BIelIm:Um:g;Bt;. m:Um:g;bEnßmKW ( ) kipsftMu −==× 5.1075.9315.115.1 cemøIy³ emKuNm:Um:g;bEnßm 15.1 6>4> Web Local Buckling in Beam-Columns karkMNt;rbs; design moment tRmUv[RtYtBinitümuxkat;sRmab; compactness . enAeBl EdlK μanbnÞúktamG½kS RTnugrbs;RKb;rUbragEdlmanenAkñúgtaragsuT§Et compact. RbsinebImanvtþ manbnÞúktamG½kS RTnugTaMgenaHGacnwgmin compact. enAeBlEdleyIg[ wth /=λ / RbsinebI pλλ ≤ rUbragKW compact.



RbsinebI rp λλλ ≤< rUbragKW noncompact. RbsinebI rλλ > rUbragKW slender. ASIC B5 enAkñúg Table B5.1 erobrab;nUvkarkMNt;xageRkam³

sRmab; 125.0≤yb

uP

Pφ

/ ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

yb

u

yp P

PF φ

λ75.21640 ¬xñat US¦

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

yb

u

yp P

PF φ

λ75.2

11680 ¬xñat IS¦

sRmab; 125.0>yb

uP

Pφ

/ yyb

u

yp FP

PF

25333.2191≥⎟

⎟⎠

⎞⎜⎜⎝

⎛−=φ

λ ¬xñat US¦

yyb

u

yp FP

PF

66533.2500≥⎟

⎟⎠

⎞⎜⎜⎝

⎛−=φ

λ ¬xñat IS¦

sRmab;témøepSg²rbs; yb

uP

Pφ

/ ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

yb

u

yr P

PF φ

λ 74.01970 ¬xñat US¦

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

yb

u

yr P

PF φ

λ 74.012550 ¬xñat IS¦

Edl ygy FAP = / bnÞúktamG½kScaM)ac;edIm,IeTAdl;sßanPaBkMNt; yielding. edaysar uP CaGBaØti eKminGacRtYtBinitü compactness rbs;RTnug nigminGacerobcMCata ragTukCamun)aneT. b:uEnþ rolled shape xøHbMeBjnUvkrNId¾GaRkk;bMput yF/665 Edlmann½yfarUb ragenaHmanRTnug compact edayminTak;TgnwgbnÞúktamG½kS. rUbragEdlmanenAkñúg column load

table in Part 3 of the Manual EdlminbMeBjlkçxNÐRtUv)ankMNt;bgðaj enaHeKRtUvRtYtBinitü compactness rbs;RTnugrbs;va. rUbragEdlmansøabmin compact k¾RtUv)ankMNt;bgðaj dUcenHRKb; rUbragTaMgGs;Edlmin)anbgðaj enaHmann½yfarUbragTaMgenaHKW compact. ]TahrN_6>3³ Edk 36A EdlmanrUbrag 6512×W RtUv)andak;[rgm:Um:g;Bt; nigbnÞúktamG½kSem KuN kips300 . RtYtBinitü compactness rbs;RTnug. dMeNaHRsay³ rUbragenHKW compact sRmab;RKb;témøbnÞúktamG½kS BIeRBaHminmankarkMNt;cMNaMNa mYyenAkñúg column load table. b:uEnþ edIm,Ibgðaj eyIgRtYtBinitü width-thickness ratio rbs;RTnug



( ) ( )( ) 125.04848.0361.199.0

300>===

ygb

u

yb

uFA

PP

Pφφ

dUcenH ( ) 74.584848.033.236

19133.2191=−=⎟

⎟⎠

⎞⎜⎜⎝

⎛−=

yb

u

yp P

PF φ

λ

74.5817.4236

253253<==

yF

dUcenH 74.58=pλ BI dimensions and properties tables/ 74.589.24 <==

wthλ

dUcenH RTnugKW compact. cMNaMfa sRmab;RKb;témørbs; yF enaH wth nwgmantémøtUcCag

yF/253 EdlCatémøEdltUcbMputrbs; pλ dUcenHRTnugrbs; 6512×W nwgenAEtCa compact. 6>5> eRKagBRgwg nigeRKagGt;BRgwg (Braced versus Unbraced Frame) AISC Specification erobrab;BI moment amplification in Chapter C, Frames and other

Structures”. eKmanemKuNbEnßmBIrEdleRbIenAkñúg LRFD: mYyedIm,IKitBIm:Um:g;bEnßmEdlCalT§plBI PaBdabrbs;Ggát; nigmYyeTotsRmab;KitBI\T§iBl sway enAeBlEdlGgát;CaEpñkrbs; unbraced

frame. viFIenHmanlkçN³RsedogKñaeTAnwgviFIEdleRbIenAkñúg ACI Building Code sRmab;ebtug BRgwgedayEdk (ACI, 1995). rUbTI 6>5 nwgbgðajBIGgát;TaMgBIr. enAkñúg rUbTI 6>5 a Ggát;RtUv)anTb; RbqaMgnwg sidesway ehIym:Um:g;TIBIrGtibrmaKW δP EdlRtUvbEnßmeTAelIm:Um:g;GtibrmaenAkñúgGgát; enaH. RbsinebIeRKagminRtUv)anBRgwg vanwgelceLIgnUvm:Um:g;TIBIr EdlbgðajenAkñúg rUbTI 6>5 b Edl begáIteday sidesway. m:Um:g;TIBIrenHmantémøGtibrma ΔP EdlbgðajBIkarbEnßménm:Um:g;cug.

edIm,IKItBI\T§iBlTaMgBIrenH emKuNm:Um:g;bEnßm 1B nig 2B RtUv)aneRbIsRmab;m:Um:g;BIrRbePT. m:Um:g;bEnßmEdleRbIsRmab;KNnaRtUv)anKNnaBIbnÞúkemKuN nigm:Um:g;emKuNdUcxageRkam³

ltntu MBMBM 21 += (AISC Equation C1-1)

Edl =ntM m:Um:g;GtibrmaEdlsnμt;faminman sidesway ekIteLIg eTaHbICaeRKagBRgwgb¤minBRgwg k¾eday ¬ nt mann½yfa no translation¦



=ltM m:Um:g;GtibrmaEdlekIteLIgeday sidesway ekIteLIg ¬ lt mann½yfa lateral transla-

tion¦. m:Um:g;enHGacekItBI lateral load b¤edaysar unbalanced gravity loads . bnÞúkTMnajGacbegáIt sidesway RbsinebIeRKagGt;sIuemRTI b¤k¾bnÞúkTMnaj enaHRtUv)an dak;edayminmanlkçN³sIuemRTI. ltM nwgmantémøesμ IsUnüRbsinebIeRKagRtUv)anBRgwg.

=1B emKuNm:Um:g;bEnßmsRmab;m:Um:g;EdlekIteLIgenAkñúgGgát;EdlRtUv)anBRgwgTb;nwg sidesway. =2B emKuNm:Um:g;bEnßmsRmab;m:Um:g;Edl)anBI sidesway. eyIgnwgerobrab;BIkarkMNt;emKuNTaMgBIr 1B nig 2B enAkñúgEpñkxageRkam.

6>6> Ggát;enAkñúgeRKagEdlBRgwg (Members in Braced Frames) emKuNm:Um:g;bEnßmEdl[edaysmIkar ^>$ RtUv)anbMEbksRmab;Ggát;EdlBRgwgRbqaMgnwg sidesway. rUbTI 6>6 bgðajBIGgát;RbePTenHEdlrgm:Um:g;enAxagcugesμ IKñaEdlbegáIt single-

curvature bending ¬kMeNagEdlbegáItkarTaj nigkarsgát;enAEtEpñkmçagrbs;Ggát;¦. m:Um:g;bEnßm GtibrmaekItenARtg;Bak;kNþalkm<s; EdlPaBdabmantémøFMbMput. dUcenHm:Um:g;TIBIrGtibrma nigm:U m:g;emGtibrmaRtUv)anbUkbBa©ÚlKña. eTaHRbsinebIm:Um:g;enAxagcugminesI μKñak¾eday RbsinebIm:Um:g;mYy vilRsbTisRTnicnaLika nigmYyeTotvilRcasRTnicnaLika vanwgbegáIt single-curvature bending

ehIym:Um:g;emGtibrma nigm:Um:g;TIBIrGtibrmanwgekIteLIgenAEk,Kña.



vanwgminEmnCakrNIeT enAeBlEdlm:Um:g;enAcugEdlGnuvtþbegáIt reverse-curvature bending

dUcbgðajenAkñúg rUbTI 6>7 . enAeBlenH m:Um:g;emGtibrmaKWenAcugmçag ehIym:Um:g;TIBIrGtibrmaekIt eLIgenAcenøaHcugTaMgBIr. m:Um:g;bEnßmGacFMCag b¤tUcCagm:Um:g;cugGaRs½ynwgbnÞúktamG½kS. dUcenHm:Um:g;GtibrmaenAkñúg beam-column GaRs½ynwgkarEbgEckm:Um:g;Bt;enAkñúgGgát;. kar EbgEckenHRtUv)anKitedayemKuN mC EdlGnuvtþenAkñúgemKuNm:Um:g;bEnßm 1B . emKuNm:Um:g;bEnßm Edl[edaysmIkar ^>$ RtUv)anbMEbksRmab;krNIGaRkk;bMput dUcenH mC nwgminRtUvFMCag 0.1 . TRmg;cugeRkayrbs;emKuNm:Um:g;bEnßmKW³ ( ) 1

/1 11 ≥

−=

eu

mPP

CB (AISC Equation C1-2)

Edl ( )2

2

21/ rKL

EAFAP g

c

yge

π

λ==

enAeBlKNna 1eP eRbI rKL / sRmab;G½kSénkarBt; ehIyemKuNRbEvgRbsiT§PaB 0.1≤K ¬Edl RtUvKñanwglkçxNÐEdlBRgwg¦. karKNnaemKuN mC emKuN mC GnuvtþEtelIlkçxNÐEdlBRgwgEtb:ueNÑaH. eKmanGgát;BIrRbePT EdlmYyman bnÞúkTTwgG½kSGnuvtþenAcenøaHcug nigmYyeTotminmanbnÞúkTTwgG½kS. rUbTI 6>8 b nig c bgðajBIkrNITaMgBIrxagelIenH ¬Ggát; AB Ca beam-column EdlRtUvKit¦.



!> RbsinebIminmanbnÞúkTTwgG½kSeFVIGMeBIenAelIGgát; ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

2

14.06.0MMCm (AISC Equation C1-3)

21 / MM CapleFobénm:Um:g;Bt;enAcugrbs;Ggát;. 1M Catémødac;xaténm:Um:g;cugEdltUcCag eK ehIy 2M CatémøFMCag enaHpleFobnwgviC¢mansRmab;Ggát;EdlekagkñúgTRmg; reversecurvature

nigGviC¢mansRmab; single-curvature bending ¬rUbTI 6>9 ¦. Reverse curvature ¬pleFobviC¢man¦ ekIteLIgenAeBlEdl 1M nig 2M vilRsbRTnicnaLikaTaMgBIr b¤RcasRTnicnaLikaTaMgBIr.

@> sRmab;Ggát;rgbnÞúkTTwgG½kS eKGacyk 85.0=mC RbsinebIcugrbs;vaRtUv)anTb;RbqaMg nwgkarvil nigesμ Inwg 0.1 RbsinebIcugrbs;vaminRtUv)anTb;nwgkarvil ¬pinned¦. CaTUeTAkarTb;cug (end restraint) ekItBIPaBrwgRkaj (stiffness) rbs;Ggát;EdlP¢ab;eTAnwg beam-column. lkçxNÐ TRm pinned CalkçxNÐmYyEdlRtUv)aneRbIsRmab;TajrkemKuNm:Um:g;bEnßm dUcenHvaminmankarkat; bnßytémøemKuNm:Um:g;bEnßmsRmab;krNIenHeT EdlvaRtUvKñanwg 0.1=mC . eTaHbICalkçxNÐcugBit



R)akdsßit enAcenøaHkarbgáb;eBj (fully fixity) nigknøas;K μankkit (frictionless pin) k¾eday eKGac eRbItémøNa mYyk¾)anEdr eRBaHvanwgpþl;lT§plCaTIeBjcitþ.

viFIsaRsþEdl)aneFVI[RbesIreLIgsRmab;Ggát;rgbnÞúkxagTTwgG½kS ¬krNITIBIr¦ RtUv)anpþl;

[enAkñúg section C1 of the commentary to the Specification. emKuNkat;bnßyKW

11

e

um P

PC ψ+=

sRmab;Ggát;TRmsamBaØ



12

2−=

LMEI

o

oδπψ

Edl oδ CaPaBdabGtibrmaEdlekItBIbnÞúkxagTTwgG½kS ehIy oM Cam:Um:g;GtibrmaenA cenøaHTRmEdl)anBIbnÞúkxagTTwgG½kS. emKuN ψ RtUv)anKNnaBIsßanPaBFm μtaCaeRcInehIyRtUv)an pþl;[enAkñúg commentary Table C-C1.1. ]TahrN_6>4³ Ggát;EdlbgðajenAkñúg rUbTI 6>10 CaEpñkrbs; braced frame. bnÞúk nigm:Um:g;RtUv)an KNnaCamYybnÞúkemKuN ehIykarBt;KWwFobnwgG½kSxøaMg. RbsinebIeKeRbI 572A Grade 50 etIGgát; enHRKb;RKan;b¤eT? .14 ftKLKL y ==

dMeNaHRsay³ kMNt;faetIRtUveRbIrUbmnþGnþrkmμmYyNa

maximum 63.5502.3

)12(14===

y

yr

LKr

KL

BI AISC Table 3-50, ksiFcrc 89.33=φ dUcenH ( ) ( ) kipsFAP crcgnc 4.64789.331.19 === φφ

2.06487.04.647

420>==

nc

uP

Pφ

dUcenHeRbI AISC Equation H1-1a. enAkñúgbøg;énkarBt;



( ) 82.3128.51214

===x

xr

LKr

KL

( )( )( )( )

kipsrLK

EAFAP

xx

g

c

yge 5399

82.311.1929000

/ 2

2

2

2

21 ====ππ

λ

9415.082704.06.04.06.0

2

1 =⎟⎠⎞

⎜⎝⎛−−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

MMCm

( ) ( ) 021.15399/4201

9415.0/1 1

1 =−

=−

=eu

mPP

CB BI Beam design charts,CamYynwg 0.1=bC nig .14 ftLb = moment strength KW

kipsftM nb −= 347φ sRmab;témø bC BitR)akd edayeyagtamdüaRkam:Um:g;enAkñúg rUbTI 6>10³

( )( ) ( ) ( ) ( ) 06.1

793764733825.28225.1

3435.25.12

max

max =+++

=+++

=CBA

b MMMMM

C

dUcenH ( ) ( ) kipsftCM bnb −=== 36834706.1347φ b:uEnþ kipsftM pb −= 358φ ¬BItarag¦ kipsft −< 368 dUcenHeRbI kipsftM nb −= 358φ m:Um:g;emKuNKW kipsftM nt −= 85 0=ltM BI AISC Equation C1-1,

( ) uxltntu MkipsftMBMBM =−=+=+= 72.83082021.121 BI AISC Equation H1-1a,

0.1857.0358

72.83986487.0

98

<=⎟⎠⎞

⎜⎝⎛+=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ Ggát;enHKWRKb;RKan;. ]TahrN_ 6>5³ Fñwm-ssredkEdlbgðajenAkñúgrUbTI 6>11 rgnUv service live loads dUcEdlbgðaj kñúgrUb. Ggát;enHRtUv)anBRgwgxagenAxagcugrbs;vaTaMgBIr ehIykarBt;KWeFobnwgG½kS x . RtYtBinitü faetIGgát;enHRKb;RKan;tam AISC Specification.



dMeNaHRsay³ bnÞúkemKuNKW

( ) kipsPu 0.32206.1 == ehIym:Um:g;GtibrmaKW ( )( ) ( )( ) kipsftM nt −=

×+

×= 52.80

810035.02.1

410206.1 2

Ggát;enHRtUv)anBRgwgTb;nwgkarbMlas;TIxagcug dUcenH 0=ltM . KNnaemKuNm:Um:g;bEnßm sRmab;Ggát;rgbnÞúkxagEdlRtUv)anBRgwgTb;nwg sidesway ehIy unrestrained end enaH 0.1=mC . témøEdlsuRkitCagEdl)anBI AISC Commentary Table C-C1.1 KW

12.01

e

um P

PC −=

sRmab;G½kSénkarBt; ( )( ) 19.34

51.312100.1

===x

xr

LKr

KL

( )

( )( )( ) kips

rKL

EAP g

e 2522219.34

3.1029000/

2

2

2

1 ===ππ

9975.02522

0.322.01 =⎟⎠⎞

⎜⎝⎛−=mC

emKuNm:Um:g;bEnßm ( ) ( ) 0.1010.1

2522/0.3219975.0

/1 11 >=

−=

−=

eu

mPP

CB

sRmab;G½kSénkarBt; ( ) kipsftMBMBM ltntu −=+=+= 33.81052.80010.121



edIm,ITTYl design strengths dMbUgemIleTA column load tables in Part 3 of the Manual Edl [ kipsPnc 262=φ BI beam design charts in Part 4 of the Manual sRmab; ftLb 10= nig 0.1=bC kipsftM nb −= 8.91φ edaysarTm¶n;FñwmtUcNas;ebIeRbobeFobnwgbnÞúkGefrcMcMNuc enaH 32.1=bC BI rUbTI 5>13 c. ( ) kipsftM nb −== 1218.9132.1φ m:Um:g;enHFMCag kipsftM pb −= 6.93φ EdlTTYl)anBI beam design chart dUcKña dUcenH design

strength RtUv)ankMNt;RtwmtémøenH. dUcenH kipsftM nb −= 6.93φ

RtYtBinitürUbmnþGnþrkmμ³ 2.01221.0

2620.32

<==nc

uP

Pφ

dUcenHeRbI AISC Equation H1-1b³ 0.1930.00

6.9333.81

21221.0

2<=⎟

⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ 358×W KWRKb;RKan; ]TahrN_ 6>6³ Ggát;EdlbgðajenAkñúg rUbTI6>12 eFVIBIEdk 242A EdlmanrUbrag 6512×W ehIy RtUvRTnUvbnÞúksgát;tamG½kSemKuN kips300 . enAcugTMenrmçagCa pinned nigcugmçageTotrgnUvm:Um:g; emKuN kipsft −135 eFobG½kSxøaMg nig kipsft −30 eFobG½kSexSay. eRbII 0.1== yx KK cUreFVIkar GegátBIGgát;enH. dMeNaHRsay³ dMbUg kMNt; yield stress yF . BI Table 1-2, Part 1 of the Manual, 6512×W CarUbragRkumTIBIr. BI Table 1-1, Edk 242A manersIusþg;EtmYyKW ksiFy 50= . bnÞab;mkeTot rk compressive strength. sRmab; ( ) ftKL 15150.1 == axial compressive design

strength BI column load table KW³ kipsPnc 626=φ cMNaMfa taragbgðajfasøabrbs; 6512×W KW noncompact sRmab; ksiFy 50= .



KNnam:Um:g;Bt;eFobG½kSxøaMg (strong axis bending moment).

( ) 6.004.06.04.06.02

1 =−=−=MMCmx

( ) 09.3428.51215

==x

xr

LK

( )( )( )( )

kipsrLK

EAP

xx

gxe 4704

09.341.1929000

/ 2

2

2

2

1 ===ππ

( ) ( ) 0.1641.04704/3001

6.0/1 1

1 <=−

=−

=xeu

mxx PP

CB

dUcenH eRbI 0.11 =xB ( ) kipsftMBMBM ltxxntxxux −=+=+= 13501350.121 BI beam design charts CamYy ftLb 15= / kipsftM nxb −= 342φ sRmab; 0.1=bC ehIy

kipsftM pxb −= 8.357φ . BI rUbTI 5>15 g, 67.1=bC ehIy ( ) ( ) kipsftCMC bnxbb −===× 57134267.10.1for φ lT§plenHFMCag pxbMφ dUcenHeRbI kipsftMM pxbnxb −== 8.357φφ KNna m:Um:g;Bt;eFobG½kSexSay (weak axis bending moment).

( ) 6.004.06.04.06.02

1 =−=−=MMCmy

( ) 60.5902.31215

==y

yr

LK



( )( )( )( )

kipsrLK

EAP

yy

gye 1539

60.591.1929000

/ 2

2

2

2

1 ===ππ

( ) ( ) 0.1745.01539/3001

6.0/1 1

1 <=−

=−

=yeu

mxy PP

CB

dUcenH eRbI 0.11 =yB ( ) kipsftMBMBM ltyyntyyuy −=+=+= 300300.121 edaysarsøabrbs;rUbragenH noncompact enaHersIusþg;m:Um:g;Bt;eFobG½kSexSayRtUv)ankMNt;eday FLB. 9.9

2==

f

ft

bλ

192.950

6565===

yp F

λ

29.221050

14110

141=

−=

−=

yr F

λ

edaysar rp λλλ <<

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=

pr

prppn MMMM


( ) kipsftZFMM yypyp −==== 8.18312

1.4450 ( ) ( )( ) kipsftkipsinSFFMM yryryr −=−=−=−== 0.97.11641.291050 edayCMnYscUleTAkñúgsmIkar AISC Equation A-F1-3 eyIgTTYl)an ( ) kipsftMM nyn −=⎟

⎠⎞

⎜⎝⎛

−−

−−== 1.179192.929.22

192.99.90.978.1838.183 ( ) kipsftM nyb −== 2.1611.17990.0φ rUbmnþGnþrkm μ[ 2.04792.0

626300

>==nc

uP

Pφ

dUcenHeRbI AISC Equation H1-1a³ 0.1980.0

2.16130

8.357135

984792.0

98

<=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ 6512×W RKb;RKan;



6>7> Ggát;enAkñúgeRKagEdlminBRgwg (Members in Unbraced Frames) Fñwm-ssrEdlcugrbs;vaGacrMkil)an m:Um:g;dMbUgGtibrmaEdl)anBI sidesway CaTUeTAeRcIn

sßitenAelIEtcugmçag. dUcEdl)anbgðajenAkñúgrUbTI 6>5 m:Um:g;TIBIrGtibrmaEdl)anBI sidesway Etg EtsßitenAelIcugmçag. dUcenHsRmab;krNIenH m:Um:g;TImYy nigm:Um:g;TIBIrGtibrmaCaTUeTARtUv)anbUk bBa©ÚlKña ehIyminRtUvkaremKuN mC eT ¬karBit 0.1=mC ¦. eTaHbICaenAeBlEdlmankarkat;bnßy k¾va mantémøtictYc nigGacecal)an. cUrBicarNaFñwm-ssrEdlbgðajenAkñúgrUbTI 6>13. m:Um:g;es μIKña enAxagcug)anmkBI sidesway ¬BIbnÞúkedk¦. bnÞúktamG½kS ¬EdlCaEpñkmYyénbnÞúkEdlmanGMeBIelI Fñwm-ssrminbNþal[man sidesway¦RtUv)anKitbBa©ÚleTAkñúgm:Um:g;cugEdr.

emKuNm:Um:g;bEnßmsRmab; sidesway moments 2B RtUv)an[smIkarBIr. eKGaceRbIsmIkar

NamYyk¾)anEdr GaRs½ynwgPaBgayRsYlsRmab;GñkKNna³

( )HLPB

ohu ∑Δ∑−=

/11

2 (AISC Equation C1-4)

b¤ ( )22 /1

1

eu PPB

∑∑−= (AISC Equation C1-5)

Edl =∑ uP plbUkbnÞúkemKuNenAelIRKb;ssrenAelICan;EdlBicarNa



=Δoh drift (sidesway displacement) rbs;Can;EdlBIcarNa =∑H plbUkénbnÞúkedkTaMgGs;EdlbegáIt ohΔ =L km<s;Can;

=∑ 2eP plbUkén Euler loads rbs;ssrTaMgGs;enAelICan;EdlBicarNa ¬enAeBlEdl KNna 2eP eKRtUveRbI rKL / sRmab;G½kSénkarBt; ehIy K CatémøEdlRtUvKñanwg unbraced condition.

plbUkén uP nigplbUkén 2eP GnuvtþeTARKb;ssrEdlsßitenAkñúgCan;EdlBicarNaCamYyKña. eKeRbIplEckrvagplbUkbnÞúkTaMgBIrsRmab;smIkarxagelIedaysar 2B GnuvtþsRmab; unbraced

frames ehIyRbsinebI sidesway nwgekItman enaHssrTaMggs;enAkñúgCan;EdlBicarNanwg sway kñúg eBlCamYyKña. enAkñúgkrNICaeRcIn eRKOgbgÁúMRtUv)anKNnaenAkñúgbøg; dUcenH uP∑ nig 2eP∑ KWsRmab; ssrenACan;rbs;eRKag ehIybnÞúkxag H CabnÞúkxagEdleFVIGMeBIenAelIeRKag nigBIelICan;Edl BicarNa. CamYynwg ohΔ EdlekIteLIgeday H∑ pleFob Hoh ∑Δ / GacQrelIbnÞúkemKuN b¤ bnÞúkK μanemKuN. TRmg;epSgeTotrbs; 2B RtUv)an[eday AISC Equation C1-5 manlkçN³Rs edognwgsmIkarsRmab; 1B elIkElgsRmab;plbUk.

AISC Equations C1-4 nig C1-5 RtUv)anbMEbkedayviFIBIrepSgKña b:uEnþenAkñúgkrNICaeRcInva nwgpþl;nUvlT§pldUcKña (Yura, 1988). enAkñúgkrNICaeRcInEdltémø 2B TaMgBIrxusKñaxøaMg tYénbnÞúk cMG½kSrbs;rUbmnþGnþrkmμnwglub ehIylT§plcugeRkaynwgminxusKñaeRcIneT. dUcEdl)anerobrab;BI xagedIm kareRCIserIsKWsßitenAelIPaBgayRsYl vaGaRs½ynwgtYenAkñúgsmIkar.

kñúgkrNIEdl ntM nig ltM eFVIGMeBIenAcMNucBIrepSgKñaenAelIGgát; dUcbgðajenAkñúgrUbTI 6>14 AISC Equation C1-1 nwgpþl;nUvlT§plEdlsnSMsMéc.

rUbTI 6>14 bgðajbEnßmeTotBI superposition concept. rUbTI 6>14 a bgðajBI braced frame rgnUvTaMgbnÞúkTMnaj (gravity load) nigbnÞúkxag (lateral load). m:Um:g;enA ntM enAkñúgGgát; AB RtUv)anKNnaedayeRbIEt gravity load. edayPaBsIuemRTI eKminRtUvkar bracing edIm,IkarBar sidesway BIbnÞúkenH. m:Um:g;enHRtUv)anbEnßmCamYyCamYynwgemKuN 1B edIm,IkarBar\T§iBl δP .

ltM m:Um:g;EdlRtUvKñanwg sway ¬EdlbegáIteLIgedaybnÞúkedk H ¦ nwgRtUv)anbEnßmeday 2B edIm,I karBarnwg\T§iBl ΔP .



enAkñúg rUbTI 6>14 b unbraced frame RTEtbnÞúkbBaÄr. edaysarkardak;bnÞúkenHminsIuemRTI

vanwgman sidesway bnþic. m:Um:g; ntM RtUv)anKNnaedayBicarNafaeRKagRtUv)anBRgwg ¬kñúgkrNI enH edaysarTRmedkkkit nigkmøaMgRbtikm μRtUvK μaEdleKehAfa tMNTb;nimitþ (artificial joint

restraint AJR). edIm,IKNnam:Um:g; sidesway eKRtUvykTRmkkitecj ehIyCMnYsedaykmøaMgEdlman témøes μ Inwg artificial joint restraint b:uEnþmanTisedApÞúyKña. kñúgkrNIenH m:Um:g;TIBIr ΔP nwgmantémø tUcNas; ehIyeKGacecal ltM )an.

RbsinebITaMgbnÞúkxag nigbnÞúkTMnajminsIuemRTI eKGacbEnßmkmøaMg AJR eTAelIbnÞúkxagBit R)akd enAeBlEdl ltM RtUv)ankMNt;. ]TahrN_ 6>7³ Edk 6512×W RbePT 572A grade 50 RbEvg ft15 sRmab;eRbICassrenAkñúg unbraced frame. bnÞúkcMG½kS nigm:Um:g;cugTTYl)anBI first-order analysis énbnÞúkTMnaj ¬bnÞúkefr



nigbnÞúkGefr¦ RtUv)anbgðajenAkñúg rUbTI 6>15 a . eRKagmanlkçN³sIuemRTI ehIybnÞúkTMnajk¾ RtUv)andak;sIuemRTIEdr. rUbTI 6>15 b bgðajBIm:Um:g;énbnÞúkxül;Edl)anBI first-order analysis. m:U m:g;Bt;TaMgGs;KWeFobnwgG½kSxøaMg. emKuNRbEvgRbsiT§PaB 2.1=xK sRmab;krNI sway nig

0.1=xK sRmab;krNI nonsway ehIy 0.1=yK . kMNt;faetIGgát;enHeKarBtam AISC

Specification b¤eT? dMeNaHRsay³ karbnSMbnÞúkTaMgGs;Edl[enAkñúg AISC A4.1 suT§EtmanbnÞúkGefr ehIyelIk ElgEtkarbnSMbnÞúkTImYyecj EdlkarbnSMbnÞúkTaMgGs;manbnÞúkxül; b¤bnÞúkGefr b¤TaMgBIr. Rbsin ebIRbePTbnÞúk ¬ ,E ,rL ,S nig R ¦ enAkñúg]TahrN_enHminRtUv)anbgðaj lkçxNÐénkarbnSMbnÞúk RtUv)ansegçbdUcxageRkam³ D4.1 (A4-1) LD 6.12.1 + (A4-2)

( )W.L.D 80or 502.1 + (A4-3) LWD 5.03.12.1 ++ (A4-4)

LD 5.02.1 + (A4-5) WD 3.19.0 ± (A4-5)

enAeBlEdlbnÞúkefrtUcCagbnÞúkGefrR)aMbIdg enaHbnSMbnÞúk (A4-1) GacminRtUvKit. bnSM

bnÞúk (A4-4) nwgmantémøFMCag (A4-3) dUcenH (A4-3) Gacdkecj)an. bnSMbnÞúk (A4-5) k¾Gac ecal)anedaysarvanwgpþl;eRKaHfñak;tUcCag (A4-2). cugeRkay karbnSMbnÞúk (A4-6) nwgmineRKaH



fñak;dUc (A4-4) ehIyk¾Gacdkecj)anBIkarBicarNa EdlenAsl;EtbnSMbnÞúkBIrEdlRtUveFVIkarGegátKW (A4-2)nig (A4-4) ³

LD 6.12.1 + nig LWD 5.03.12.1 ++ rUbTI 6>16 bgðajBIbnÞúktamG½kS nigm:Um:g;Bt;EdlKNnaecjBIbnSMbnÞúkTaMgBIrenH kMNt;G½kSeRKaHfñak;sRmab;ersIusþg;kmøaMgsgát;tamG½kS

ftLK y 15= ( ) ftft

rrLK

yx

x 1529.1075.1152.1

/<==

dUcenHeRbI ftKL 15= BI column load tables CamYynwg ftKL 15= / kipsPnc 626=φ sRmab;lkçxNÐbnÞúk (A4-2)/ kipsPu 454= / kipsftM nt −= 8.104 nig 0=ltM ¬eday

sarEtsIuemRTI vaminmanm:Um:g; sidesway¦. emKuNm:Um:g;Bt;KW 2565.0

8.104904.06.04.06.0

2

1 =⎟⎠⎞

⎜⎝⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

MMCm

sRmab;G½kSénkarBt; ( )( ) 09.34

28.512150.1

===x

xr

LKr

KL

¬krNIenHKμan sidesway dUcenHeKeRbI xK sRmab; braced condition¦. enaH

( )( )( )( )

kipsrKL

EAP g

e 470409.34

1.1929000/ 2

2

2

2

1 ===ππ

emKuNm:Um:g;bEnßmsRmab;m:Um:g; nonsway KW

( ) ( ) 0.1284.04704/4541

2565.0/1 1

1 <=−

=−

=eu

mPP

CB

dUcenHeRbI 0.11 =B ( ) kipsftMBMBM ltntu −=+=+= 8.10408.1040.121

BI beam design charts CamYynwg ftLb 15= kipsftM nb −= 343φ ¬sRmab; 0.1=bC ¦



kipsftM pb −= 358φ

rUbTI 6>17 bgðajBIdüaRkamm:Um:g;Bt;sRmab;m:Um:g;énbnÞúkTMnaj. ¬karKNna bC KWQrelItémø dac;xat dUcsBaØaenAkñúgdüaRkamenHminmansar³sMxan;eT¦. dUcenH

CBAb MMMM

MC3435.2

5.12

max

max+++

=

( )( ) ( ) ( ) ( ) 24.2

1.5637443.4138.1045.28.1045.12

=+++

×=

sRmab; 24.2=bC ( ) kipsftMM pbnb −=>= 35834324.2 φφ

dUcenHeRbI kipsftM nb −= 358φ



kMNt;smIkarGnþrkmμEdlsmRsb

2.07252.0626454

>==nc

uP

Pφ

eRbIsmIkar AISC Equation H1-1a. 0.1985.00

3588.104

987252.0

98

<=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

sRmab;lkçxNÐbnÞúk (A4-4), kipsPu 212= / kipsftM nt −= 6.47 ehIy kipsftMlt −= 6.171 . sRmab; unbraced condition/

2597.06.475.404.06.04.06.0

2

1 =⎟⎠⎞

⎜⎝⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

MMCm

kipsPe 47041 = ¬ 1eP minGaRs½ynwglkçxNÐbnÞúk¦

( ) ( ) 0.1272.04704/2121

2597.0/1 1

1 <=−

=−

=eu

mPP

CB

dUcenH 0.11 =B eyIgminmanTinñy½nRKb;RKan;edIm,IKNnaemKuNm:Um:g;bEnßm[)ansuRkitsRmab; sway

moment 2B BI AISC Equation C1-4 b¤ C1-5. RbsinebIeyIgsnμt;fapleFobrvagbnÞúktamG½kS EdlGnuvtþmkelIGgát; nig Euler load capacity mantémødUcKñasRmab;RKb;ssrenAkñúgCan; nigsRmab; ssrEdleyIgBicarNa enaHeyIgGacsresr Equation C1-5³

( ) ( )222 /1

1/1

1

eueu PPPPB

−≈

∑∑−=

sRmab; 2eP eRbI xK EdlRtUvnwg unbraced condition³ ( )( ) 91.40

28.512152.1

===x

xr

LKr

KL



( )( )( )( )

kipsrKL

EAP g

e 326691.40

1.1929000/ 2

2

2

2

2 ===ππ

BI AISC Equation C1-5/

( ) ( ) 069.13266/2121

1/1

1

22 =

−=

−≈

eu PPB

m:Um:g;bEnßmsrubKW ( ) ( ) kipsftMBMBM ltntu −=+=+= 0.2316.171069.16.470.121

eTaHbICam:Um:g; ntM nig ltM mantémøxusKñak¾eday k¾BYkvaRtUv)anEbgEckdUcKña ehIy bC nwgenAdEdl . enARKb;GRtaTaMgGs; BYkvamantémøFRKb;RKan;Edl kipsftM pb −= 358φ Ca design

strength edayminKitBIm:Um:g;NamYyeLIy. 2.03387.0

626212

>==nc

uP

Pφ

dUcenHeRbI AISC Epuation H1-1a³ 0.1912.00

3580.231

983387.0

98

<=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ Ggát;enHbMeBjtRmUvkarrbs; AISC Specification. 6>8 KNnamuxkat;Fñwm-ssr (Design of Beam-Column) edaysarenAkñúgrUbmnþGnþrkmμmanGBaØtiCaeRcIn enaHkarKNnamuxkat;Fñwm-ssrCadMeNIrkar KNnaEdlRtUvkarCacaM)ac;nUv trial-and-error process. sRmab;kareRCIserIscugeRkay KWeKeRCIserIs rUbragNakan;EtEk,r kan;Etl¥. muxkat;sakl,gRtUv)aneRCIserIs nigRtUv)anepÞógpÞat;eLIgvijeday eRbIrUbmnþGnþrkmμ. dMeNIrkard¾manRbsiT§PaBbMputkñúgkareRCIserIsmuxkat;sakl,gRtUv)anbegáIteLIg CadMbUgsRmab; allowable stress design (Burgett, 1973), ehIyRtUv)anTTYl ykmkeRbIsRmab; LRFD Edlmanerobrab;enAkñúg part 3 of the Manual, “Column Design”. lkçN³sMxan;sRmab;viFI enHKWCa karbMElgBIm:Um:g;Bt;eTACabnÞúktamG½kSsmmUl. bnÞúkEdl)anBIkarbMElgRtUv)anykeTA bEnßmelIbnÞúkCak;Esþg ehIyrUbragEdlRtUvRTbnÞúksrubRtUv)aneRCIserIsBI column load tables. bnÞab;mkeKRtUvBinitürUbragsakl,genHCamYy Equation H1-1a b¤ H1-1b. bnÞúktamG½kSRbsiT§PaB srubRtUv)an[eday



muMmMPP uyuxuu ++=eq Edl =uP bnÞújktamG½kSemKuNCak;Esþg

=uxM m:Um:g;emKuNeFobG½kS x =uyM m:Um:g;emKuNeFobG½kS y

=m témøefrEdlmanenAkúñgtarag =n témøefrEdlmanenAkúñgtarag

eKalkarN_énkarviFIenHGacRtUv)anRtYtBinitüedaysresrsmIkar ^># eLIgvijdUcxageRkam. dMbUgKuNGgÁTaMgBIreday nc Pφ ³

ncnyb

uync

nxb

uxncu P

MMP

MMPP φ

φφ

φφ

≤++

b¤ ( ) ( ) ncuyuxu PMMP φ≤×+×+ constant aconstant a GgÁxagsþaMénvismIkarCa design strength rbs;Ggát;EdlBicarNa ehIyGgÁxageqVgGacCa

bnÞúkemKuNxageRkAEdlRtUvTb;Tl;. tYnImYy²énGgÁxageqVgmanxñatkmøaMg dUcenHtémøefrCaGñkbM Elgm:Um:g;Bt; uxM nig uyM eTACakMub:Usg;bnÞúktamG½kS.

témøefrmFüm m RtUv)anKNnasRmab;RkumepSgKñarbs; W-shape ehIyRtUv)an[enAkñúg Table 3-2 in Part 3 of the Manual. témø u RtUv)an[enAkñúg column load table sRmab;rUbrag nImYy²EdlmanenAkñúgtarag. edIm,IeRCIserIsrUbragsakl,gsRmab;Ggát;CamYynwgbnÞúktamG½kS nigm:U m:g;Bt;eFobG½kSTaMgBIr eKRtUvGnuvtþdUcxageRkam.

!> eRCIserIstémøsakl,g m edayQrelIRbEvgRbsiT§PaB KL . yk 0.2=u @> KNnabnÞúksgát;tamG½kSRbsiT§PaB³ muMmMPP uyuxuu ++=eq eRbIbnÞúkenHedIm,IeRCIserIsrUbragBI column load tables. #> eRbItémø u Edl[enAkñúg column load tables nigtémøfμ Irbs; m BI Table 3-2 edIm,I

KNnatémøfμIrbs; eq uP . eRCIserIsrUbragepSgeTot. $> eFVIeLIgvijrhUtdl;témø eq uP ElgERbRbYl.



]TahrN_ 6>8³ Ggát;eRKOgbgÁúMxøHenAkñúg braced frame RtUvRTbnÞúksgát;tamG½kSemKuN kips150 nig m:Um:g;cugemKuN kipsft −75 eFobnwgG½kSxøaMg ehIy kipsft −30 eFobnwgG½kSexSay. m:Um:g;TaMgBIr enHeFVIGMeBIenAelIcugmçag ÉcugmçageTotCaTRm pinned. RbEvgRbsiT§PaBeFobnwgG½kSnImYy²KW ft15 . minmanbnÞúkxageFVIGMeBIelIGgát;enHeT, eRbIEdk 36A nigeRCIserIs W-shape EdlRsalCageK. dMeNaHRsay³ emKuNm:Um:g;bEnßm 1B Gacsnμt;esμ Inwg 0.1 edIm,IeFVIkareRCIserIsmuxkat;sakl,g. sRmab;G½kSnImYy² ( ) kipsftMBM ntxux −=≈= 75750.11

( ) kipsftMBM ntyuy −=≈= 30300.11 BI Table 3-2, part 3 of the Manual, 75.1=m edayeFVI interpolation

eRbItémøedIm 0.2=u ( ) ( )( ) kipsmuMmMPP uyuxuu 3860.275.13075.175150eq =++=++= cab;epþImCamYynwgrUbragtUcCageKenAkñúg column load tables, sakl,g 678×W ¬ kipsPnc 412=φ /

03.2=u ¦³ 1.2=m ( ) ( )( ) kipsPu 43503.21.2301.275150eq =++= témøenHFMCag design strength= kipsft −412 dUcenHeKRtUvsakl,gmuxkat;epSgeTot. sakl,g 6010×W ¬ kipsPnc 416=φ / 0.2=u ¦³ 85.1=m ( ) ( )( ) kipskipsPu 41640000.285.13085.175150eq <=++= (OK)

dUcenH 6010×W CarUbragsakl,gEdlGaceRbIkar)an. RtYtBinitü sW12 nig sW14 . sakl,g 5812×W ¬ kipsPnc 397=φ / 41.2=u ¦³

55.1=m ( ) ( )( ) kipskipsPu 39737841.255.13055.175150eq <=++= (OK)

dUcenH 5812×W CarUbragsakl,gEdlGaceRbIkar)an. 14W EdlRsalCageKsRmab;eFVIkarCamYy nwgbnÞúkxageRkAKW 6114×W EtvaF¶n;Cag 5812×W . dUcenHeRbI 5812×W CarUbragsakl,g³ 2.03778.0

397150

>=nc

uP

Pφ



dUcenHeRbI AISC Equatiom H-1-1a KNnam:Um:g;Bt;eFobG½kS x ( ) 09.34

28.51215

==x

xr

LK

( )

( )( )( )

kipsrKL

EAP g

e 418709.34

0.1729000/ 2

2

2

2

1 ===ππ

( ) ( ) 6.0/04.06.0/4.06.0 221 =−=−= MMMCm ¬sRmab;G½kSTaMgBIr¦ ( ) ( ) 0.1622.0

4187/15016.0

/1 11 <=

−=

−=

eu

mPP

CB

dUcenHeRbI 0.11=B ( ) kipsftMBM ntxux −=== 75750.11 bnÞab;mk kMNt; design strength. BI beam designth curves, sRmab; 1=bC nig ftLb 15= /

kipsftM nb −= 220φ . BIrUbTI 5>15g, 67.1=bC . sRmab; 67.1=bC design strength KW ( ) kipsftCb −==× 36722067.1220 m:Um:g;enHFMCag kipsftM pb −= 233φ dUcenHeRbI kipsftM nb −= 233φ KNnam:Um:g;Bt;eFobG½kS y ( ) 71.71

51.21215

==y

yr

LK

( )

( )( )( )

kipsrKL

EAP g

e 2.94671.71

0.1729000/ 2

2

2

2

1 ===ππ

( ) ( ) 0.1713.02.946/1501

6.0/1 1

1 <=−

=−

=eu

mPP

CB

dUcenHeRbI 0.11=B ( ) kipsftMBM ntyuy −=== 30300.11

5812×W CarUbrag compact sRmab;RKb;témørbs; uP dUcenH nomical strength KW yypy MM 5.1≤ . Design strength KW

( )( ) kipsinFZMM yybpybnyb −==== .1053365.3290.0φφφ kipsft −= 75.87



b:uEnþ 5.152.14.21/5.32/ >==yy SZ Edlmann½yfa nybMφ KYrEtykesμ Inwg ( ) ( ) ( )( )( ) kipsftkipsinSFM yybyyb −=−=== 67.86.10404.21365.190.05.15.1 φφ

BI AISC Equation H1-1a, ⎟

⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

67.8630

23375

983778.0

98

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

0.1972.0 <= (OK)

cemøIy³ eRbI 5812×W . ebIeTaHbICaviFIEdleTIbnwgbgðajsRmab;eRCIserIsrUbragsakl,gqab;rkeXIjk¾eday k¾viFIEdl manlkçN³smBaØCagenHRtUv)anesñIeLIgeday Yura (1988). bnÞúktamG½kSEdlsmmUlEdlRtUv)an eRbIKW

bM

dM

PP yxequiv

5.72++= ¬^>%¦

Edl =P bnÞúktamG½kSemKuN =xM m:Um:g;emKuNeFobG½kS x =yM m:Um:g;emKuNeFobG½kS y =d km<s;Fñwm =b TTwgFñwm

tYTaMgGs;enAkñúgsmIkar ^>@ RtUvEtmanxñatRtUvKña.

]TahrN_ 6>9³ eRbI Yura’s method edIm,IeRCIserIsrUbragsakl,g 12W sRmab;Fñwm-ssrén]TahrN_ 6>8. dMeNaHRsay³ BIsmIkar 6>5 bnÞúktamG½kSsmmUlKW ( ) ( ) kips

bM

dM

PP yxequiv 525

1212305.7

1212752150

5.72=

×+

×+=++=

EdlTTwg b RtUv)ansnμt;es μ Inwg inches12 . BI column load tables, sakl,g 7212×W ¬ kipsPnc 537=φ ¦. CamYynwg Yura’s method eKTTYl)anrUbragsakl,gFMCag Manual method Etvaminy:agdUcenH



rhUteT. enAeBlEdltYm:Um:g;Bt;lub ¬]TahrN_ Ggát;manlkçN³CaFñwmCagssr¦ Yura ENnaMfa bnÞúk tamG½kSRtUvbMElgeTACam:Um:g;Bt;smmUleFobG½kSG½kS x . bnÞab;mkrUbragsakl,gRtUv)aneRCIserIs BI beam design charts in part 3 of the Manual. m:Um:g;smmUlKW³

2dPMM xequiv +=

karKNnamuxkat;Fñwm-ssrEdlminBRgwg Design of Unbraced Beam-Column karKNnamuxkat;dMbUgrbs;Fñwm-ssrenAkñúg braced frame RtUv)anbgðajrYcehIy. emKuNm:U m:g;bEnßm 1B RtUv)ansnμt;esμ I 0.1 edIm,IeRCIserIsmuxkat;sakl,g bnÞab;mk 1B RtUv)ankMNt;sRmab; rUbragenaH. sRmab;Fñwm-ssrRbQmnwg sidesway emKuNm:Um:g;bEnßm 2B EdlQrelIGBaØtiCaeRcIn EdlminsÁal;rhUtdl;ssrTaMgGs;enAkñúgeRKagRtUv)aneRCIserIs. RbsinebI AISC Equation C1-4

RtUv)aneRbIsRmab; 2B enaHeKminman sidesway deflection ohΔ sRmab;karKNnamuxkat;dMbUgeT. Rb sinebIeKeRbI AISC Equation C1-5 enaHeKGacminsÁal; 2eP∑ . viFIxageRkamRtUv)anesñIeLIg edIm,Irk 2B . viFITI1> snμt; 0.12 =B . bnÞab;BIeRCiserIsrUbragsakl,g KNna 2B BI AISC Equation C1-5 eday

snμt;fa 2/ eu PP ∑∑ KWdUcKñanwg 2/ eu PP sRmab;Ggát;EdlBicarNa ¬dUcenAkñúg]TahrN_6>7¦.

viFITI2> eRbIkarkMNt;dMbUg (predetermined limit) sRmab; drift index Loh /Δ EdlCapleeFob story drift elIkm<s;Can;. kareRbInUv drift index GnuBaØatGtibrmasRmab; serviceability

requirement RsedogKñanwgkarkMNt;PaBdabrbs;Fñwm. eKENnaM[eRbI drift index cenøaHBI 500/1 eTA 200/1 . cMNaMfa ohΔ Ca drift EdlekItBI H∑ dUcenHRbsinebI drift index

QrenAelI service load enaHbnÞúkxag H RtUvEtCa service load Edr. ]TahrN_ 6>10³ rUbTI 6>18 bgðajBI single-story unbraced frame EdlrgnUvbÞúkefr bnÞúkGefrelI dMbUl nigxül;. rUbTI 6>18 a bgðajBI service gravity load nig rUbTI6>18 b bgðajBI service wind



load ¬EdlrYmbBa©ÚlTaMg uplift b¤ suction enAelIdMbUl¦. eRbIEdk 572A grade 50 nigeRCIserIs rUbrag 12W sRmab;ssr ¬Ggát;bBaÄr¦. KNnamuxkat;sRmab; drift index 400/1 edayQrelI service wind load. m:Um:g;Bt;eFobnwgG½kSxøaMg ehIyssrnImYy²BRgwgxagenAxagcug nigKl;.

dMeNaHRsay³ eRKagenHCaeRKagsþaTicminkMNt;mYydWeRk. karviPaKrcnasm<½n§minkMNt;minRtUv)aneFVI enATIenHeT. lT§plénkarviPaKeRKagRtUv)anbgðajenAkñúgrUbTI 6>19edaysegçb. bnÞúktamG½kS nig m:Um:g;cugRtUv)an[dac;edayELkBIKñasRmab;bnÞúkefr bnÞúkGefr bnÞúkxül;EdlmanGMeBIelIdMbUl nig bnÞúkxül;xag. bnÞúkbBaÄrTaMgGs;RtUv)andak;sIuemRTIKña ehIycUlrYmEtCamYynwgm:Um:g; ntM b:ueNÑaH. bnÞúkxagbegáItm:Um:g; ltM . bnSMbnÞúkEdlBak;B½n§CamYynwgbnÞúkefr D / bnÞúkGefrelIdMbUl rL nigbnÞúkxül; W KWdUcxageRkam³ A4-2: rLD 5.02.1 + ( ) ( ) kipsPu 8.29265.0142.1 =+=

( ) ( ) kipsftM nt −=+= 107945.0502.1 0=ltM

A4-3: WLD r 8.06.12.1 ++ ( ) ( ) ( ) kipsPu 0.521908266.1142.1 =+−++=

( ) ( ) ( ) kipsftM nt −=−++= 8.184328.0946.1502.1 ( ) kipsftMlt −== 0.16208.0

A4-4: WLD r 3.15.02.1 ++ ( ) ( ) ( ) kipsPu 4.19263.1265.0142.1 =++=



( ) ( ) ( ) kipsftM nt −=−++= 4.65323.1945.0502.1 ( ) kipsftMlt −== 26203.1

bnSMbnÞúk A4-3 pþl;nUvtémøFMCageK.

sRmab;eKalbMNgénkareRCIserIsrUbragsakl,g snμt;fa 0.11 =B . témørbs; 2B Gac RtUv)anKNnaBI AISC Equation C1-4 nig design drift index³

( ) ( )( ) ( )[ ]( ) 107.1400/17.2/0.5221

1//1

1/1

12 =

−=

Δ∑∑−=

∑Δ∑−=

LHPHLPB

ohuohu

bnÞúkedkKμanemKuN H∑ RtUv)aneRbIBIeRBaH drift index KWQrelI drift GtibrmaEdlbNþalmkBI service load. dUcenH

( ) ( ) kipsftMBMBM ltntu −=+=+= 5.20216107.18.1840.121 edayminsÁal;TMhMrbs;Ggát; eKminGaceRbI alignment chart sRmab;emKuNRbEvgRbsiT§PaB)aneT. Table C-C2.1 enAkñúg Commentary to the Specification bgðajfakrNI (f) RtUvKñay:agxøaMgeTAnwg lkçxNÐcugsRmab;krNI sidesway én]TahrN_enH ehIyEdl 0.2=xK . sRmab; braced condition, eKeRbI 0.1=xK . edaysarEtGgát;TaMgGs;RtUv)anBRgwgTisedA mYyeTotEdr enaHeKyk 0.1=yK . bnÞab;mk eKGaceRCIserIsmuxkat;sakl,gEdlman[enAkñúg



Part 3 of the Manual. BI Table 3-2 emKuNm:Um:g;Bt; 5.1=m sRmab; 12W CamYynwg ftKL 15= . ( ) kipsmuMmMPP uyuxuu 35605.15.2020.52eq =++=++= sRmab; ftLKKL y 15== / 5312×W man design strength kipsPnc 451=φ . sRmab;G½kS x ( ) ftft

rrLK

yx

x 152.1411.2150.2

/<==

dUcenH ftKL 15= lub sakl,g 5312×W . sRmab; braced condtition

( )( ) 42.3423.5

15150.1==

x

xr

LK

( )( )( )( )

376942.34

6.1529000/ 2

2

2

2

1 ===ππ

xx

gxe

rLK

EAP

6.004.06.04.06.022

1 =⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

MMMCm

BI AISC Equation C1-2

( ) ( ) 0.1608.03769/0.521

6.0/1 1

1 <=−

=−

=eu

mPP

CB

dUcenHeRbI 0.11 =B cMNaMfa 0.11 =B Catémøsn μt;dMbUg ehIyedaysarEt 2B minRtUv)anpøas;bþÚr enaHtémø

kipsftMu −= 5.202 Edl)anKNnaBIdMbUgk¾minRtUv)anpøas;bþÚrEdr. BI beam design chart in Part

4 of the manual CamYynwg ftLb 15= design moment sRmab; 5312×W CamYynwg 0.1=bC KW kipsftM nb −= 262φ

sRmab;m:Um:g;Bt;EdlERbRbYlsmamaRtBIsUnüenAcugmçag eTAGtibrmaenAcugmçageTot témørbs; 67.1=bC ¬emIlrUbTI 5>15 g¦. dUcenHtémøEdlEktRmUvén design moment KW

( ) kipsftM nb −== 43826267.1φ b:uEnþ m:Um:g;enHFMCag plastic moment capasity kipsftM pb −= 292φ / EdleKGacek)anenA

kñúg charts. dUcenH design strength RtUv)ankMNt;Rtwm kipsftMM pbnb −== 292φφ

kMNt;rUbmnþGnþrkmμEdlsmRsb



2.01153.045152

<==nc

uP

Pφ

dUcenHeRbI AISC Equation H1-1b:

0.1751.00292

5.2022

1153.02

<=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

edaysarlT§plenHtUcCag 0.1 xøaMg dUcenHsakl,grUbragEdltUcCagenHBIrTMhM. sakl,g 4512×W . sRmab; ,15 ftLKKL y == kipsPnc 299=φ . sRmab;G½kS x

( ) ftftrrLK

yx

x 153.1165.2150.2

/<==

dUcenH ftKL 15= lub sRmab; braced condtition

( )( ) 95.3415.5

15150.1==

x

xr

LK

( )( )( )( )

309395.34

2.1329000/ 2

2

2

2

1 ===ππ

xx

gxe

rLK

EAP

BI AISC Equation C1-2,

( ) ( ) 0.1610.03093/0.521

6.0/1 1

1 <=−

=−

=eu

mPP

CB

dUcenHeRbI 0.11 =B BI beam design charts CamYynwg ftLb 15= m:Um:g;KNnasRmab; 4512×W CamYynwg

0.1=bC KW kipsftM nb −= 201φ sRmab; 67.1=bC ( ) kipsftMkipsftM pbnb −=>−== 5.24233620167.1 φφ dUcenH design strength KW kipsftMM pbnb −== 5.242φφ kMNt;rUbmnþGnþrkmμEdlsmRsb³ 2.01739.0

2990.52

<==nc

uP

Pφ



dUcenHeRbI AISC Equation H1-1b:

0.1922.005.2425.202

21739.0

2<=⎟

⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ eRbI 4512×W . enA]TahrN_6>10 karkMNt; drift index CaviFIkñúgkarKNna ehIyeKminmanviFINaedIm,I KNnaemKuNm:Um:g;bEnßm 2B . RbsinebIeKminR)ab; drift index témørbs; 2B GacRtUv)ankMNt;ecj BI AISC Equation C1-5 dUcxageRkam ¬edayeRbIlkçN³rbs; 4512×W ¦³ ( )( ) 90.69

15.512150.2

==x

xr

LK

( )

( )( )( )

kipsrLK

EAP

xx

gxe 2.773

90.692.1329000

/ 2

2

2

2

2 ===ππ

( ) ( ) ( )[ ] 072.12.7732/0.5221

1/1

1

22 =

−=

∑∑−=

eu PPB

6>9> Trusses With Top Chord Loads Between Joints RbssinebIGgát;rgkarsgát;rbs; truss RtUvRTbnÞúkEdlmanGMeBIenAcenøaHcugsgçagrbs;va enaH vanwgRtUvrgnUvm:Um:g;Bt; k¾dUcCabnÞúksgát;tamG½kS dUcenHGgát;enHCa beam-colum. krNIenHGacekIt manenAelI top chord of the roof truss edayédrEngsßitenAcenøaHtMN. eKk¾RtUvKNna top chord of

an open-web steel joist Ca beam-column Edr BIeRBaH open-web steel joist RtUvRTbnÞúkTMnajEdl BRgayes μ IenAelI top chord rbs;va. edIm,IkarBarbnÞúkenH eKRtUveFVIm:UEdl truss CakarpSMeLIgeday man continuous chord member nig pin-connected web members. bnÞab;mkeKGacedaHRsayrk bnÞúktamG½kS nigm:Um:g;Bt;edayeRbIkarviPaKeRKOgbgÁúMdUcCag stiffness method. eK)anesñIeLIgnUvviFI saRsþdUcxageRkam³

!> KitGgát;nImYy²rbs; top chord CaFñwmbgáb;cug. eRbIm:Um:g;bgáb;cugCam:Um:g;GtibrmaenAkñúg Ggát;. Cak;Esþg top chord CaGgát;Cab; CagCaesrIénGgát;tMNsnøak; dUcenHkarcat;TukenH manlkçN³suRkitCagkarEdlcat;TukGgát;nImYy²CaFñwmsmBaØ.

@> bEnßmkmøaMgRbtikm μBIFñwmbgáb;cugenHeTAbnÞúkenARtg;tMNedIm,ITTYl)anbnÞúkelItMNsrub.



#> viPaK truss CamYynwgbnÞúkRtg;tMNTaMgenH. bnÞúktamG½kSEdlCalT§plenAkñúg top chord

member CabnÞúksgát;tamG½kSEdlRtUvykeTAeRbIkñúgkarKNna. viFIenHRtUv)anbgðajCalkçN³düaRkamenAkñúg rUbTI 6>20. müa:gvijeTot eKGacrkm:Um:g;Bt; nigRbtikmμrbs;Fñwmedaycat;Tuk top chord CaFñwmCab;EdlmanTRmenARtg;tMNnImYy².

]TahrN_ 6>11³ rUbTI 6>21 bgðajBI parallel-chord roof trussEdl top chord RTédrENgenA Rtg;tMN nigenARtg;cenøaHtMN. bnÞúkemKuNEdlbBa¢ÚnedayédrENgRtUv)anbgðaj. KNnamuxkat; top chord. eRbIEdk 36A nigeRCIserIs structural tee Edlkat;ecjBI W-shape. dMeNaHRsay³ m:Um:g;Bt; nigkmøaMgelItMNEdlbNþalmkBIbnÞúkEdlmanGMeBIenAcenøaHtMNRtUv)anrk edaycat;Tuk top chord nImYy²CaFñwmbgáb;cug. BI Part 4 of the Manual, “Beam and girder

Design,”m:Um:g;bgáb;cugsRmab;Ggát; top chord nImYy²KW ( ) kipsftPLMM nt −==== 0.3

8104.2

8



m:Um:g;cug nigkmøaMgRbtikm μTaMgenHRtUv)anbgðajenAkñúg rUbTI 6>22 a. enAeBlEdleKbEnßmkmøaMg Rbtikm μeTAelIbnÞúkelItMN enaHeKTTYl)ankardak;bnÞúkdUcbgðajenAkñúgrUbTI 6>22 b. kmøaMgsgát; GtibrmatamG½kSnwgekItmanenAkñúgGgát; DE ¬nwgenAkñúgGgát;EdlenAEk,r EdlenAxagsþaMG½kSrbs; ElVg¦ nigGacRtUv)anrkedayBicarNalMnwgrbs;GgÁesrIrbs;Epñkrbs; truss EdlenAxageqVgmuxkat; a-a³ ( )( ) ( ) ( ) 0420108.4304.22.19 =++−−=∑ DEI FM kipsFDE 90−= ¬rgkarsgát;¦ KNnamuxkat;sRmab;bnÞúktamG½kS kips90 nigm:Um:g;Bt; kipsft −0.3

Table 3-2 in Part 3 of the Manual min)anpþl;[sRmab; structural tee. eKGaceRbI Yura’s

method (Yura, 1988) Edl)anbegáIteLIgsRmab;Ggát; I- nig H-shape. eKRtUvkarrUbragtUc BIeRBaH bnÞúktamG½kStUc ehIym:Um:g;k¾tUcebIeFobnwgbnÞúktamG½kS. RbsinebIeKeRbI tee Edlmankm<s; .6in

( )( ) kipsbM

dM

PP yxequiv 1020

6123290

5.72=++=++=

BI column load table CamYynwg ftLK x 10= nig ftLK y 5= / sakl,g 5.176×WT ¬ kipsPnc 124=φ ¦. m:Um:g;Bt;KWeFobnwgG½kS x ehIyGgát;RtUv)anBRgwgRbqaMgnwg sidesway³ kipsftM nt −= 0.3 / 0=ltM edaysarmankmøaMgxagmanGMeBIelIGgát; ehIycugRtUv)anTb;enaH 85.0=mC ¬Commentary

approach minRtUv)aneRbIenATIenHeT¦. KNna 1B ³ ( ) 18.68

76.11210

===x

xr

LKr

KL



( )( )( )( )

kipsrKL

EAP g

e 3.31818.68

17.529000/ 2

2

2

2

1 ===ππ

( ) ( ) 185.13.318/901

85.0/1 11

1 =−

=−

=e

mPP

CB

m:Um:g;bEnßmKW ( ) kipsftMBMBM ltntu −=+=+= 555.300.3185.121 RbsinebImuxkat;RtUv)ancat;fñak;Ca slender enaH nominal moment strength rbs; structural tee

nwgQrelI local buckling EtRbsinebImindUecñaHeT vanwgQrelI lateral-torsional buckling ¬emIl AISC Equation F1.2c nig Epñk 5>14 kñúgesovePAenH¦. sRmab;søab ( ) 308.6

520.02560.6

2===

f

ft

bλ

λλ >==9

= 83.1536

955

yr F



sRmab;RTnug 83.20

300.025.6

===wtdλ

λλ >=== 17.2126

127127

yr F

edaysar rλλ < sRmab;TaMgsøab nigRTnug rUbragminEmnCa slender eT ehIy lateral-torsional

buckling lub. BI AISC Equation F1-15/

⎟⎠⎞

⎜⎝⎛ ++== 21 BB

L

GJEIMM

b

ycrn

π (AISC Equation F1-15)

yM5.1≤ sRmab;eCIg b¤tYxøÜnrgkarTaj yM0.1≤ sRmab;eCIg b¤tYxøÜnrgkarsgát;

BI AISC Eqution F1-16, ( ) ( ) 378.1

369.02.12

12525.63.2//3.2 ±=⎥

⎦

⎤⎢⎣

⎡±=±= JILdB yb

ehIy nominal strength BI AISC Equation F1-15 KW` ( )( )( )

( ) ( ) ⎟⎠⎞

⎜⎝⎛ ++±= 2378.11378.1

125369.0112002.1229000π

nM

( ) kipsin −=+±= .6168703.1378.12002 b¤ kipsin −.5.650 témøviC¢manrbs; B RtUvKñanwgkmøaMgTajenAkñúgtYxøÜnrbs; tee ehIysBaØaGviC¢manRtUv)aneRbIedIm,ITTYl ersIusþg;enAeBltYxøÜnrgkmøaMgsgát;. sRmab;kardak;bnÞúkenAkñúg]TahrN_enH m:Um:g;GtibrmaekItman enATaMgcugbgáb; nigkNþalElVg dUcenHersIusþg;RtUv)anRKb;RKgedaykmøaMgsgát;enAkñúgtYxøÜn ehIy kipsftkipsinM n −=−= 12.54.5.650 RbQmnwgtémøGtibrmaén ( )( ) kipsftkipsftSFM xyy −<−=== 21.54690.9

1223.3360.10.10.1

dUcenHeRbI kipsftM n −= 690.9 ( ) kipsftM nb −== 721.8690.990.0φ kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI 2.07258.0

12490

>==nc

uP

Pφ



dUcenHeRbI AISC Equation H1-1a: ⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++ 0

721.8555.3

987258.0

98

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

0.109.1 >= (N.G) enAkñúg]TahrN_enH m:Um:g;Bt;mantémøtUc ehIydUcKñasRmab; bending strength dUcenHehIyeFVI[tY m:Um:g;Bt;rbs;rUbmnþGnþrkmμmantémøFM. kñúgkareRCIserIsmuxkat;EdlsmRsb GñkKNnaRtUvdwgc,as; fa bending strength nig axial compressive strength mantémøFM. rUbragbnÞab;enAkñúg column load

tables KW 206×WT CamYynwg axial compressive strength kips133 . tamkarGegátenAelI dimensions and peoperties tables bgðajfaeyIgkMBugbBa©ÚlRkumrUbragEdlmanG½kS x CaG½kS exSay. dUcenHkarBt;rbs;eyIg\LÚvenHKWeFobnwgG½kSexSay ehIyvaK μansßanPaBkMNt; lateral-

torsional buckling. elIsBIenH RbsinebIrUbrag slender enaH nominal strength nwgQrelI yielding ehIyesμ Inwg plastic moment capacity EdlRtUvnwgEdlx<s;bMputRtwm yM5.1 . dUcenHsakl,g 206×WT ¬ kipsPnc 133=φ ¦. dMbUg KNna 1B ³ ( ) 43.76

57.11210

===x

xr

LKr

KL

( )

( )( )( )

kipsrKL

EAP g

e 6.28843.76

89.529000/ 2

2

2

2

1 ===ππ

( ) ( ) 235.16.288/901

85.0/1 11

1 =−

=−

=e

mPP

CB

m:Um:g;bEnßmKW ( ) kipsftMBM ntu −=== 705.30.3235.11 RtYtBinitü slenderness parameters. sRmab;søab ( ) 83.15772.7

515.02005.8

2=<=== r

f

ft

bλλ

sRmab;RTnug 17.212.20295.0970.5

=<=== rwtd λλ

edaysarkarBt;eFobnwgG½kSexSay ( ) kipsftFZMM yxpn −==== 9.15

123630.5

RbQmnwgtémøGtibrmaén



( )( ) kipsftSFM xyy −=== 28.1312

95.2365.15.15.1 edaysarEt yp MM 5.1> ( ) ( ) kipsftMM ybnb −=== 95.1128.1390.05.1φφ kMNt;rkrUbmnþGnþrkmμEdlRtUveRbI 2.06767.0

13390

>==nc

uP

Pφ

dUcenHeRbI AISC Equation H1-1a:

0.1952.0095.11

705.3986767.0

98

<=⎟⎠⎞

⎜⎝⎛ ++=⎟

⎟⎠

⎞⎜⎜⎝

⎛++

nyb

uy

nxb

ux

nc

uM

MM

MP

Pφφφ

(OK)

cemøIy³ eRbI 206×WT .


tMNsamBaØ 241 T.Chhay

VII. tMNsamBaØ Simple Connections

7>1> esckþIepþIm (Introduction) kartP¢ab;rbs;eRKOgbgÁúMEdkCaEpñkmYyEdlmansar³sMxan;bMput. kartP¢ab;Edlminman

lkçN³minRKb;RKan; EdleKGac[eQμaHfa “weak link” enAkñúgeRKOgbgÁúM GacbegáItnUvkar)ak;Ca eRcInkrNI. kar)ak;rbs;Ggát;eRKOgbgÁúMKWkRmnwgekIteLIgNas; kar)ak;rbs;rcnasm<½n§PaKeRcInKW bNþalmkBIkar KNnakartP¢ab; nigkarlMGitkartP¢ab;. bBaðaenHbNþalmkBIkarTTYlxusRtUvkñúg karKNnakartP¢ab;. kñúgkrNIxøH kartP¢ab;minRtUv)anKNnaedayvisVkrEdlKNnaGgát;rbs;eRKOg bgÁúMeT EtvaRtUv)anpþl;[edayplitkrEdlpÁt;pÁg;smÖar³sRmab;KMerageTAvij. b:uEnþvisVkreRKOgbgÁúM Edlplitbøg;KNna CaGñkTTYlxusRtUvkñúgkarKNnaTaMgGs;rYmTaMgkartP¢ab;. kñúgkrNIEdltMN RtUv)anKNnaedayvisVkrepSgeTot epSgBIvisVkrEdlKNnaGgát;eRKOgbgÁúM dUcenHeKRtUvkarvisVkr EdlmanCMnajc,as;las;kñúgkarKNnakartP¢ab;.

eRKOgbgÁúMEdkTMenIbRtUv)antP¢ab;edaykarpSar nigedayb‘ULúúg ¬ersIusþg;x<s; b¤Fm μta¦ b¤eday

bnSMénkartP¢ab;TaMgBIr. BIeBlmun kartP©ab;eFVIeLIgedaykarpSar b¤edayrIev. enAkñúgqñaM 1947 Research Council of Riveted and Bolted Structural Joints RtUv)anbegáIteLIg ehIy Specifi-

cation dMbUgrbs;vaRtUv)anecjpSayenAkñúgqñaM 1951. ÉksarenH)anGnuBaØat[CMnYs edayb‘ULúg ersIusþg;x<s;sRmab;rIev. taMgBIeBlenaHmk b‘ULúgersIusþg;x<s;TTYl)anRbCaRbiyPaBy:agelOn ehIy eKk¾gakmkeRbIb‘ULúgersIsþg;x<s;enAkñúgsMNg;sIuvilvij. eKmanmUlehtuCaeRcInkñúgkarpøas;bþÚrenH. kmμkrBInak;EdlKμanCMnajGacdMeLIgb‘ULúgersIusþg;x<s;)an cMENkkardMeLIgrIevvij eKRtUvkarkm μkr


T.Chhay 242 Simple Connections

EdlmanCMnajdl;eTAbYnnak;. elIsBIenHeTot vapþl;nUvsemøg nigeRKaHfñak;tictYckñúgRbtibtþkarN_ tP¢ab;rIev edaysarkarpþl;kMedAkñúgkardMeLIgrIev. b:uEnþkartP¢ab;edayrIevk¾enAEtmanerobrab;enAkñúg

AISC Specfication nig Manual of steel construction edaysarEtsMNg;cas;²eRbItMNrIev dUcenH karyl;dwgBIkarRbRBwtþeTArbs;vamansar³sMxan;Nas;sRmab;karvaytémøersIusþg; nigkarCYsCulnUv sMNg;TaMgenaH. karKNna nigkarviPaKtMNrIevmanlkçN³RsedogKñanwgtMNb‘ULúgFm μtaEdr Etvaxus KñaRtg;lkçN³smÖar³Etb:ueNÑaH.

tMNpSarmanGtßRbeyaCn_eRcInCagtMNb‘ULúg. kartP¢ab;edaykarpSarmanlkçN³samBaØ nig RtUvkarrn§ticCagtMNb‘ULúg. kartP¢ab;EdlmanlkçN³s μ úKsμajCamYynwgeRKOgP¢ab;GacmanlkçN³ gayRsYlCamYynwgkarpSar dUckrNIkñúgrUbTI 7>1. muneBlEdlkarpSarmanlkçN³eBjniym kar dMeLIgrUbrag built-up RbePTenHRtUv)anplitedayrIev. edIm,IP¢ab;bnÞHEdksøabeTAnwgbnÞHEdkRTnug EdkEkg (angle shape) RtUv)aneRbIedIm,IbMElgbnÞúkcenøaHFatuTaMgBIr. RbsinebIeKbEnßmbnÞHEdkBIelI mYyeTot enaHplitplsMercnwgmanlkçN³kan;Ets μ úKsμaj. b:uEnþkartP¢ab;edaykarpSarmanlkçN³ gayRsYlCag. b:uEnþsRmab;tMNpSar eKRtUvkarkm μkrCMnajxagpSar ehIyvaBi)akkñúgkarGegát nig cMNayR)ak;eRcIn. EtKuNvibtþienHeKGacedaHRsay)anedaykarpSarenAkñúgeragCagCMnYs[kar pSarenAkardæanenARKb;eBlEdlGaceFVIeTA)an. enAeBlEdlkartP¢ab;eFVIeLIgedaybnSMénkarpSar nig b‘ULúg enaHeKeRcInpSarenAeragCag ehIycab;b‘ULúgenAkardæan. sRmab; single-plate beam-to-

column connectioction EdlbgðajenAkñúgrUbTI 7>2 bnÞHEdkRtUv)anpSarP¢ab;eTAnwgsøabrbs;ssrenA eragCag ehIycab;b‘ULúgCamYynwgRTnugrbs;FñwmenAkardæan.

edIm,IBicarNaBIkarRbRBwtþeTAénRbePTepSg²rbs;tMN eKRtUvEbgEckvaeTAtamRbePTénkar

dak;bnÞúk. rUbTI 7>3 a bgðajBI tension member lap splice EdlmaneRKOgP¢ab;rgnUvkmøaMgkat;. dUc Kña tMNpSarenAkñúgrUbTI 7>3 b RtUvTb;Tl;nwgkmøaMgkat;TTwg. tMNrbs; bracket eTAnwgsøabssr



dUckñúgrUbTI 7>3 c edaykarpSar b¤edayb‘ULúg eFIV[eRKOgP¢ab; b¤TwkbnSarrgnUvkmøaMgkat;enAeBl EdlbnÞúkGnuvtþmkelIva. tMNBÜürEdlbgðajenAkñúgrUbTI 7>3 d dak;[eRKOgP¢ab;rgkmøaMgTaj. kartP¢ab;EdlbgðajenAkñúgrUbTI 7>3 e begáItTaMgkmøaMgkat;TTwg nigkmøaMgTajenAkñúgeRKOgP¢ab;CYr xagelI. ersIusþg;rbs;eRKOgP¢ab;KWGaRs½yelIfaetIvargnUvkmøaMgkat; b¤kmøaMgTaj b¤k¾kmøaMgTaMgBIr. karpSarmankmøaMgexSaysRmab;kugRtaMgkmøaMgkat; ehIyCaTUeTAvaRtUv)ansnμt;fadac;edaykmøaMgkat; edayminKitBITisedAénkardak;bnÞúk.

enAeBlEdlkmøaMgkñúgeRKOgP¢ab;mYy b¤kmøaMgkñúgmYyÉktþaRbEvgrbs;TwkbnSarRtUv)ankMNt;

vaCaerOgmYyEdlgayRsYlkñúgkarkMNt;PaBRKb;RKan;rbs;tMN. karkMNt;enHQrelIeKalkarN_én



kartP¢ab;cMbgBIr. RbsinebIExSskm μrbs;kmøaMgpÁÜbEdlRtUvTb;Tl;kat;tamTIRbCMuTm¶n;rbs;tMN enaH EpñknImYy²rbs;tMNRtUv)ansnμt;faTb;Tl;nwgbnÞúkEdlEbgEckesμ I ehIytMNEbbenHRtUv)aneK[ eQ μaHfa tMNsamBaØ. enAkñúgtMNEbbenH ¬EdlbgðajenAkñúgrUbTI 7>3 a nig b¦ eRKOgP¢ab;nImYy² nigRbEvgÉktþrbs;TwkbnSarnwgTb;Tl;nUvkmøaMgesμ IKña*. bnÞab;mkeKGacrklT§PaBTb;Tl;bnÞúkrbs; tMNedayKuNlT§PaBTb;Tl;kmøaMgrbs;eRKOgP¢ab;nImYy² b¤RbEvgÉktþarbs;TWkbnSar CamYynwgcMnYn eRKOgP¢ab;srub b¤RbEvgsrubrbs;TwkbnSar. kartP¢ab;énkmøaMgcakp©it RtUv)anerobrab;enAkñúgCMBUkTI 8 EdlExSskmμrbs;bnÞúkmineFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;tMN. kartP¢ab;enAkñúgrUbTI 7>3 d nig e Ca RbePTéntMNenH. kñúgkrNIenHbnÞúkRtUv)anTb;Tl;esμ IKñaedayeRKOgP¢ab;nImYy² b¤RbEvgÉktþarbs;Twk bnSareT ehIykarkMNt;énkarEbgEckbnÞúkKWCaktþad¾sμ úKs μajkñúgkarKNnaénRbePTtMNenH.

AISC Specification erobrab;BIkartP¢ab;EdlrYmman b‘ULúg rIev nig karpSarenAkñúg Chapter

J, ”Connections, Joints and Fasteners”. EtenAkñúgesovePAenH eyIgmin)anBicarNaBItMNrIeveT. 7>2> Bolted Shear Connections: Failure Mode

munnwgBicarNaBIersIusþg;Cak;lak;rbs;b‘ULúg eyIgRtUvBicarNaBIrebobénkardac;EdlGacekIt manenAelItMNEdlmaneRKOgP¢ab;rgkmøaMgkat;TTwg. eKmanrebobénkardac;FMBIr³ kardac;rbs;eRKOg P¢ab; nigkardac;rbs;EpñkEdlRtUvP¢ab;. BicarNa lap joint EdlbgðajenAkñúgrUbTI 7>4 a. kardac;rbs; eRKOgP¢ab;GacRtUv)ansnμt;fanwgekIteLIgdUcEdl)anbgðaj. kmøaMgkat;TTwgmFümenAkñúgkrNIenHKW

* Cak;EsþgvamancMNakp©ittUcenAkñúgtMNTaMgBIrenH EtvaRtUv)anecal



4/2dP

APfv

π==

Edl P CabnÞúkEdlmanGMeBIelIeRKOgP¢ab;nImYy² A CaRkLaépÞmuxkat;rbs;eRKOgP¢ab; nig d CaGgát; p©itrbs;va. enaHbnÞúkenHGacsresrCa AfP v= eTaHbICakardak;bnÞúkkñúgkrNIenHmincMcMNucl¥k¾eday k¾cMNakp©itmantémøtUcEdlGacecal)an. kar tenAkñúgrUbTI 7>4 b manlkçN³RsedogKña EtkarviPaKdüaRkamGgÁesrIrbs;eRKOgP¢ab;bgðajfamuxkat; nImYy²rgEtBak;kNþalbnÞúksrub b¤eKGacniyayfamuxkat;TaMgBIrTb;Tl;nUvkmøaMgsrub. kñúgkrNIenH kmøaMg AfP v2= ehIybnÞúkenHRtUv)aneKehAfa double shear. karbEnßmbnÞHenAkñúgkartnwgbegáIn cMnYnbøg;kat; ehIyvanwgkat;bnßykmøaMgenAkúñgbøg;nImYy². b:uEnþ vanwgbegáInRbEvgrbs;eRKOgP¢ab; ehIy vanwgrgkugRtaMgBt;. rebobénkadac;mYyeTotsRmab; shear connection Bak;B½n§nwgkardac;rbs;EpñkEdlRtUv)an P¢ab; ehIyCaTUeTAvaRtUv)anEbgEckCaBIrEpñk³ !> kardac;EdlbNþalBI karTaj kmøaMgkat; b¤m:Um:g;Bt;FMenAkñúgEpñkEdlRtUvtP¢ab;. RbsinebI Ggát;rgkarTajRtUv)antP¢ab; kmøaMgTajelI gross area nig effective net area RtUv)anGegát. GaRs½ynwgrUbragénkartP¢ab; block shear k¾RtUv)anBicarNa. eKk¾RtUvRtYtBinitü block shear enA kñúgkartP¢ab; beam-to-column ¬Edlmanerobrab;enAkñúgCMBUkTI 3 nigTI5 ehIyvak¾RtUv)anerobrab;enA kñúg AISC J4.3¦. GaRs½ynwgRbePTénkartP¢ab; nigkardak;bnÞúk ral;kartP¢ab;eTAnwg gusset plate nig framing angle TamTarnUvkarviPaKsRmab; kugRtaMgkat; kugRtaMgTaj kugRtaMgBt; nig block shear. karKNnakartP¢ab;rbs;Ggát;rgkarTajRtUv)aneFVIeLIgRsbKñaCamYynwgkarKNnaGgát;rgkarTajBI eRBaHdMeNIrkarTaMgBIrenHTak;TgKñaeTAvijeTAmk.

@> kardac;rbs;EpñkEdlRtUvP¢ab;edaysar bearing EdlbegáIteLIgedayeRKOgP¢ab;. RbsinebI RbehagmanTMhMFMCageRKOgP¢ab;bnþicbnþÜc ehIyeRKOgP¢ab;RtUv)ansnμt;faRtUv)andak;y:agENnenAkñúg Rbehag épÞb:HrvageRKOgP¢ab; nigEpñkEdlRtUvP¢ab;nwgekItmaneRcInCagBak;kNþalénbrimaRtrbs; eRKOgP¢ab;enAeBlEdlbnÞúkGnuvtþ. krNIenHRtUv)anbgðajenAkñúgrUbTI 7>5. kugRtaMgnwgERbRbYlBI GtibrmaenARtg; A eTAsUnüenARtg; B . edIm,IgayRsYl eKeRbIkugRtaMgmFümEdlRtUv)anKNna edayEckkmøaMgnwgépÞRbeyalb:H.



dUcenH bearing stees RtUv)anKNnaeday ( )dtPf p /= Edl P CakmøaMgEdlGnuvtþ mkelIeRKOgP¢ab;/ d CaGgát;p©iteRKOgP¢ab; nig t CakRmas;rbs;EpñkEdlrgnUv bearing. dUcenH bearing load KW dtfP p= karKNna bearing GacmanlkçN³sμ úKsμajedaysarvtþmanrbs;b‘ULúgEdlenAEk,r b¤eday sarcm¶ayBIrn§eTARCugEKmkñúgTisedArbs;bnÞúkmancm¶ayxøI dUcbgðajenAkñúgrUbTI 7>6. KMlatrvagb‘U Lúg nigcm¶ayBIrn§eTARCugEKmman\T§iBlelI bearing strength.

7>3> Bearing Strength, Spacing and Edge-distance Requirements Bearing strength minTak;TgnwgRbePTrbs;eRKOgP¢ab;eT BIeRBaHkugRtaMgEdlRtUvBicarNasßit enAelIEpñkEdlRtUvP¢ab; minEmnenAelIeRKOgP¢ab;eT. sRmab;mUlehtuenH bearing strength k¾dUcCag



tRmUvkarKMlat nig edge-distance k¾minTak;TgnwgRbePTeRKOgP¢ab;Edr ehIyvaRtUv)anBicarNamunkug RtaMgkat;kñúgb‘ULúg nigersIusþg;Taj. karpþl;[rbs; AISC Specification sRmab; bearing strength k¾dUcCatRmUvkarepSg²sRmab; b‘ULúgersIusþg;x<s; KWQrelIkarpþl;[rbs; specification of the Research Council on Structural

Connections of the Engineering Foundation (RCSC, 1994). kare)aHBum<pSayf μ I²rbs;ÉksarenH minTan;CaEpñkrbs; AISC Specification (AISC, 199a) EtvaRtUv)aneRbIenAkñúgesovePAenH drabNa manlkçN³minRtUvKña eKnwgeRbIkarpþl;[eday AISC. enAeBlsmIkarenAkñúg RSCS Specification RtUv)anbgðajelxsmIkarmkBIÉksarenaHnwgRtUv)aneRbI ¬]TahrN_/ RCSC Equation LRFD 4.3¦. karerobrab;xageRkam EdlQrelI Commentary EdlENnaMeday RCSC Specification nwgBnül;BI eKalkrN_rbs;smIkar RCSC sRmab; bearing strength. rebobdac;EdlGacekItmanEdl)anBI bearing FM KWkmøaMgkat;rEhk (shear tear-out) enAxag cugrbs;FatuEdlRtUvtP¢ab; dUcbgðajenAkñúgrUbTI 7>7 a. RbsinebIépÞdac;manlkçN³l¥dUcrUbTI 7>7 b,

failure load enAelIépÞmYyénépÞTaMgBIres μ Inwg shear fracture stress KuNnwgRkLaépÞkat; b¤ tLFR

cun 6.0

2=

Edl =uF6.0 shear fracture strees rbs;EpñkEdlRtUvP¢ab; =cL cm¶ayBIRCugEKRmbs;RbehageTAcugrbs;EpñkEdlRtUvP¢ab; =t kRmas;rbs;EpñkEdlRtUvP¢ab; ersIusþg;srubKW ( ) tLFtLFR cucun 2.16.02 == ¬&>!¦

kmøaMgkat; tear-out enHekItmanenAxagcugrbs;EpñkEdlRtUvtP¢ab; dUcEdlbgðaj b¤enAcenøaH rn§BIrkñúgTisedAén bearing load. edIm,IkarBarsac;lUtFMrbs;Rbehag eKRtUvkMNt;EdnkMNt;x<s;bMput rbs; bearing load Edl[edaysmIkar &>!. EdkkMNt;enHsmamaRteTAnwg fracture stress KuNnwg

bearing area b¤ dtCFFCR uun =××= area bearing ¬&>@¦ Edl =C témøefr =d Ggát;p©itb‘ULúg



=t Ggát;rbs;EpñkEdlRtUvtP¢ab;

RCSC Specification eRbIsmIkar &>! sRmab; bearing strength RbQmnwgEdnkMNt;Edl[eday smIkar &>@. RbsinebIeKminKitkMhUcRTg;RTay témøefr C Gacykesμ Inwg 0.3 . RbsinebIkMhUcRTg; RTayFMRtUv)anKit C Gacykesμ Inwg 4.2 ehIyCaTUeTAvaCatémøEdleKykmkeRbI. témøenHRtUvKñanwg sac;lUtrbs;RbehagRbEhl mmin 6.4/1 = ¬RCSC, 1994¦. enAkñúgesovePAenH eyIgBicarNa kMhUcRTg;RTaysRmab;karKNna. RCSC bearing strength sRmab;b‘ULúgeTalGacRtUv)ansMEdgCa

nRφ Edl 75.0=φ nig uucn dtFtFLR 4.22.1 ≤= ¬RCSC Equation LRFD 4.3¦ Edl =cL clear distance enAkñúgTisRsbnwgbnÞúkEdlGnuvtþ BIcugénrn§b‘ULúgeTARCugEKmrbs;rn§Edl

enAEk,r b¤eTARCugEKmrbs;smÖar³. =t kRmas;rbs;eRKOgP¢ab; =d Ggát;p©itb‘ULúg ¬minEmnGgát;p©itrbs;RbehageT¦ =uF ultimate tensile stress rbs;EpñkEdlRtUvP¢ab; ¬minEmnrbs;b‘ULúg¦

rUbTI 7>8 bgðajbEnßmeTotBIcm¶ay cL . enAeBlEdlKNna bearing strength sRmab;b‘ULúg eKRtUv BicarNacm¶ayBIb‘ULúgenaHeTAb‘ULúgEdlenAEk,r b¤eTARCugEKmkñúgTisedArbs; bearing load elIEpñk



EdlRtUvP¢ab;. sRmab;krNIEdl)anbgðaj bearing load sßitenAEpñkxageqVgrbs;rn§nImYy². dUcenH ersIusþg;sRmab;b‘ULúg ! RtUv)anKNnaCamYy cL Edlvas;eTAb‘ULúg @ ehIyersIusþg;sRmab;b‘ULúg @ RtUv)anKNnaCamYy cL Edlvas;eTARCugEKmrbs;EpñkEdlRtUvP¢ab;.

RCSC Equation LRFD 4.3 mantémøsRmab; standard, oversized, short-slotted and long

slotted holes CamYynwg slot EdlRsbeTAnwgbnÞúk. eyIgeRbIEt standard holes enAkñúgesovePAenH ¬RbehagEdlmanGgát;p©itFMCagGgát;p©itb‘ULúg mmin 2.16/1 = ¦.

enAeBlEdlKNnacm¶ay cL eRbIGgát;p©itRbehagCak;Esþg nigmincaM)ac;bUkbEnßm mm2 dUc EdlRtUvkarenAkñúg AISC B.2 sRmab;KNna net area rbs;Ggát;rgkarTaj. müa:gvijeTot eRbIGgát; p©it mmdind 2.16/1 +=+ minEmn mmdind 4.8/1 +=+ . RbsinebI h bgðajBIGgát;p©itRbehag enaH

.16/1 indh += karKNnarbs; bearing strength BI RCSC Equation LRFD 4.3 GacRtUv)ansRmYlxøHdUcxageRkam. EdnkMNt;nwgmanRbsiT§PaBenAeBl uuc dtFtFL 4.22.1 = b¤ eRkayeBlEdlsRmYlehIy dLc 2= TMnak;TMngenHGacRtUv)aneRbIedIm,IKNnaenAeBlEdlEdnkMNt; udtF4.2 lub³ RbsinebI dLc 2≤ eRbI tLFR cun 2.1= RbsinebI dLc 2> eRbI dtFR un 2.1=



Spacing and Edge-Distance Requirments edIm,IrkSacenøaHTMenrrvagex©Ab‘ULúg nigedIm,Ipþl;nUvTIFøaRKb;RKan;sRmab; wrench socket AISC

J3.3 tRmUvfaKMlatBIG½kSeTAG½kS (center-to-center spacing) rbs;eRKOgP¢ab; ¬enARKb;Tis¦ minRtUv tUcCag d3

22 ehIyCakarniymKWminRtUvtUcCag d3 Edl d CaGgát;p©iteRKOgP¢ab;. cm¶ayBIRCugEKm smÖar³ ¬RKb;Tis¦ Edlvas;BIG½kSrbs;Rbehag RtUv)an[enAkñúg AISC Table3.4 CaGnuKmn_eTA nwgTMhMrbs;b‘ULúg nigRbePTrbs;RCug ¬sheared, rolled or gas cut¦. KMlat nigcm¶ayeTARCugEKm EdlsMKal;eday s nig eL RtUv)anbgðajenAkñúgrUbTI 7>9.

Summary fo Bearing Strength, Spacing and Edge-Distance Requirements (standard hole)

a. Bearing strength: ( ) ( )uucn dtFtFLR 4.275.02.175.0 ≤=φ (RCSC Equation LRFD 4.3)

b¤ eyIgGacsresrmüa:geTot RbsinebI dLc 2≤ / ( )ucn tFLR 2.175.0=φ RbsinebI dLc 2> / ( )un dtFR 4.275.0=φ

b. KMlat nigsMgayeTARCugEKmGb,brma³ sRmab;RKb;Tis TaMgRsbnwgExSskmμ nigEkgnwgExS skmμ

ds 322≥ ¬CakareBjniym d3 ¦

≥eL témøBI AISC J3.4

sRmab; single- nig double-angle shapes CaTUeTA gage distances RtUv)an[enAkñúg Part 9 of

the Manual, Volume II (emIlEpñk 3>6)EdlGaceRbICMnYs[témøGb,brma.



]TahrN_ 7>1³ RtYtBinitü KMlatb‘ULúg nigcm¶ayeTARCugEKmsRmab;kartP¢ab;EdlbgðajenAkñúgrUbTI 7>10.

dMeNaHRsay³ BI AISC J3.3, KMlatGb,brmasRmab;RKb;TisTaMgGs;KW

.243667.22 3

2 ind =⎟⎠⎞

⎜⎝⎛=

KMlatCak;Esþg .2.5.2 inin >= (OK) cm¶ayeTARCugEKmGb,brmasRmab;RKb;TisTaMgGs;EdlTTYlBI AISC Table J3.4. RbsinebI

eyIgsnμt; sheared edges ¬krNIEdlGaRkk;CageK¦ enaHcm¶ayeTARCugEKmGb,brmaKW .1 41 in

dUcenH cm¶ayeTARCugEKmCak;Esþg .

411 in= (OK)

edIm,IKNna bearing strength eRbIGgát;p©itrn§ .

1613

161

43

161 indh =+=+=

RtYtBinitü bearing TaMgelIGgát;rgkarTaj nig gusset plate. sRmab;Ggát;rgkarTaj nigEdl enAEk,rRCugEKmrbs;Ggát;CageK

.8438.0216/1325.1

2inhLL ec =−=−=

( ) ( )uucn dtFtFLR 4.22.1 φφφ ≥= ( ) ( )( ) ( ) kipstFL uc 02.2258

218438.02.175.02.1 =⎟⎠⎞

⎜⎝⎛φ

( ) ( ) ( ) kipskipsdtFu 02.2215.395821

434.275.04.2 >=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=φ

dUcenHyk boltkipsRn /02.22=φ sRmab;rn§epSgeTot



.688.116135.2 inhsLc =−=−=

( ) ( )uucn dtFtFLR 4.22.1 φφφ ≤= ( ) ( )( ) ( ) kipstFL uc 06.4458

21688.12.175.02.1 =⎟⎠⎞

⎜⎝⎛=φ

( ) kipskipsdtFu 06.4415.394.2 <=φ dUcenHyk boltkipsRn /15.39=φ sRmab;Ggát;rgkarTaj bearing strength KW ( ) ( ) kipskipsRn 6512215.39202.222 >=+=φ (OK) sRmab; gusset plat nigrn§EdlenAEk,rRCugEKmrbs;bnÞHCageK .8438.0

216/1325.1

2inhLL ec =−=−=


838438.02.175.02.1 =⎟⎠⎞

⎜⎝⎛=φ

( ) ( ) ( )5883

434.275.04.2 ⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=udtFφ

kipskips 52.1636.29 >= dUcenHyk boltkipsRn /52.16=φ sRmab;rn§déTeTot .688.1

16135.2 inhsLc =−=−=


83688.12.175.02.1 =⎟⎠⎞

⎜⎝⎛=φ

( ) ( ) ( ) kipskipsdtFu 04.3336.295883

434.275.04.2 <=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=φ

dUcenHyk kipsRn 04.33=φ bearing strength sRmab; gusset plate KW ( ) ( ) kipsRn 8.9136.29252.162 =+=φ gusset plate man bearing strength tUcCag bearing strength rbs;Ggát; dUcenH gusset plate lub kipskipsRn 658.91 >=φ (OK)



cemøIy³ tRmUvkar bearing strength, KMlat nig cm¶ayeTARCugEKmmanlkçN³RKb;RKan;. KMlatb‘ULúg nigcm¶ayeTARCugEKmenAkñúg]TahrN_ 7>1 mantémødUcKñasRmab;Ggát;rgkarTaj nig gusset plate. vaxusKñaEtkRmas; dUcenH gusset plate lub. sRmab;krNIdUc]TahrN_enH eKRtYt BinitüEteRKOgbgÁúMNaEdlmankRmas;esþIgCag. b:uEnþRbsinebIcm¶ayeTAcugEKmmantémøxusKña dac;xat eKRtUvEtRtYtBinitüTaMgGgát;rgkarTaj nig gusset plate. 7>4> b‘ULúgFm μta (Common Bolts) eyIgcab;epþImkarerobrab;BIersIusþg;rbs;eRKOgP¢ab;CamYynwg b‘ULúgFmμta EdlxusKñaBIb‘ULúger-sIusþg;x<s;minRtwmEtlkçN³smÖar³b:ueNÑaHeT EfmTaMgkmøaMgrwtbNþwgb‘ULúgeTotpg. b‘ULúgFm μta Edl eKsÁal;Ca unfinished bols RtUv)ansMKal;Ca ASTM A307. Design shear strength rbs; A307 KW nRφ / EdlemKuNersIusþg; 75.0=φ ehIy nominal

shear strength KW bvn AFR = Edl =vF ultimate shearing stress

=bA RkLaépÞmuxkat;rbs;EpñkEdlKμaneFμjrbs;b‘ULúg ¬EdleKsÁal;Ca nominal bolt area b¤ nominal body area¦

Ultimate shearing stress RtUv)an[enAkñúg AISC Table J3.2 KW MPaksi 16524 = Edl [ nominal strength bbvn AAFR 24== ]TahrN_ 7>2³ kMNt; design strength rbs;kartP¢ab;EdlbgðajenAkñúgrUbTI 7>11 edayQrelI kmøaMgkat;TTwg nig bearing. dMeNaHRsay³ kartP¢ab;GacRtUv)ancat;cMNat;fñak;CatMNsamBaØ ehIyeRKOgP¢ab;mYy²RtUv)anBicar- NaedIm,ITb;Tl;karEbgEckkmøaMgesμIKña. kñúgkrNICaeRcInvamanlkçN³gayRsYlkñúgkarkMNt;ersIusþg; rbs;eRKOgP¢ab;mYy rYcbnÞab;mkKuNnwgcMnYneRKOgP¢ab;srub.



Shear strength: vaCakrNI single shear ehIy design shear strength rbs;b‘ULúgmYyKW ( )bbvn AAFR 2475.0== φφ Nominal bolt area KW ( ) 2

224418.0

44/3

4indAb ===

ππ dUcenH design shear strength sRmab;b‘ULúgmYyKW ( )( ) kipsRn 952.74418.02475.0 ==φ sRmab;b‘ULúgBIrKW ( ) kipsRn 9.15952.72 ==φ Bearing strength: edaysarcm¶ayeTARCugEKRmbs;Ggát;rgkarTaj nigrbs; gusset plate dUcKña enaH beaing strength rbs; gusset plate nwglub BIeRBaHkRmas;rbs;vaesþIgCagkRmas;rbs;Ggát;rgkarTaj. sRmab;karKNna bearing strength eRbIGgát;p©itRbehag .

1613

161

43

161 indh =+=+=

sRmab;rn§EdlenAEk,rRCugEKRmbs; gusset plate CageK .094.1

216/135.1

2inhLL ec =−=−=

.5.14322 ind =⎟⎠⎞

⎜⎝⎛=

edaysar dLc 2< ( ) ( )( ) ( ) kipstFLR ucn 42.2158

83094.12.175.02.1 =⎟⎠⎞

⎜⎝⎛== φφ

sRmab;rn§déTeTot .2.188.2

16133 ininhsLc >=−=−=



dUcenH ( ) ( ) kipsdtFR un 36.295883

434.275.0)4.2( =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛==φφ

Bearing strength sRmab;tMNKW kipsRn 8.5036.2942.21 =+=φ

Bearing strength enHFMCag shearing strength dUcenH shear strength lub ehIyersIusþg;rbs;tMNKW kipsRn 9.15=φ cMNaMfaRKb;tRmUvkarKMlat nigcm¶ayeTARCugEKmTaMgGs;RtUvEtRKb;RKan;. sRmab; sheared edge cm¶ayeTARCugEKmEdlTamTareday AISC Table J3.4 KW mmin 30.1 4

1 = ehIykarTamTarenHKW RKb;RKan;sRmab;TaMgTisbeNþay nigTisTTwg. KMlatb‘ULúgKW mmin 753 = EdlFMCag =d3

22 ( ) .2667.2 4

3 in= .

cemøIy³ edayQrelI shear nig bearing, design strength rbs;tMNKW kips9.15 . ¬cMNaMfa sßanPaB kMNat;déTepSgeTotEdlminTan;)anRtYtBinitüdUcCa kugRtaMgTajenAelI net area rbs;Ggát;Gacnwg CaGñkkMNt; design strength¦.

]TahrN_ 7>3³ r)arEdk .8/34 in× RtUv)aneRbICaGgát;rgkarTajedIm,ITb;Tl;nwg service dead load

kips8 nig service live load kips22 . Ggát;enHRtUv)anKNnaeRkamkarsnμt;fa b‘ULúg 307A Ggát; p©it .4/3 in mYyCYrRtUv)aneRbIedIm,IP¢ab;Ggát;enHeTA gusset plate EdlmankRmas; .8/3 in . TaMgGgát; rgkarTaj nig gusset plate CaEdk 36A . etIeKRtUvkarb‘ULúgb:unμanRKab;? dMeNaHRsay³ bnÞúkemKuNKW ( ) ( ) kipsLDPu 80.44226.182.16.12.1 =+=+= KNnalT§PaBrbs;b‘ULúgmYy. BI]TahrN_ 7>2 shear strength KW boltkipsRn /952.7=φ sRmab; bearing strength, eKminsÁal;KMlat nigcm¶ayeTARCugEKm dUcenHeyIgsnμt;fa EdnkMNt;

udtF4.2φ nwglub enaHeyIgTTYl)an ( ) ( ) boltkipsRn /36.2958

83

434.275.0 =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=φ



Bearing strength Cak;EsþgsRmab;tMNenHnwgGaRs½yelItémørbs; cL sRmab;b‘ULúgnImYy². enA eBl EdltémøenHRtUv)ankMNt;enAkñúgkarKNnacugeRkay enaH bearing strength RtUv)anRtYtBinitü eLIgvijb:uEnþ shear enAEtTMngCalub. cMnYnb‘ULúgEdlRtUvkarKW bolts

boltkipskips 63.5

/952.780.44

=

cemøIy³ eRbIb‘ULúg 307A Ggát;p©it .4/3 in cMnYnR)aMmYyRKab;. 7>5> b‘ULúgersIusþg;x<s; (High-Strength Bolts) b‘ULúgersIusþg;x<s;sRmab;tMNrbs;eRKOgbgÁúMmanBIry:agKW ASTM 325A nig ASTM 490A . karpþl;[rbs; AISC sRmab;ersIusþg;x<s;KWCaEpñkxøHrbs;karpþl;[rbs; specification of the

Research Council on Structural Connections of the Engineering Foundation (RCSC, 1994). b‘ULúg 490A man ultimate tensile strength FMCagb‘ULúg 325A ehIyRtUv)ankMNt;faman nominal strength FMCag. b‘ULúg 490A RtUv)andak;[eRbIR)as;ry³eBly:agyUrbnÞab;BIb‘ULúg

325A RtUv)aneRbICaTUeTA sRmab;eRbICamYyEdkEdlmanersIusþg;x<s; ¬Bethlehem, 1969¦. b‘ULúg 490A mantémøéføCag 325A b:uEnþCaTUeTAeKRtUvkarvacMnYnticCag.

kñúgkrNIxøH b‘ULúg 490A nig 325A RtUv)andMeLIgCamYynwgkRmittwgEdleFVI[BYkvargnUv kmøaMgTajFMEmnETn. ]TahrN_ kmøaMgTajdMbUgenAkñúgb‘ULúg 325A Ggát;p©it .8/5 in GacFMesμ Inwg

KNkips 8519 = . bBa¢IénkmøaMgTajGb,brmasRmab;tMNTaMgenaHRtUvkarRtUv)an[enAkñúg AISC

Table J3.1, Minimum Bolt Tension. témønImYy²esμ Inwg %70 énersIusþg;TajGb,brmarbs;b‘ULúg. eKalbMNgEdleKRtUvkarkmøaMgTajFMEbbenHKWedIm,ITTYl)ankmøaMgrwtEdlbgðajenAkñúgrUbTI 7>12. b‘ULúgEbbenHRtUv)aneKehAfa fully tensioned. enAeBlEdlex©ARtUv)anmYlP¢ab;eTAnwgb‘ULúg EpñkEdlRtUvP¢ab;rgnUvkmøaMgsgát; ehIyb‘ULúglUt. düaRkaGgÁesrI (free body diagram) enAkñúgrUbTI 7>12 a bgðajfakmøaMgsgát;srubEdlmanGMeBIelI EpñkEdlRtUvP¢ab;es μ InwgkmøaMgTajenAkñúgb‘ULúg. RbsinebIeKGnuvtþkmøaMgxageRkA P kmøaMgkkitnwg ekItmanenAcenøaHEpñkP¢ab;. kmøaMgGtibrmaEdlGacekItmanKW NF μ=



Edl μ CaemKuNkkitsþaTicrvagEpñkEdlRtUvP¢ab; ehIy N CakmøaMgsgát;EdlmanGMeBIenAelIépÞxag kñúg. témørbs; μ GaRs½ynwglkçxNÐépÞrbs;Edk ]TahrN_dUcCa épÞrbs;vamanlabfñaM b¤manERcHsIu. dUcenHb‘ULúgnImYy²enAkñúgkartP¢ab;RtUvmanlT§PBedIm,ITb;Tl;nwgbnÞúk FP = . RbsinebIkmøaMgkkit minFM vanwgminman bearing b¤ shear. RbsinebI P FMCag F slip ekIteLIg enaH shear nig bearing nwg CH\T§iBldl;lT§PaBrbs;tMN.

kardMeLIg (Installation)

etIeKTTYl)ankmøaMgTajFMEdlmanPaBsuRkitedayrebobNa? bc©úb,nñeKmanviFIsaRsþEdl GnuBaØat[cMnYnbYnsRmab;kardMeLIgb‘ULúgersIusþg;x<s; (RCSC, 1994).

!> Turn-of-the-nut method. viFIenHQrelIlkçN³bnÞúk-kMhUcRTg;RTay (load-deforma-

tion characteristic) rbs;eRKOgP¢ab; nigEpñkEdlRtUvP¢ab;. ex©AEdlmYlP¢ab;eTAnwgb‘ULúgGaceFVI[ b‘ULúg lUtsac;. TMnak;TMng stress-strain sRmab;smÖar³b‘ULúgGacRtUv)aneRbIedIm,IKNnakmøaMgTaj



enAkñúgb‘ULúg. dUcenHsRmab;RKb;TMhM nigRbePTrbs;b‘ULúg cMnYnCMumYlex©AEdlRtUvkaredIm,IbegáItkmøaMg TajGacRtUv)anKNna. Table 5 enAkñúg high-strength bolt specification (RCSC, 1994) [nUvcMnYn CMurbs;ex©AEdlRtUvkarsRmab;TMhMepSg²rbs;b‘ULúgkñúgTMrg;pleFobRbEvgelIGgát;p©it. viFIsaRsþenHeK eRbI ordinary spud wrench.

@> Calibrated wrench tightening. kñúgviFIsa®sþenHeKRtUveRbI torque wrench. kmøaMgrmYl EdlRtUvkaredIm,ITTYlkmøaMgTajkMNt;enAkñúgb‘ULúgRtUv)ankMNt;edaykarrwtbNþwgb‘ULúgenHCamYy]bkrN_EdlbgðajkmøaMgTaj.

#> Alternated wrench bolts. eKRtUvkar wrench BiessedIm,IdMeLIgb‘ULúg. karRtYtBinitükar gardMeLIgenHmanlkçN³gayRsYlCaBiess.

$> Direct tension indicators. smÖar³EdleKniymeRbIenAkñúgviFIsaRsþenHKW washer Edlman protrusion enAelIépÞrbs;va. enAeBlEdleKrwtb‘ULúg protrusion rgnUvkmøaMgsgát;EdlsmamaRteTA nwgkmøaMgTajenAkñúgb‘ULúg.

7>6> Shear Strength of High-Strength Bolts Design shear strength rbs;b‘ULúg 325A nig 490A KW nRφ EdlemKuNersIusþg; 75.0=φ . dUc Kñanwgb‘ULúgFm μtaEdr nominal shear strength rbs;b‘ULúgersIusþg;x<s;RtUv)an[eday ultimate

shearing stress KuNnwg nominal bolt area. Etb‘ULúg 307A mindUcb‘ULúg 325A nig 490A Rtg; shear

strength rbs;b‘ULúgersIusþg;x<s;GaRs½ynwgeFμjrbs;b‘ULúgsßitenAkñúgbøg;kat;b¤ minsßitenAkñúgbøg;kat;. edIm,IsRmYlkñúgkareRbI reduced cross-sectional area enAeBlEdlEpñkEdlmaneFμjrgnUvkmøaMgkat; TTwg enaH ultimate shearing stress rbs;vaRtUvKuNnwg 75.0 EdlCapleFobRbhak;RbEhlénRkLa épÞEdlmaneFμj elIRkLaépÞEdlKμaneFμj. ersIusþg;RtUv)an[enAkñúg AISC Table J3.2 ehIyRtUv)an segçbenAkñúgtarag 7>1 . AISC Table J3.2 sMedAeFμjenAkñúgbøg;kat;Ca “not excluded from shear

planes” ehIysMedAeFμjEdlminenAkñúgbøg;kat;Ca “excluded from shear planes”. RbePTTImYy eFμjsßitenAkñúgbøg;kat; eKsMedACaRbePTtMN “N” ehIyb‘ULúg 325A énRbePTenHGacsmÁal; eday

NA −325 . karsMKal; “X” GacRtUv)aneRbIedIm,IbgðajfaeFμjminsßitenAkñúgbøg;kat;eT ]TahrN_ XA −325 .



tarag 7>1 Nominal shear strength

bvn AFR = eRKOgP©ab; US IS

325A / eFμjenAkñúgbøg;kat; bA48 bA330 325A / eFμjminenAkñúgbøg;kat; bA60 bA415 490A / eFμjenAkñúgbøg;kat; bA60 bA415 490A / eFμjminenAkñúgbøg;kat; bA75 bA520

]TahrN_7>4³ kMNt; design strength rbs;tMNEdlbgðajenAkñúgrUbTI 7>13. GegÁt bolt shear, bearing nig tensile strength rbs;Ggát;. b‘ULúgEdleRbICaRbePT 325A Ggát;p©it .8/7 in ehIyeF μj rbs;vaminsßitenAkñúgbøg;kat;. Ggát;CaRbePTEdk 572A Grade 50 .

dMeNaHRsay³ shear strength sRmab;b‘ULúgmYy ( ) 2

2.6013.0

48/7 inAb ==

π ( )( ) kipsAFR bvn 06.276013.06075.0 === φφ sRmab;b‘ULúgbI ( ) kipsRn 2.8106.273 ==φ Bearing strength³ sRmab;karKNna bearing strength eRbIGgát;p©itrn§



.1615

161

87

161 indh =+=+=

RtYtBinitü bearing EdlekItmanTaMgelI Ggát;rgkarTaj nig gusset plate. sRmab;Ggát;rgkarTaj nigb‘ULúgEdlenAEk,rRCugEKmCageKrbs;Ggát; .7812.0

216/1525.1

2inhLL ec =−=−=

( ) .75.18/722 ind == edaysar dLc 2<

( ) ( )( ) ( ) kipstFLR ucn 85.2265217812.02.175.02.1 =⎟⎠⎞

⎜⎝⎛== φφ

sRmab;RbehagepSgeTot dinhsLc 2.812.1

161575.2 >=−=−=

dUcenH ( ) ( ) ( ) kipsdtFR un 19.516521

874.275.04.2 =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛== φφ

Bearing strength sRmab;Ggát;rgkarTajKW ( ) kipsRn 12519.51285.22 =+=φ KNna bearing strength rbs; gusset plate. sRmab;rn§EdlenAEk,rRCugEKRmbs; gusset CageK dinhLL ec 2.031.1

216/155.1

2<=−=−=

dUcenH ( ) ( )( ) ( ) kipstFLR ucn 62.226583031.12.175.02.1 =⎟⎠⎞

⎜⎝⎛==φφ

sRmab;RbehagdéTeTot dinhsLc 2.812.1

161575.2 >=−=−=

dUcenH ( ) ( ) ( ) kipsdtFR un 39.386583

874.275.04.2 =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛==φφ

Bearing strength rbs; gusset plate KW ( ) kipsRn 4.9992.38262.22 =+=φ Gusset plate man strength tUcCag dUcenH bearing strength sRmab;tMNKW kipsRn 4.99=φ RtYtBinitü tensile strength rbs;Ggát;rgkarTaj. Tension on the gross atea:



( ) kipsAFP gytnt 5.672135090.0 =⎟⎠⎞

⎜⎝⎛ ×==φφ

Tension on the net area: muxkat;TaMgGs;rbs;Ggát;RtUv)antP¢ab; dUcenHvaminman shear lag eT dUcenHeyIg)an ne AA = . eRbIGgát;Rbehag .0.1

81

87

81 indh =+=+=

Design strength KW ( ) ( ) ( )[ ] kipshwtFAFP guteutnt 8.480.113

216575.0 =−⎟⎠⎞

⎜⎝⎛=∑−== φφφ

karTajenAelI net section mantémøtUcCageK cemøIy³ Design strength rbs;tMNKW kips8.48 7>7> Slip-Critical Connections eKcat;cMNat;fñak;kartP¢ab;EdleRbIb‘ULúgersIusþg;x<s;Ca slip-critical connection b¤ bearing-

type connection. Slip-critical connection CakartP¢ab;EdleKminGnuBaØat[man slip EdlminRtUv FMCagkmøaMgkkit. sRmab; bearing-type connection eKGnuBØat[man slip ehIy shear nig bearing

ekIteLIgFm μta. enAkñúgRbePTeRKOgbgÁúMxøH CaBiesss<an kmøaMgEdlmanGMeBIelItMNGacekIteLIgCa lkçN³xYb. kñúgkrNIEbbenH fatigue rbs;eRKOgP¢ab;GackøayCaeRKaHfñak;RbsinebIeKGnuBaØat[man slip rYmCamYynwgkarekIteLIgsarcuHsareLIg enaHeKRtUvRtYtBinitü slip-critical connec-tion. enAkñúg eRKOgbgÁúMCaeRcIn eKGnuBaØat[man slip ehIy bearing-type connection RtUvEt RKb;RKan;. ¬b‘ULúg

307A RtUv)aneRbIsRmab;Et bearing-type connection¦. sRmab; slip-critical connection eKcaM)ac; RtUvEteFVIkardMeLIg[)anl¥ edIm,ITTYlnUvkmøaMgTajdMbUgRKb;RKan;dUcEdl)anerobrab;. AISC J1.11 erobrab;BIsßanPaBkMNt;Edlb‘ULúgersIusþg;x<s;RtUvEtmankmøaMgTajeBj. enAkñúg bearing-type

connection tRmUvkarcaM)ac;EtmYyKt;kñúgkardMeLIgb‘ULúgKWeKRtUvpþl;nUvkmøaMgTajRKb;RKan;edIm,I[épÞ b:HKñaGacTb;Tl;Kña)aneTAvijeTAmk. kardMeLIgenHbegáItnUv snug-tight condition Edl)anerobrab; enAkñúg turn-of-the-nut method. eTaHbICatamRTwsþI slip-critical connection minRbQmnwg shear nig bearing k¾eday k¾eKRtUv



Etman shear strength nig bearing strength RKb;RKan;sRmab;krNI overload EdlGaceFVI[ekItman slip. edIm,IkarBar slip eKRtUvmanEdnkMNt;sRmab; service load b¤ factored load. eTaHbICakar karBar slip mansar³sMxan;sRmab; serviceability requiremnent k¾eday k¾ AISC Specification GnuBaØat[ slip-critical strength GacQrelI service load b¤ factored load. dUcEdl)anerobrab;BIxagelI lT§PaBTb;nwg slip CaGnuKmn_énplKuNrvagemKuNkkitsþaTic nig normal force cenøaHEpñkP¢ab;. TMnak;TMngenHRtUv)anbgðajenAkñúg RCSC Specification Edl eyIgeRbIenATIenHsRmab; slip-critical connection (RCSC, 1994). Slip-critical strength rbs;tMN KW strRφ Edl 0.1=φ sRmab; standard hole ehIy sbmstr NNTR μ13.1= (RCSC Equation LRFD 5.3) Edl =μ mean slip coefficient ¬emKuNkkitsþaTic¦ 33.0= sRmab;épÞ Class A =mT kmøaMgTajrbs;eRKOgP¢ab;Gb,brmaEdl)anBI AISC Table J3.1 b¤ RCSC Table 4

=bN cMnYnb‘ULúgenAkñúgtMN =sN cMnYn slip plan ¬bøg;kat;¦ épÞ Class A CaépÞEdlmanEdkG‘uksIutenAépÞrbs;va. enAkñúg Specification manENnaMnUvRbePTépÞ CaeRcIneTot EtenAkñúgesovePAenH eyIgeRbIEtépÞ Class A Edlpþl;nUv slip coefficient tUcCageKbMput. Slip-critical design strength sRmab;b‘ULúgmYyén single shear KW ( ) ( )( ) ( )( )1133.013.10.113.1 msbmstr TNNTR == μφφ

kipsTm373.0=

]TahrN_ 7>5³ kartP¢ab;EdlbgðajenAkñúgrUbTI 7>14 eRbIb‘ULúg 325A Ggát;p©it .4/3 in EdleF μj rbs;vasßitenAkñúgbøg;kat;. eKminGnuBaØat[man slip. TaMgGgát;rgkarTaj nig gusset plate CaRbePT Edk 36A . kMNt; design strength. dMeNaHRsay³ Shear strength: sRmab;b‘ULúgmYy ( ) 2

2.4418.0

44/3 inAb ==

π ( )( ) kipsAFR bvn 90.154418.04875.0 ===φφ



sRmab;b‘ULúgbYnRKab; ( ) kipsRn 60.6390.154 ==φ Slip-critical strength: edaysareKminGnuBaØat[man slip enaHkartP¢ab;enHRtUv)ancat;Ca slip-

critical. BI AISC Table J3.1 kmøaMgTajkñúgb‘ULúgGb,brmaKW kipsTm 28= . BIsmIkar &>#/ ( ) bpltkipsTR mstr /4.1028373.0373.0 ===φ

sRmab;b‘ULúgbYn ( ) kipsRstr 6.414.104 ==φ Bearing strength: edaysarcm¶ayeTARCugEKmmanRbEvgdUcKña ehIy gusset palte esþIgCagr)ar enaH eyIgenwgeRbI gusset plate EdlmankRmas; .8/3 in edIm,IKNna bearing strength. Ggát;p©itRbehag .

1613

161

43

161 indh =+=+=

sRmab;RbehagEdlenACitRCugEKRmbs; gusset plate CageK .094.1

216/135.1

2inhLL ec =−=−=

.5.14322 ind =⎟⎠⎞

⎜⎝⎛=

edaysar dLc 2< ( ) ( )( ) ( ) boltkipstFLR ucn /42.2158

83094.12.175.02.1 =⎟⎠⎞

⎜⎝⎛==φφ

sRmab;déTeTot



dinhsLc 2.188.216133 >=−=−=

dUcenH ( ) boltkipsdtFR un /36.294.2 == φφ Bearing strength sRmab;kartMNKW ( ) ( ) kipsRn 10236.29242.212 =+=φ RtYtBinitü tensile strength rbs;Ggát;rgkarTaj karTajenAelI gross area: ( ) kipsAFP gytnt 2.97

2163690.0 =⎟⎠⎞

⎜⎝⎛ ×== φφ

karTajenAelI net area: muxkat;TaMgmUlrbs;Ggát;RtUv)antP¢ab; dUcenHvaKμan shear lag eT enaHeyIg TTYl)an ne AA = . Ggát;p©itRbehag .

87

81

43

81 indh =+=+=

Design strength KW ( ) ( ) kipshwtFAFP guteutnt 4.92

8726

215875.0 =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=∑−== φφφ

Block shear stredngth: failure block sRmab; gusset plate manTMhMdUcTMhMsRmab;Ggát;rgkarTaj Edr EtxusKñaRtg;kRmas; ¬rUbTI 7>14 b¦. Gusset plate EdlmankRmas;esþIgCagnwgmanersIusþg;tUc Cag. vaman shear-failure plane cMnYnBIr³ ( ) 2.375.35.13

832 inAgv =+×=

edaysarvaman 5.1 Ggát;p©itRbehagkñúgmYyCYredkrbs;b‘ULúg ( ) ( ) 2.391.2

875.15.13

832 inAnv =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+×=

sRmab;RkLaépÞrgkarTaj ( ) 2.125.13

83 inAgt ==

2.7969.0873

83 inAnt =⎟

⎠⎞

⎜⎝⎛ −=

AISC Equation J4-3a [ [ ] ( )( ) ( )[ ]7969.058375.3366.075.06.0 +=+= ntugvyn AFAFR φφ



[ ] kips3.8922.4690.7275.0 =+= AISC Equation J4-3b [

[ ] ( )( ) ( )[ ]125.136391.2586.075.06.0 +=+= gtynvyn AFAFR φφ [ ] kips8.9250.4021.8375.0 =+= tY fracture ¬EdlBak;B½n§nwg uF ¦ enAkñúgsmIkarTIBIrmantémøFMCagenAkñúgsmIkarTImYy dUcenH AISC Equation 4.3b lub. design strength sRmab; block shear kips8.92= kñúgcMeNamsßanPaBkMNt;TaMgGs;Edl)aneFVIkarGegát eyIgeXIjfaersIusþg;EdlRtUvKñanwg slip man témøtUcCageK. cemøIy³ Design strength rbs;tMNKW kips6.41 ]TahrN_ 7>6³ Ggát;rgkarTajkRmas; .8/5 in RtUv)antP¢ab;eTAnwg splice plate kRmas; .4/1 in cMnYnBIr dUcEdl)anbgðajenAkñúgrUbTI 7>15. bnÞúkEdl)anbgðajCabnÞúk service load. eKeRbIEdk

36A nig b‘ULúg 325A Ggát;p©it .8/5 in . RbsinebIeKGnuBaØat[man slip etIeKRtUvkarb‘ULúg b:unμanRKab;? G½kSrbs;b‘ULúgnImYy²EdlbgðajKWCaCYrrbs;b‘ULúgkñúgTisTTwgrbs;bnÞHEdk.

dMeNaHRsay³ Shear: sRmab; shear, norminal bolt area KW



( ) 22

.3068.04

8/5 inAb ==π

snμt;fa eFμjb‘ULúgsßitenAkúñgbøg;kat;. enaH design strength sRmab;b‘ULúgmYyKW ( )( )( ) kipsAFR bvn 09.2223068.04875.0shear of planes2 ==×= φφ Bearing: Beating force enAelIGgát;rgkarTajkRmas; .8/5 in nwgFMCag bearing force enAelI splice

plate kRmas; .4/1 in nImYy² BIrdg. edaysarbnÞúksrubenAelI splice plates es μInwgbnÞúkenAelIGgát; rgkarTaj enaH splice plate nwgmaneRKaHfñak;enAeBlEdlkRmas;srubrbs; splice plate esþIgCag kRmas;rbs;Ggát;rgkarTaj. eRbIGgát;p©itRbehag .

1611

161

85

161 indh =+=+=

sRmab;RbehagEdlenAEk,rRCugEKmCageK .156.1

216/115.1

2inhLL ec =−=−=

.25.18522 ind =⎟⎠⎞

⎜⎝⎛=

edaysar dLc 2< / bearing strength KW ( ) ( )( ) ( ) boltkipstFLR ucn /17.3058

41

41156.12.175.02.1 =⎟

⎠⎞

⎜⎝⎛ +==φφ

sRmab;rn§déTeTot dinhsLc 2.312.2

16113 >=−=−=

dUcenH ( ) ( ) ( ) boltkipsdtFR un /62.325841

41

854.275.04.2 =⎟

⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛==φφ

Shearing strength kñúgb‘ULúgmYyKWtUcCagtémø bearing TaMgBIr dUcenHersIusþg;rbs;tMNKW kips09.22 . bnÞúkemKuNKW ( ) ( ) kipsLDPu 70256.1252.16.12.1 =+=+= cMnYnb‘ULúgEdlRtUvkar

boltper loadload total

=

bolts17.309.22

70==

cemøIy³ eRbIb‘ULúgbYn EdlkñúgmYyCYrmanBIrRKab; enAelIRCugnImYy²rbs; splice. b‘ULúgcMnYn R)aMbI RKab;GacRtUvkarsRmab;kartP¢ab;enH.



]TahrN_ 7>7³ 136×C EdlbgðajenAkñúgrUbTI 7>16 RtUv)aneRCIserIsedIm,ITb;Tl;nwgbnÞúkTajem KuN kips108 . Ggát;enHRtUv)anP¢ab;eTAnwg gusset plate kRmas; .8/3 in CamYynwgb‘ULúg 325A Edl manGgát;p©it .8/7 in . ]bmafaeFμjrbs;b‘ULúgsßitenAkñúgbøg;énkmøaMgkat;TTwg ehIyeKGnuBaØat[man slip sRmab;kartP¢ab;enH. kMNt;cMnYn nigeFVIkarteRmobb‘ULúgy:agNaedIm,ITTYl)anRbEvgtP¢ab; h Gb,brma. eKeRbIEdk 36A .

dMeNaHRsay³ kMNt;lT§PaBrbs;b‘ULúgeTal kmøaMgkat;TTwg³ ( ) 2

2.6013.0

48/7 inAb ==

π ( )( ) kipsAFR bvn 65.216013.04875.0 === φφ bearing³ edaysarkRmas;rbs; gusset plate esþIgCaRTnugrbs;Edk channel dUcenH bearing

strength rbs; gusset plate nwgtUcCagEdk channel. snμt;faRbEvg cL EdlRsbnwgkmøaMgEdl GnuvtþmantémøFMCag d2 sRmab;b‘ULúgTaMgGs;. enaH ( ) ( ) ( ) kipsdtFR un 26.3458

83

874.275.04.2 =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛== φφ

enaH kmøaMgkat;TTwglub. dUcenH cMnYnb‘ULúgEdlRtUvkar 99.4

65.21108

== eTaHbICab‘ULúg 5 pþl;nUversIusþg;RKb;RKan;k¾eday k¾eKsakl,gb‘ULúg 6RKab;EdlGacerobCalkçN³ sIuemRTI edaymanb‘ULúg 3RKab;BIrCYr dUcbgðajenAkñúgrUbTI 7>17. ¬b‘ULúgBIrCYrRtUv)aneRbIedIm,I TTYl)anRbEvgtP¢ab;Gb,brma¦. eyIgmin)andwgfaetIkarKNnamuxkat;Ggát;rgkarTajenHQrelI



karsnμt;eRKOgP¢ab;b:unμanCYr dUcenHlT§PaBTb;karTajrbs;Edk channel CamYynwgb‘ULúgBIrCYrRtUv)an RtYtBinitümunnwgdMeNIrkarKNnakartP¢ab;bnþ.

karTajenAelI gross area: ( )( ) kipsAFP gynt 12483.33690.090.0 ===φ net area ( )( ) 2.96.2437.00.1283.3 inAn =−= edaysareyIgminTan;sÁal;RbEvgtP¢ab;BitR)akd dUcenHeyIgRtUveRbItémømFümrbs; U BI Commentary. ( ) 2.51.296.285.0 inUAA ne === kmøaMgTajenAelI net area ( )( ) kipsAFP eunt 10951.25875.075.0 ===φ ¬lub¦ dUcenH lT§PaBrbs;Ggát;rgkarTajKWQrelIb‘ULúgBIrCYr. RtYtBinitüKMlat nigRbEvgeTARCugEKmtamTisEkgnwgkmøaMg. BI AISC J3.3

KMlatGb,brma .33.287667.2 in=⎟⎠⎞

⎜⎝⎛=

BI AISC Table J3.4

RbEvgeTARCugEKmGb,brma .1 81 in=

KMlat .3in nigRbEvgeTARCugEKm .1 21 in nwgRtUv)aneRbIkñúgTisEkgnwgkmøaMg.

eKGackMNt;RbEvgtP¢ab;Gb,brmarbs;kartP¢ab;edayeRbIKMlat nigRbEvgeTARCugEKmGnuBaØat Gb,brmakñúgTisbeNþay ¬RsbnwgkmøaMg¦. KMlatGb,brmakñúgTisnImYy²KW .33.22 3

2 ind = . sakl,g .2 2

1 in . RbEvgeTARCugEKmGb,brmaKW .1 81 in . cm¶ayGb,brmaTaMgenHnwgRtUv)aneRbI



sRmab;epÞógpÞat; bearing strength rbs;kartP¢ab;. sRmab;karKNna bearing strength eKeRbIGgát;p©it rn§

.1615

161

87

161 indh =+=+=

sRmab;RbehagEdlenAEk,rRCugEKmrbs; gusset plate CageK .6562.0

216/15125.1

2inhLL ec =−=−=

( ) .75.18/722 ind == edaysar dLc 2< bearing strength KW

( ) ( )( ) ( ) boltkipstFLR ucn /85.1258836562.02.175.02.1 =⎟⎠⎞

⎜⎝⎛== φφ


16155.2 <=−=−=

dUcenH ( ) ( )( ) ( ) boltkipstFLR ucn /58.305883562.12.175.02.1 =⎟⎠⎞

⎜⎝⎛== φφ

Bearing strength srubsRmab;kartP¢ab;KW ( ) ( ) kipsPkipsR un 10814858.30485.122 =>=+=φ (OK)

rUbTI 7>18 bgðajBIkartP¢ab;sakl,gsRmab;RtYtBinitüemIl block shear enAkñúg gusset

plate ¬sRmab;ragGrNImaRtén failure block enAkñúgEdl channel KWdUcKña b:uEnþ gusset plate man kRmas;esþIgCag¦.

Shear areas:

( )( ) 2.594.42125.15.25.283 inAgv =++=



ehIyedaysarEtvamanRbehag 5.2 enAtamépÞkat;nImYy² ( )[ ]( ) 2.719.220.15.2125.6

83 inAnv =−=

Tension area

( ) 2.125.1383 inAgt ==

ehIy ( ) 2.75.00.1383 inAnt =−=

RtYtBinitüsRmab; tension yield nig shear fracture CamYynwg AISC Equation J4-3a:

[ ]ntugvyn AFAFR += 6.0φφ ( )( ) ( )[ ] [ ] kips0.10750.4323.9975.075.058594.4366.075.0 =+=+=

RtYtBinitüsRmab; tension fracture nig shear yield CamYynwg AISC Equation J4-3b: [ ]gtynvun AFAFR += 6.0φφ

( )( ) ( )[ ] [ ] kips3.10150.4062.9475.0125.136719.2586.075.0 =+=+= tY fracture ¬tYEdlBak;B½n§nwg uF ¦ enAkñúgsmIkarTIBIrmantémøFMCagtY fracture enAkñúgsmIkarTImYy dUcenH smIkarTIBIrlub. Design strength sRmab; block shear kipskips 1083.101 <= (N.G.)

viFIEdlsamBaØbMputkñúgkarbegáIn block shear strength sRmab;kartP¢ab;enHKWbegáIn shear area eday begáInKMlatb‘ULúg. RbsinebIeKbegáInKMlat AISC Equation J4-3b enAEtlubdEdl. ebIeTaHbICaKM latEdlRtUvkarGackMNt;eday trial and error k¾eday k¾eKGacedaHRsayedaypÞal;dUcEdleyIg nwgeFVIenATIenH. BI AISC Equation J4-3b, eK[ ( )[ ] kipsAnv 10850.40586.075.0 =+ dUcenHeKRtUvkar 2.974.2 inAnv = ( )( ) 2.974.225.2125.12

83 insAnv =−+=

dUcenH .67.2 ins = yk .3ins =

CamYynwgKMlat .3in net shear area KW ( )( ) 2.469.325.2125.133

83 inAnv =−++=

ehIy block shear strength BI AISC Equation J4-3b KW



[ ]gtynvun AFAFR += 6.0φφ ( )( ) ( )[ ] [ ] kips9.12050.407.12075.0125.136469.3586.075.0 =+=+=

edayeRbIKMlat nigRbEvgeTARCugEKmEdl)ankMNt; dUcenHRbEvgGb,brmaKW inh 5.8125.132125.1 =+×+= cemøIy³ eRbIkartP¢ab;lMGitEdlbgðajenAkñúgrUbTI 7>19.

karteRmobb‘ULúgenAkñúg]TahrN_ 7>7 manlkçN³sIuemRTIeFobnwgG½kSRsbnwgG½kSTIRbCMu Tm¶n;. dUcenHkmøaMgpÁÜbEdlTb;Tl;kmøaMgEdlpþl;[edayeRKOgP¢ab;k¾eFVIGMeBItamG½kSenH ehIyrag FrNImaRt enHRtUvKñanwgkartP¢ab;samBaØ. RbsinebIeKRtUvkarcMnYnb‘ULúgess ehIyeKeRbIBIrCYr vanwg minmanPaBsIuemRTIeT ehIykartP¢ab;nwgmanlkçN³cakp©it. kñúgkrNIEbbenH GñkKNnamuxkat;nwg manCeRmIseRcIn³ ¬!¦ minKitcMNakp©it edaysnμt;fa\T§BlenHGacecal)an/ ¬@¦ KitcMNakp©it/ ¬#¦ eRbIkartM erobqøas; (staggered pattern) EdlGacrkSanUvPaBsIuemRTI/ b¤ ¬$¦ bEnßmcMnYnb‘ULúgedIm,I TTYl)ankarteRmobEdlmanlkçN³sIuemRTI. visVkrPaKeRcInRbEhlCanwgeRCIserIsCeRmIscugeRkay. ]TahrN_ 7>8³ Ggát;rgkarTajRbEvg ft13 nigkartP¢ab;rbs;vaRtUv)anKNnasRmab; service dead

load kips8 nig service live load kips22 . eKminGnuBaØat[man slip sRmab;kartP¢ab;enHeT. Ggát;enHRtUv)antP¢ab;eTAnwg gusset plate kRmas; .8/3 in dUcbgðajenAkñúgrUbTI 7>20. eRbIEdkEkg eTal (single angle) sRmab;Ggát;rgkarTaj. eRbIb‘ULúg 325A nigEdk 572A grade

50sRmab;Ggát;rgkarTaj nig gusset plate.



dMeNaHRsay³ bnÞúkemKuNEdlRtUvTb;Tl;KW ( ) ( ) kipsLDPu 8.44226.182.16.12.1 =+=+= edaysarTMhMb‘ULúg nigkarteRmobb‘ULúgCH\T§iBldl; net area rbs;Ggát;rgkarTaj eyIgnwgcab;epþIm CamYynwgkareRCIserIsb‘ULúg. yuT§saRsþKWkareRCIserIssRmab;karsakl,g/ kMNt;cMnYnb‘ULúgEdlRtUv kar/ rYcbnÞab;mksakl,gTMhMepSgeTotRbsinebITMhMEdl)ansakl,gFMeBk b¤tUceBk. Ggát;p©itb‘U LúgsßitenAcenøaHBI mmin 13.2/1 ≈ eTA mmin 38.1 2

1 ≈ edayekIneLIgmþg mmin 3.8/1 ≈ sakl,gb‘ULúg .8/5 in . Nominal bolt area KW ( ) 2

2.3068.0

48/5 inAb ==

π Shear strength KW ( ) ( )( )3068.04875.04875.0 === bbvn AAFR φφ

boltkips /04.11= ¬edaysnμt;faeFμjsßitenAkñúgbøg;kat;¦ edayeKminGnuBaØat[man slip dUcenHkartP¢ab;enHCa slip-critical. eyIgsnμt;épÞ Class A ehIy sRmab;b‘ULúgGgát;p©it .8/5 in kmøaMgTajGb,brmaKW kipsTm 19= ¬BI AISC Table J3.1). BI RCSC

Equation LRFD 5.3, slip critical strength sRmab;b‘ULúgeTalKW ( ) ( )( )( )( )( ) boltkipsNNTR sbmstr /085.7111933.013.10.113.1 === μφφ eday slip-critical strength tUcCag shear strength dUcenH slip-critical strength lub. eyIgnwgkM Nt;cMnYnb‘ULúgedayQrelI slip-critical strength ehIyRtYtBinitü bearing bnÞab;BIeRCIserIsGgát; ¬edaysar bearing strength minGackMNt;)an Tal;EteKsÁal;kRmas;Ggát;sin¦. dUcenH cMnYnb‘ULúg

boltper loadload total

= bolts3.67.08544.8

==



dUcenHeKRtUvkarb‘ULúgy:agtic 7 RKab;. RbsinebIeKeRbIBIrCYr eKRtUvbEnßmb‘ULúgmYyRKab;edIm,IrkSaPaB sIuemRTI. rUbTI 7>21 bgðajBIkarteRmobb‘ULúgEdlmanCaeRcInTRmg;. karteRmobb‘ULúgTaMgenHeKGaceRbI)anTaMgGs; EtRbEvgénkartP¢ab;GacRtUv)ankat;bnßyedayeRbITMhM b‘ULúgFM nigcMnYntic. sakl,gb‘ULúgEdlmanGgát;p©it .8/7 in . Nominal bolt area KW

( ) 22

.6013.04

8/7 inAb ==π

Shear strength KW ( ) ( )( )6013.04875.04875.0 == bn ARφ

boltkips /65.21= ¬edaysnμt;faeFμjsßitenAkñúgbøg;kat;¦ kmøaMgTajGb,brmasRmab;b‘ULúg 325A Ggát;p©it .8/7 in KW kipsTm 39= dUcenH slip-critical

strength KW ( )( )( )( )( ) boltkipsNNTR sbmstr /54.14113933.013.10.1)13.1( === μφφ ¬lub¦

eKRtUvkarb‘ULúgEdlmanGgát;p©it .8/7 in cMnYn bolts1.3

54.148.44=

dUcenHeyIgeRbIb‘ULúg 325A EdlmanGgát;p©it .8/7 in cMnYn 4 RKab;. BI AISC J3.3, KMlatGb,brmaKW .33.2

87667.2667.2 inds =⎟⎠⎞

⎜⎝⎛== ¬b¤sRmab;karniym/ .62.2

8733 ind =⎟⎠⎞

⎜⎝⎛= ¦

BI AISC Table J3.4, cm¶ayeTARCugEKmKW .5.1 inLe = ¬edaysnμt; sheared edges¦



edaysakl,gkarteRmobdUcbgðajenAkñúgrUbTI 7>22 eRCIserIsGgát;rgkarTaj. Gross area Edl RtUvkarKW ( )

2.996.0509.08.44

9.0in

FPA

y

ug ==≥

Effective net area EdlRtUvkarKW ( )

2.9190.03675.08.44

75.0in

FPA

y

ue ==≥

edaysar effective net area KW ne UAA = / net area EdlRtUvkarKW

UrequiredAA e

n = BIkarteRmobb‘ULúgEdlbgðajenAkñúgrUbTI 7>22/ CamYynwgb‘ULúgeRcInCagBIrkñúgTisénkmøaMgEdlGnuvtþ témømFümrbs; U BI Commentary to the AISC Specification KW 85.0 . ¬enAeBlEdleKeRCIserIs Ggát;rYcehIy eKGackMNt;témø U CamYynwg AISC Equation B3-2¦. dUcenH 2.08.1

85.09190.0 inAn =≥

cMNaMfa net area EdlRtUvkarKWFMCag gross area EdlRtUvkar. kaMniclPaBGb,brmaEdlRtUvkarKW ( ) .52.0

3001213

300min inLr === sakl,g 4

12

12

1 23 ××L 22 .996.0.44.1 ininAg >= (OK)

.52.0.544.0min ininrr z >== (OK) sRmab;karKNna net area, eRbIGgát;p©itrn§ .0.18

18

7 in=+ 22 .08.1.190.1

410.144.1 ininAAA holegn >=⎟⎠⎞

⎜⎝⎛−=−= (OK)



KNna U CamYynwg AISC Equation B3-2:

9.01 ≤−=LxU

913.09785.01 =−=

edaysartémøenHFMCag 9.0 / dUcenHeRbI 9.0=U . Effective net area KW ( ) 22 .9190.0.071.1190.19.0 ininUAA ne >=== (OK) RtYtBinitü bearing strength. cm¶ayeTARCugEKmsRmab;EdkEkges μ Inwgcm¶ayeTARCugEKmsRmab; gusset plate ehIyedaysarEdkEkgmankRmas;esþIgCag gusset plate dUcenHeyIgeRbIEdkEkgEdl mankRmas; .4/1 in sRmab;KNna bearing strength. sRmab;karKNna bearing strength, eyIgeRbIGgát;p©itRbehag .

1615

161

87

161 indh =+=+=

sRmab;RbehagEdlenAEk,RCugEKmGgát;CageK .031.1

216/155.1

2inhLL cc =−=−=

( ) .75.18/722 ind == edaysar dLc 2< / bearing strength KW ( ) ( )( ) ( ) boltkipstFLR ucc /08.1565

41031.12.175.02.1 =⎟⎠⎞

⎜⎝⎛== φφ


16153 >=−=−=

dUcenH ( ) ( ) ( ) boltkipsdtFR un /59.256541

874.275.04.2 =⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛== φφ

Bearing strength srubsRmab;kartP¢ab;KW ( ) kipsPkipsR un 8.449.9159.25308.15 =>=+=φ (OK) RtYtBinitü block shear. CamYynwgb‘ULúgEdlP¢ab;enAelIeCIgEvgCamYynwgcm¶ayKMlat ¬emIlCMBUk

III/ rUbTI 3>22¦ failure block RtUv)anbgðajenAkñúgrUbTI 7>23. Shear area KW ( ) 2.625.295.1

41 inAgv =+=

( )[ ] 2.750.10.15.395.141 inAnv =−+= ¬Ggát;p©itRbehagmancMnYn 5.3 ¦



Tension area KW ( ) 2.3750.05.1

41 inAgt ==

( )[ ] 2.25.00.15.05.141 inAnt =−= ¬Ggát;p©itRbehagmancMnYn 5.0 ¦

AISC Equation J4-3a [ [ ]ntugvyn AFAFR += 6.0φφ

( )( ) ( )[ ] ( ) kips2.7125.1675.7875.025.065625.2506.075.0 =+=+= AISC Equation J4-3b [ [ ]gtynvun AFAFR += 6.0φφ

( )( ) ( )[ ] ( ) kips2.6575.1825.6875.0375.05075.1656.075.0 =+=+= smIkar J4-3bmantY fracture FMCag dUcenHsmIkarenHlub. dUcenH block shear strength KW kipsPkipsR un 8.442.65 =>=φ (OK)



cemøIy³ eRbI 41

21

21 23 ××L CamYynwgkartP¢ab;enAelIeCIgEvg. eRbIb‘ULúg 325A Ggát;p©it .8

7 in dUcbgðajenAkñúgrUbTI 7>24.

7>8> b‘ULúgersIusþg;x<s;rgkarTaj High-Strength Bolts in Tension enAeBlEdlkmøaMgTajEdlGnuvtþelIb‘ULúgedayKμankmøaMgTajedIm (initial tension) kmøaMg TajenAkñúgb‘ULúges μ InwgkmøaMgEdlGnuvtþ. b:uEnþ RbsinebIb‘ULúgrgeRbkugRtaMg Epñkd¾FMrbs;kmøaMgEdl GnuvtþRtUv)aneRbIedIm,Ibn§ÚrkmøaMgsgát; b¤kmøaMgrwt (clamping force) enAelIEpñkEdlRtUvtP¢ab; dUcEdl kMNt;eday Kulak, Fisher, nig Struik (1987) ehIyRtUv)anbkRsayenATIenH. rUbTI 7>25 bgðajBI tMNBüÜr (hanger connection) EdlpSMeLIgeday structural tee shape EdlRtUv)ancab;b‘ULúgeTAnwg søabxageRkamrbs; W-shape nigrgnUvkmøaMgTaj. b‘ULúgeTal nwgcMENkénEpñkEdlRtUvtP¢ab; RtUv )ansikSamun nigeRkayeBldak;bnÞúk.

düaRkamGgÁesrIrbs;kartP¢ab;muneBldak;bnÞúkRtUv)anbgðajenAkñúgrUbTI 7>26 a. ral;kmøaMg TaMgGs;CakmøaMgkñúg. edIm,IPaBgayRsYl kmøaMgTaMgGs;RtUv)ansn μt;sIuemRTIeFobG½kSrbs;b‘ULúg ehIycMNakp©itminRtUv)anKit. RbsinebIeKBicarNaEpñkEdlRtUvtP¢ab;dac;edayELk kmøaMgrYmman kmøaMgTajrbs;b‘ULúg oT nigkmøaMgrwt Ekg (normal clamping force) oN EdlbgðajenATIenHRtUv)an BRgayes μ I. edIm,I[manlMnwg eKRtUvkar oo NT = . enAeBlEdleKGnuvtþkmøaMgxageRkA kmøaMgenAelI kartP¢ab;RtUv)anbgðajenAkñúgrUbTI 7>26 b Edl F tMNag[kmøaMgTajsrubEdlGnuvtþmkelIb‘ULúg mYy. rUbTI 7>26 c bgðajkmøaMgEdlmanGMeBIelIdüaRkamGgÁesrIrbs;Epñkénsøabrbs; structural tee

nigEpñkEdlRtUvKñarbs;b‘ULúg. bUkkmøaMgtamTisG½kSb‘ULúg eyIgTTYl)an NFT +=



kmøaMg F nwgbegáInkmøaMgTajrbs;b‘ULúg ehIyeFVI[valUt)an bδ . kmøaMgsgát;enAkñúgsøab rbs; structurel atee nwgRtUv)ankat;bnßy CalT§plvamanbMlas;TI flδ EdlmanTisdUc bδ . TMnak; TMngrvagkmøaMgGnuvtþn_ nigbERmbRmYlkmøaMgTajrbs;b‘ULúgGacRtUv)ankMNt;dUcxageRkam³

BI elementary mechanics of materials, kMhUcRTg;RTaytamG½kSrbs;bnÞúktamG½kSEdl

GnuvtþelIGgát;KW³

AEPL

=δ ¬&>$¦ Edl =P kmøaMgtamG½kS =L RbEvgedIm =A RkLaépÞmuxkat; =E m:UDuleGLasÞic BIsmIkar &>$ eyIgGacTajrkkmøaMg

LAEP δ

= ¬&>%¦



dUcenHbERmbRmYlkmøaMgenAkñúgb‘ULúgEdlRtUvKñaeTAnwgkMhUcRTg;RTay bδ KW

b

bbbLEAT δ

=Δ ¬&>^¦

BIsmIkar &>% eKTTYl)anbERmbRmYlkmøaMg N

fl

flflflLEA

Nδ

=Δ ¬&>&¦

Edl flL CakRmas;rbs;søab. RbsinEpñkEdlRtUvP¢ab; ¬søabTaMgBIr¦ enAb:HKña kMhUcRTg;RTayrbs; b‘ULúg bδ nigkMhUcRTg;RTaysøab flδ nwges μ IKña. edaysar flE esÞIres μ Inwg bE (Bickford, 1981), ehIy flA FMCag bA

b

bbb

fl

flflflLEA

LEA δδ

>>

dUcenH TN Δ>>Δ pleFob NΔ elI TΔ sßitenAcenøaHBI 05.0 eTA 1.0 (Kulak, Fisher, nig Struik, 1987). dUcenH TΔ minRtUvFMCag NΔ1.0 EdlbgðajfakmøaMgEdlGnuvtþPaKeRcInKWbn§ÚrkmøaMgsgát;rbs;EpñkEdlRtUvtP¢ab;. KNnakmøaMgEdlRtUvkaredIm,IeFVI[EpñkEdlRtUvP¢ab;XøatecjBIKña emIlrUbTI 7>27. enAeBlEdlEpñk TaMgBIrXøatecjBIKña FT = b¤ FTTo =Δ+ ¬&>*¦ enAeBlEdlCitdl;cMNucEdlRtUvXøatKña sac;lUtrbs;b‘ULúg nigKMlatrbs;søabKWes μIKña fl

b

bbb

b

bbL

EAL

EAT δδ ==Δ ¬&>(¦

Edl flδ CakMhUcRTg;RTayEdlRtUvKñanwgkmøaMgsgát;edIm oN . BIsmIkar &>$

flfl

flofl EA

LN=δ

CMnYsvaeTAkñúgsmIkar &>( eyIg)an

ooflflfl

bbbo

flflfl

bbb

flfl

flo

b

bb TTLEALEAN

LEALEA

EALN

LEAT 1.0

//

//

≈⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ

BIsmIkar &>* FTT oo =+ 1.0 b¤ oTF 1.1=



dUcenH enAxN³eBlEdlcab;epþImXøat kmøaMgTajenAkñúgb‘ULúgFMCagkmøaMgTajedImEdlmanenAeBl dMeLIgb‘ULúgRbEhl %10 . b:uEnþ enAeBlEdlEpñkEdlRtUvP¢ab;Xøatecj kmøaMgxageRkAEdlekIneLIg nwgRtUv)anTb;edaykmøaMgEdlekIneLIgRtUvKñaenAkñúgb‘ULúg. RbsinebIeKsnμt;fakmøaMgTajenAkñúgb‘ULúg RtUv)andak;[esμ IkmøaMgxageRkA ¬RbsinebIKμankmøaMgTajedIm¦ ehIykartP¢ab;rgnUvbnÞúkrhUtdl;Epñk EdltP¢ab;XøatecjBIKña enaHkmøaMgTajenAkñúgb‘ULúgRtUv)anKNnaticCag %10 . sRmab;krNIenH b‘ULúgersIusþg;x<s;RtUvrgnUveRbkugRtaMgtamtémøEdlmanenAkñúg AISC Table J3.1 eTaHCakartP¢ab; enH Ca slip-critical b¤minEmnk¾eday. CarYm eKRtUvKNnakmøaMgTajenAkñúgb‘UøLúgedayKitbBa©ÚlTaMgkmøaMg TajedIm. Prying Action sRmab;kartP¢ab;PaKeRcInEdleRKOgP¢ab;rgkmøaMgTaj kMhUcRTg;RTayrbs;EpñkEdlRtUvP¢ab; GacbegáInkmøaMgTajEdlGnuvtþeTAelIeRKOgP¢ab;. RbePT hanger connection Edl)anerobrab;xag elICaRbePTkartP¢ab;EdlmanlkçN³eFVIkardUcEdl)anerobrab;. kmøaMgTajbEnßmRtUv)aneKehAfa prying force ehIyRtUv)anbgðajenAkñúgrUbTI 7>28 EdlrUbenHbgðajBIkmøaMgenAelIGgÁesrIrbs; hanger. muneBlEdlbnÞúkxageRkAGnuvtþ kmøaMgsgát;Ekg (normal compressive force) oN RbmUl pþúMenAelIGgS½rbs;b‘ULúg. enAeBlEdlbnÞúkGnuvtþ RbsinebIsøab flexible RKb;RKan; enaHvanwgxUcRTg; RTaydUcEdlbgðaj ehIykmøaMgsgát;nwgrMkileTAxagcugrbs;søab. karBRgaykmøaMgeLIgvijenH nwg EkERbTMnak;TMngrvagbnÞúkTaMgGs; ehIykmøaMgTajrbs;b‘ULúgnwgekIneLIg. b:uEnþ RbsinebIEpñkEdl RtUvP¢ab;manlkçN³rwgRKb;RKan; vanwgminmankarpøas;bþÚrkmøaMgeT ehIyk¾minman prying action Edr. eKTTYl)antémøGtibrmarbs; prying force enAeBlEdlkac;RCugrbs;søabenAEtb:HCamYynwgEpñk EdlRtUvP¢ab;déTeTot.



enAkñúgkartP¢ab;RbePTenH bending EdlekIteLIgeday prying force EtgEtmanlkçN³lub kñúgkarKNnaEpñkEdlRtUvP¢ab;. AISC J3.6 tRmUv[KitbBa©Úl prying force eTAkñúgkarKNnakmøaMg TajEdlGnuvtþelIeRKOgP¢ab;.

viFIsaRsþsRmab;karKNna prying force EdlQrelI Guide to design Criteria for Bolted

and Riveted Joints (Kulak, Fisher, nig Strick, 1987) manenAkñúg Manual in Part 11, “Connec-

tions for Tension and Compression” (Volume II). krNICak;lak;EdlRtUv)anRtYtBinitüCakart P¢ab; structural tee shape ehIyEdkEkgKUrEdlxñgTl;xñg ( a pair of back-to-back angle) nwg RtUv)anKitkñúgpøÚvdUcKñaEdr. viFIEdlbgðajenATIenHmanTMrg;xusKñabnþicEtpþl;nUvlT§pldUcKña. viFIEdleRbIKWQrelIKRmUEdlbgðajenAkñúgrUbTI 7>29. RKb;kmøaMgTaMgGs;KWsRmab;EteRKOg P¢ab;mYy. dUcenH T CakmøaMgTajemKuNxageRkAEdlGnuvtþeTAelIEtb‘ULúgmYy/ Q Ca prying force EdlRtUvKñanwgb‘ULúgmYy nig cB CakmøaMgb‘ULúgsrub. Prying force )anrMkileTAcugrbs;søab ehIy vamantémøGtibrma. smIkarxageRkamRtUv)anbMEbkBIsmIkarlMnwgrbs;GgÁesrIkñúgrUbTI 7>29. BIplbUkm:Um:g;Rtg; muxkat; B-B enAkñúgrUbTI 7>29 b QaMTb aa =− − ¬&>!0¦



BIrUbTI 7>29 c QaM bb =− ¬&>!!¦ cugeRkay/ kmøaMglMnwgRtUvkarKW QTBc += ¬&>!@¦ smIkarlMnwgTaMgbIenHGacbBa©ÚlKñaedIm,ITTYl)ansmIkareTalsRmab;kmøaMgb‘ULúgsrub EdlrYmbBa©Úl TaMg\T§iBl prying force. dMbUgeyIgkMNt;Gefr α CapleFobrvagm:Um:g;kñúgmYyÉktþaRbEvgtam beNþayG½kSb‘ULúgelIm:Um:g;kñúgmYyÉktþaRbEvgenARtg;épÞKl;. sRmab;G½kSb‘ULúg/ RbEvgCa net length, dUcenH ( )

aa

bb

aa

bb

aa

bbMM

pdMM

pMdpM

−

−

−

−

−

− =⎟⎟⎠

⎞⎜⎜⎝

⎛−

=−

=δ

α/'1

1/

'/ ¬&>!#¦

Edl =p RbEvgrgsMBaFrbs;søabsRmab;b‘ULúgmYy ¬emIlrUbTI 7>29 a¦ ='d Ggát;p©itrbs;Rbehagb‘ULúg

face at web area grosslinebolt at areanet '1 =−=

pdδ

( )4/at strength design 2yfbpbaa FptMaaM φφ ==−=−



eyIgGacbBa©ÚlsmIkarlMnwgbI &>!0-&>!@ edIm,ITTYl)ankmøaMgb‘ULúgsrub/ :cB ( ) ⎥

⎦

⎤⎢⎣

⎡+

+=abTBc δα

δα1

1 ¬&>!$¦

CamYynwg bnÞúkEdlTTYl)anBIsmIkar &>!$ eyIgnwgTTYl)ankMhUcRTg;RTayFMEdleFVI[kugRtaMgTaj pÁÜbenAkñúgb‘ULúgminRtYtsIuKñaCamYyG½kSrbs;b‘ULúg. dUcenH kmøaMgkñúgb‘ULúgEdl[edaysmIkar &>!$ minRtUvKñaCamYynwglT§plBiesaFn_. edIm,ITTYl)anlT§plEdlcg;)an luHRtaEtkmøaMg cB rMkileTA kan;Kl;rbs; tee edaybrimaN 2/d Edl d CaGgát;p©itb‘ULúg. dUcenHtémø b nig a RtUv)anEkERbCa

2' dbb −= nig

2' daa +=

¬edIm,I[RtUvnwglT§plBiesaFn_kan;Etl¥ témørbs; a minRtUvFMCag b25.1 eT¦ CamYynwgkarpøas;bþÚrenHeyIgGacsresrsmIkar &>!$ Ca ( ) ⎥

⎦

⎤⎢⎣

⎡+

+=''

11

abTBc δα

δα ¬&>!%¦

eyIgGackMNt; α BIsmIkar &>!% eday[kmøaMgenAkñúgb‘ULúg cB es μ IeTAnwg design tensil strength

EdleyIgsMKal;Ca B . lT§plEdlTTYl)anKW ( )[ ]( )

( )[ ]( ){ }'/'1/1'/'1/baTB

baTB−−

−=δ

α ¬&>!^¦

eKGacmansßanPaBkMNt;BIr³ tensil failure rbs;b‘ULúg nig bending failure rbs; tee. eK snμt;fa failure rbs; tee ekItmanenAeBlEdlsnøak;)aøsÞic (plastic hinges) ekItmanRtg;muxkat; a-a, Rtg;Kl;rbs; tee, nigenARtg;muxkat; b-b. edayehtuenHvanwgbegáItCa beam mechanism. m:Um:g;énTI taMgTaMgenHnwges μ Inwg pM EdlCalT§PaBm:Um:g;)aøsÞicénRbEvgrbs;RbEvgrgsMBaFrbs;søabsRmab;b‘U LúgmYy. RbsinebItémødac;xatrbs; α EdlTTYl)anBIsmIkar &>!^ tUcCag 0.1 enaHm:Um:g;enARtg; G½kSb‘ULúgtUcCagm:Um:g;enARtg;Kl; tee Edlvabgðajfa beam mechanism minRtUv)anbegáIteT ehIy sßanPaBkMNt;RtUv)ankMNt;Ca tensile failure rbs;b‘ULúg. kmøaMgb‘ULúg cB kñúgkrNIenH nwgesμ Inwg design strength B . RbsinebItémødac;xatrbs; 0.1≥α enaH plastc hinges nwgekItmanenARtg; a-a nig b-b ehIysßanPaBkMNt;KW flexural failure rbs;søabrbs; tee. edaysarEtm:Um:g;Rtg;kEnøgTaMg BIrenHRtUv)ankMNt;Rtwmm:Um:g;)aøsÞic pM enaH α KYrEtUv)ankMNt;es μ Inwg 0.1 . smIkarlMnwgbI &>!0-&>!@ k¾GacRtUv)anrYmbBa©ÚlKñakøayCasmIkarEtmYysRmab;kMNt;kRmas; søab ft . BIsmIkar &>!0 nig &>!! eyIgGacsresr



bbaa MMTb −− =−' Edl 'b RtUv)anCMnYs[ b . BIsmIkar &>!# aaaa MMTb −− =− δα' ¬&>!&¦ [ aaM − es μInwg design strength eKTTYl)an

4

2yf

bpbaaFpt

MM φφ ==− Edl ft CakRmas;søabEdlRtUvkar. CMnYs aaM − eTAkñúgsmIkar &>!& eyIgTTYl)an ( )δαφ +

=1

'4

ybf pF

Tbt

Edl 90.0=bφ ( )δα+

=1

'444.4

yf pF

Tbt ¬&>!*¦

karKNnakartP¢ab;EdlrgnUv prying action CatMeNIrkarKNna trial-and-error. enAeBl eRCIserIsTMhM nigcMnYnrbs;b‘ULúg eyIgRtUvEtKiteRtomTuksRmab; prying force. kareRCIserIskRmas; tee mankarlM)akCagedaysarvaTak;TgeTAnwgkareRCIserIsb‘ULúg nigTMhM tee. eKGaceRbI Prelimi-

nary Hanger Connection Selection Table EdlmanenAkñúg Part 11 of the Manual sRmab;CYy sRmYldl;kareRCIserIsrUbragsakl,g. enAeBlEdleKeRCIserIsmuxkat;sakl,g/ dwgcMnYnb‘ULúg nig karteRmobb‘ULúgrYcehIy eKGaceRbIsmIkar &>!% nig &>!* edIm,IepÞógpÞat;. RbsinebIkRmas;søabCak;EsþgxusBItémøEdlRtUvkar témøCak;Esþgrbs;α nig cB k¾GacxusBIGVI EdleK)anKNnaknøgmkEdr. RbsinebIeKRtUvkmøaMgb‘ULúgCak;Esþg EdlrYmbBa©ÚlTaMg prying force Q enaHeKRtUvkMNt; α eLIgvijdUcxageRkam. aabb MTbM −− −= ' BIsmIkar &>!#/

aa

bbMM

−

−=δ

α

δδ1/'' −

=−

= −

−

− aa

aa

aa MTbM

MTb

eday[ aaM − es μ IwTAnwg design moment eK)an



⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛==− 4

90.02

yfpbaa

FptMM φ

enaH ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−=

−

= 1'444.411

4/90.0'

2

2

yf

yf

FptTbFpt

Tb

δδα ¬&>!(¦

eKGacrkkmøaMgb‘ULúgsrubBIsmIkar &>!% ]TahrN_ 7>9³ 665.10 ×WT RbEvg .8in RtUv)anP¢ab;eTAnwg)atsøabrbs;Fñwm dUcbgðajenAkñúgrUbTI 7>30. Hanger enHrgnUvbnÞúkemKuN kips90 . kMNt;cMnYnb‘ULúg 325A Ggát;p©it .8/7 in EdlRtUvkar nigepÞógpÞat;nUvPaBRKb;RKan;rbs; tee. EdkEdleRbICaRbePTEdk 36A .

dMeNaHRsay³ RkLaépÞb‘ULúgKW ( ) 2

2.6013.0

48/7 inAb ==

π ehIy design strength rbs;b‘ULúgmYyKW ( )( ) kipsAFRB btn 59.406013.09075.0 ==== φφ



cMnYnb‘ULúgEdlRtUvkarKW 22.259.40/90 = . cMnYnb‘ULúgGb,brmaEdlRtUvkarKW 4 edIm,IrkSaPaBsIuem-RTI. BITMhMEdlbgðajenAkñúgrUbTI 7>30 ( ) .425.2

2650.05.5 inb =

−= ( ) .470.3

25.544.12 ina =

−=

( ) .470.3.031.3425.225.125.1 ininb <== yk .031.3 ina =

.988.12

8/7425.22

' indbb =−=−= .468.3

28/7031.3

2' indaa =+=+=

bnÞúkxageRkAemKuNkñúgmYyb‘ULúg edayKitTaMg prying force KW kipsT 5.224/90 == . KNna δ ³ .1

81

87

81' indd =+=+=

.428 inp ==

75.0411'1 =−=−=

pdδ

KNna α ³ 8040.01

5.2259.401 =−=−

TB

744.1988.1468.3

''

==ba

BIsmIkar &>!^/ ( )[ ]( )

( )[ ]( ){ }( )

( )[ ] 65.4744.18040.0175.0

744.18040.0'/'1/1

'/'1/−=

−=

−−−

=baTB

baTBδ

α

edaysar 0.1>α / yk 0.1=α . BIsmIkar &>!* ( )

( )( )( )( )75.01364

988.15.22444.41

'444.4+

=+

=δαy

f pFTbt

.035.1.888.0 inin <= (OK)

TaMgcMnYnb‘ULúgEdleRCIserIs nwgkRmas;søabKWRKb;RKan; ehIyminRtUvkarkarKNnateTAmuxeToteT. b:uEnþ edIm,IbgðajBIviFIsaRsþKNna eyIgKNna prying force edayeRbIsmIkar &>!( nig &>!%. BI smIkar &>!(/



( )( )( ) ( )

3848.0136035.14988.15.22444.4

75.011'444.41

22 =⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−=

yf FptTb

δα

BIsmIkar &>!%/ kmøaMgb‘ULúgsrub edayKitTaMg prying force KW ( ) ⎥

⎦

⎤⎢⎣

⎡+

+=''

11

abTBc δα

δα ( )( ) kips39.25

468.3988.1

3848.075.013848.075.015.22 =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

++=

Prying force KW kipsTBQ c 89.25.2239.25 =−=−= cemøIy³ 665.10 ×WT RKb;RKan;. eRbIb‘ULúg 325A Ggát;p©it .8/7 in RbsinebIkRmas;søabminRKb;RKan; eKGacsakl,g tee shape EdlmanTMhMFMCag b¤k¾eRbIcMnYn b‘ULúgbEnßmedIm,Ikat;bnßy T EdlCakmøaMgxageRkAkñúgmYyb‘ULúg. Prying force enAkñúg]TahrN_ 7>9 bEnßmRbEhl %13 eTAelIkmøaMgxageRkA. karecalnUvkmøaMgTajbEnßmenHnwgpþl;nUvplvi)ak y:agF¶n;F¶r. 7>9> kmøaMgpÁÜbrvagkmøaMgTaj nigkmøaMgTajenAkñúgb‘ULúg (Combined Shear and Tension

in Fasteners) enAkñúgsßanPaBCaeRcInkartP¢ab;EtgRbQmnwgkmøaMgkat; nigkmøaMgTaj. tMNEdlTTYlbnÞúk cMNakp©itRtUv)anerobrab;enAkñúgCMBUkTI 8. b:uEnþ sRmab;tMNsamBaØxøH eRKOgP¢ab;sßitkñúgsßanPaB kmøaMgpÁÜb. rUbTI 7>31 bgðajBIkMNat; structural tee EdlP¢ab;eTAnwgsøabrbs;ssrkñúgeKalbMNg edIm,IP¢ab;Ggát;BRgwg (bracing member). Ggát;BRgwgenHRtg;)andak;tMrg;y:agNaedIm,I[ExSskmμ rbs;kmøaMgkat;tamTIRbCMuTm¶n;rbs;kartP¢ab;. bgÁúMkmøaMgbBaÄrnwgeFVI[eRKOgP¢ab;rgkugRtaMgkat; ehIy bgÁúMkmøaMgedknwgbegáItkmøaMgTaj ¬EdlGacmankarpSMCamYynwg prying force¦. edaysarExSskmμ rbs;kmøaMgeFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;tMN eRKOgP¢ab;nImYy²RtUv)ansnμt;faTTYlkugRtaMgedaycM ENkesμ I²Kña.



kñúgkrNIbgÁúMkmøaMgepSgeTot eKGaceRbIviFIrUbmnþGnþrkm μ (interaction formula approach) . ersIusþg;kmøaMgkat; nigersIusþg;kmøaMgTajsRmab;b‘ULúgRbePT bearing KWQrelIlT§plénkarBiesaF nwgRtUv)anykBI elliptical interaction curve EdlbgðajenAkñúgrUbTI 7>32. smIkarrbs;ExSenHKW

( ) ( ) 0.122

=⎥⎥⎦

⎤

⎢⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

vn

u

tn

uRV

RP

φφ

Edl =uP kmøaMgTajemKuNenAelIb‘ULúg ( ) =tnRφ design strength rbs;b‘ULúgrgkarTaj

=uV kmøaMgkat;TTwgemKuNenAelIb‘ULúg ( ) =vnRφ design strength rbs;b‘ULúgrgkarkat;

bnSMkmøaMgkat; nigkmøaMgTajEdlGacTTYlyk)anKWvaCYbKñaRtg;kEnøgEdlsßitenABIeRkamExS

ekag. enHCatRmUvkarrbs; RCSC Specification Edl

( ) ( ) 0.122

≤⎥⎥⎦

⎤

⎢⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

vn

u

tn

uRV

RP

φφ (RCSC Equation LRFD 4.2)



sRmab; slip-critical connection Edlb‘ULúgrgnUvkmøaMgkat; nigkmøaMgTaj \T§iBlrbs;kmøaMg TajKWbn§Úrbnßy clamping force EdleFVI[mankarkat;bnßykmøaMgkkit. AISC Specification kat; bnßy slip-critical shear strength sRmab;krNIenH. BI AISC Appendix J, slip-critical shear

strength RtUv)anKuNedayemKuN

⎥⎦

⎤⎢⎣

⎡−

bm

uNT

T13.1

1 (AISC Equation A-J3-2)

Edl =uT kmøaMgTajemKuNenAelItMN =mT kmøaMgTajb‘ULúgedImEdl)anBI AISC Table J3.1 =bN cMnYnb‘ULúgenAkñúgtMN cMNaMfa RCSC Equation LRFD 4.2 Edl)anbgðajenATIenHRtUv)anGnuvtþeTAelIb‘ULúgeTal Et

AISC Equation A-J3-2 Edl)anbgðajenATIenHGnuvtþeTAelItMNTaMgmUl. smIkarnImYy²Gac RtUv)anEkERbedIm,IGnuvtþsRmab;viFIepSgeTot. ]TahrN_ 7>10³ eKeRbI 315.10 ×WT Ca bracket edIm,IbBa¢Ún service load kips60 eTAssr

9014×W dUcEdl)anbgðajenAkñúgrUUbTI 7>31. bnÞúkpSMeLIgedaybnÞúkefr kips15 nigbnÞúkGefr kips45 . eKeRbIb‘ULúg 325A Ggát;p©it .8/7 in cMnYn 4 RKab;. TaMgssr nig bracket eFVIBIEdk 36A .

snμt;fatRmUvkarKMlat nigcm¶ayeTARCugEKmTaMgGs;KWRKb;RKan; edayrYmbBa©ÚlTaMgPaBcaM)ac;sRmab; kareRbIR)as; design strengn GtibrmasRmab; bearing ¬dUcCa [ ]udtF4.2φ ¦ nigkMNt;nUvPaBRKb;RKan; rbs;b‘ULúgsRmab;kartP¢ab;xageRkam³ ¬!¦ bearing –types connection EdlmaneFμjsßitenAkñúgbøg;kat;. ¬@¦ slip-critical connection EdlmaneFμjsßitenAkñúgbøg;kat;. dMeNaHRsay³ bnÞúkemKuNKW ( ) ( ) kipsLD 90456.1152.16.12.1 =+=+ ¬!¦ sRmab; bearing-type connection EdlmaneFμjsßitenAkñúgbøg;kat; kmøaMgkat;TTwgsrubKW ( ) kips5490

53

= kmøaMgkat;TTwgsRmab;b‘ULúgmYyKW



kipsVu 5.134

54==

nig ( ) 22

.6013.04

8/7inAb ==

π ( ) ( )( )6013.04875.0== bvvn AFR φφ

kipskips 5.1365.21 >= Bearing strength ¬søabrbs; tee lub¦ KW ( ) ( ) ( )( )58615.0

874.275.04.2 ⎟⎠⎞

⎜⎝⎛== un dtFR φφ

kipskips 5.1318.56 >= (OK) kmøaMgTajsrubKW ( ) kips7590

54

= kmøaMgTajsRmab;b‘ULúgmYyKW kipsPu 18

472

== BI AISC Table J3.2, ( ) ( )( ) kipskipsAFR bttn 1859.406013.09075.0 >=== φφ (OK) BI RCSC Equation LRFD 4.2,

( ) ( ) 0.1585.065.215.13

59.4018 2222

<=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

vn

u

tn

uRV

RP

φφ (OK)

cemøIy³ kartP¢ab;manlkçN³RKb;RKan;Ca bearing-type connection. ¬edIm,IkMu[Bi)akyl;kñúgkar bnSMbnÞúkrbs;]TahrN_enH prying action minRtUv)anrYmbBa©ÚleTAkñúgkarviPaKeT¦. ¬@¦ sRmab; slip-critical connection, EdlmaneFμjsßitenAkñúgbøg;kat; BIEpñk ¬!¦ shear, bearing/ and tension strength KWmanlkçN³RKb;RKan;. BI RCSC Equation LRFD 5.3, slip-critical strenght KW ( )sbmstr NNTR μφφ 13.1= BI AISC Table J3.1, kmøaMgTajsRmab;b‘ULúg 325A Ggát;p©it .8/7 in KW kipsTm 39= RbsinebIeyIgsnμt;épÞb:HCa Class A, slip coefficent KW 33.0=μ nigsRmab;b‘ULúgbYnRKab; ( ) ( )( )( )( )( ) kipsNNTR sbmstr 17.58143933.013.10.113.1 === μφφ



edaysarvamankmøaMgTajenAelIb‘ULúg/ slip-critcal strength RtUv)ankat;bnßyedayemKuN ( )( ) 5916.0

43913.1721

13.11 =⎥

⎦

⎤⎢⎣

⎡−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−

bm

uNT

T

dUcenHresIusþg;Edl)ankat;bnßyehIyKW ( ) kipskipsRstr 544.3417.585916.0 <==φ (N.G.)

cemøIy³ kartP¢ab;minmanlkçN³RKb;RKan;Ca slip-critical connection eT. kartP¢ab;edayb‘ULúgEdlrgnUvkmøaMgkat;TTwg nigkmøaMgTajGacRtUv)anKNnaedaypÞal;. eK GaceRbI RCSC Equation 4.2 edIm,IedaHRsayTMhMb‘ULúgdUcxageRkam³

( ) ( )

2222

⎟⎟⎠

⎞⎜⎜⎝

⎛∑

+⎟⎟⎠

⎞⎜⎜⎝

⎛∑

=⎥⎥⎦

⎤

⎢⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

bv

u

bt

u

vn

u

tn

uAF

VAF

PRV

RP

φφφφ

( ) ( )22

2

211

bv

u

bt

u

AFV

AFP

∑⎟⎟⎠

⎞⎜⎜⎝

⎛+

∑⎟⎟⎠

⎞⎜⎜⎝

⎛=

φφ

Edl =uP kmøaMgTajsrubenAelItMN =tF ultimate tensile stress rbs;b‘ULúg =uV kmøaMgkat;TTwgsrubenAelItMN =vF ultimate shear stress rbs;b‘ULúg =∑ bA RkLaépÞmuxkat;b‘ULúgsrub CMnYseTAkñúg RCSC Equation LRFD 4.2, eyIg)an

( ) ( )

0.1112

2

2

2≤

∑⎟⎟⎠

⎞⎜⎜⎝

⎛+

∑⎟⎟⎠

⎞⎜⎜⎝

⎛

bv

u

bt

u

AFV

AFP

φφ

b¤ 22

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛≥∑

v

u

t

ub F

VFP

Aφφ

¬&>@0¦

Edl bA∑ CaRkLaépÞmuxkat;b‘ULúgsrub ]TahrN_ 7>11³ tMNEdlrgbnÞúkcMp©itrgnUv service load shear force kips50 nig service tensile

force kips100 . bnÞúk %25 CabnÞúkefr nig %75 CabnÞúkGefr. eRKOgP¢ab;rgnUv single shear ehIy baring strength nwgRtUv)anKNnaCamYynwgEpñkEdlRtUvP¢ab;EdlmankRmas; .16/5 in . snμt;



fa KMlat nigcm¶ayeTARCugEKmTaMgGs;manlkçN³RKb;RKan; nigsnμt;faeKGnuBaØat[eRbI bearing

strength Gtibrma ( )udtF4.2φ . kMNt;cMnYnb‘ULúg 325A Ggát;p©it .4/3 in EdlcaM)ac;sRmab;krNIxag eRkam³ ¬!¦ bearing-type connection CamYynwgeFμjsßitenAkñúgbøg;kat; ¬@¦ slip-critical connection CamYynwgeFμjsßitenAkñúgbøg;kat; épÞb:HTaMgGs;man clean mill scale. karKNnaenHmin)anBicarNa prying action sMxan;eT. dMeNaHRsay³ kmøaMgkat;TTwgemKuN ( )[ ] ( )[ ] kips755075.06.15025.02.1 =+=

kmøaMgTajemKuN ( )[ ] ( )[ ] kips15010075.06.110025.02.1 =+= ¬!¦ sRmab; bearing-type connection CamYynwgeFμjsßitenAkñúgbøg;kat; smIkar &>@0 [

( ) ( )2

222.046.3

4875.075

9075.0150 in

FV

FP

Av

u

t

ub =⎥

⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡=⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛≥∑

φφ

RkLaépÞrbs;muxkat;eTalKW ( ) 2

2.4418.0

44/3 inAb ==

π dUcenHcMnYnb‘ULúgEdlRtUvkarKW 89.6

4418.0046.3

==∑

b

bAA

sakl,gb‘ULúg 7 RKab; ehIyRtYtBinitü bearing: ( ) 74.2 ×= un dtFR φφ

( ) ( )( ) kipskips 75171758165

874.275.0 >=⎟

⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=

¬eKminRtUvkarRtYtBinitüKMlat nigcm¶ayeTARCugEKmsRmab;karKNnacugeRkayeT¦ cemøIy³ eRbIb‘ULúg 7 RKab;. ¬RbsinebIeKerobb‘ULúgCaBIrCYr enaHeRbIb‘ULúg 8 RKab;edIm,IPaBsIuemRTI¦ ¬@¦ sRmab; slip-critical connection, slip-critical strength Edl[eday RCSC Equation LRFD

RtUv)anKuNedayemKuNkat;bnßyrbs; AISC Equation A-J3-2:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

bm

usbmstr NT

TNNTR

13.1113.1 μφφ ¬&>@!¦



BI AISC Table J3.1, sRmab;b‘ULúg 325A Ggát;p©it .4/3 in / kipsTm 28= . CMnYs mT eTAkñúgsmIkar &>@!/ eyIg)an ( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

bm

usbmstr NT

TNNTR

13.1113.1 μφφ

( )( )( )( )( ) ( ) ⎥⎦

⎤⎢⎣

⎡−=

bb N

N2813.1

150112833.013.10.1

( )741.444.10741.4144.10 −=⎟⎟⎠

⎞⎜⎜⎝

⎛−= b

bN

N

dak;lT§plEdlTTYl)anenH nigkmøaMgkat;TTwgEdlGnuvtþ[esμ IKña enaHeyIgGacrkcMnYnb‘ULúgEdl RtUvkaredIm,IkarBar slip³ ( ) kipsNb 75741.444.10 =− 9.11=bN edaysarb‘ULúg 7 RKab;RKb;RKan;sRmab; shear, bearing nig tension dUcenHeKminRtUvkarRtYt BinitüsßanPaBkMNt;TaMgenHeT. cemøIy³ eRbIb‘ULúg 325A Ggát;p©it .4/3 in 7>10> tMNpSar (Welded connections) karpSarCadMeNIrkareFVI[EpñkEdlRtUvP¢ab;Cab;Kña. ]TahrN_ Ggát;rgkarTajEdlman lap

joint dUcbgðajenAkñúgrUbTI 7>33 a GacRtUv)aneFVIeLIgedaykarpSartamcugTaMgsgçagrbs;EpñkEdl RtUvP¢ab;. kMBs;d¾tUcbMputrbs;smÖar³RtUv)anrlay eRkayBITuk[RtCak; eRKOgbgÁúMEdk nig weld

metal eFVIkardUcEpñkEdlCab;KñaenAkEnøgtMN. EdkbEnßmRtUv)andak;BI special electrode EdlCaEpñk rbs;crnþGKÁisnIeTAelIEpñkEdlRtUvP¢ab; b¤ base metal.



enAkñúgdMeNIrkar shielded metal arc welding (SMAW) EdlbgðajenAkñúgrUbTI 7>34 FñÚ GKÁisnI (current arc) kat;tamcenøaHrvag electrode nig base metal edayrMlayEpñkEdlRtUvP¢ab; nigdak;Epñkrbs;eGLicRtUteTAkñúg base metal Edlrlay. Specail coating enAelI electrode begáIt protective gaseous shield edaykarBar molten weld metal BIGuksIutkm μmunnwgvarwg. eKrMkil electrode kat;tamtMN ehIy weld bead RtUv)andak; TMhMrbs;vaGaRs½ynwgGRtaéndMeNIrrbs; electrode. enAeBlEdlTwkbnSaRtCak; impuriries elceLIgenAelIépÞ EdlbegáItCa coating EdleK ehAfa slag ehIy slag enHRtUv)anykecjmunnwglabfñaMelIGgát; b¤EpñkepSg²EdlRtUv)anbegáIteLIg eday electrode.

CaTUeTA Shielded metal arc welding EdlRtUv)aneFIVeLIgedayéd ehIyCadMeNIrkareKeRbICa

sklenAelIkardæan. sRmab;karpSarenAeragCag eKniymeRbIdMeNIrkarsV½yRbvtþ b¤Bak;kNþalsV½y Rbvtþ. karRtYtBinitüKuNPaBsRmab;kartP¢ab;edaykarpSarKWmanlkçN³Bi)ak edaykarTwkbnSarEdl minl¥sßitenABIeRkamépÞ b¤k¾PaBminl¥d¾tictYcEdlmanenAépÞbnSar GaceKcputBIExSEPñkrbs;eyIg)an. sRmab;karpSarenARtg;kEnøgEdleRKaHfñak;eKRtUvkarCagpSarEdlmanCMnajRtwmRtUv ehIyeKRtUveRbI bec©keTsBiessdUcCa radiography b¤ ultresonic testion.

eKniymeRbIkarpSarBIrRbePTKW fillet weld nig groove weld. Lap joint EdlbgðajenAkñúgrUb TI 7>33 a nig b RtUv)anbegáIteLIgeday fillet weld . Groove weld RtUv)aneRbIsRmab; butt, tee nig corner dUcbgðajenAkñúgrUbTI 7>35 a nig b. rUbTI 7>36 bgðajBI plug and slot wled Edl eBlxøHva RtUvkaredIm,IbEnßmBIelIkarpSartamRCug. rn§ragmUl b¤RTEvgRtUv)ankat;ecjBIEpñkmYyedIm,I



GacbMeBjTwkbnSar)an.

kñúgcMeNamkarpSarTaMgBIrRbePTenH eyIgnwgelIkykkar pSar fillet weld mkbkRsaylMGit

enATIenH. karKNnasRmab; complete penetration groove weld minmanlkçN³minsMxan;Edlkar pSar manersIusþg;dUcKñanwg base metal nigEpñkEdlRtUvP¢ab;. ersIusþg;rbs; partial penetration

groove weld GaRs½yeTAnwgbrimaNén penetration. dMeNIrkarénkarKNna groove weld Rsedog KñanwgkarKNna fillet weld.

7>11> Fillet Welds

karKNna nigkarviPaKsRmab; fillet weld KWQrelIkarsnμt;famuxkat;rbs;TwkbnSarCa RtIekaNEkgEdlmanmMu o45 dUcbgðajkñúgrUbTI 7>37. TTwgrbs; fillet weld RtUv)ansMKal;eday w .



TMhMTWkbnSarbTdæanKWekIneLIgmþg mmin 2.16/1 = . eTaHbICaRbEvgrbs;karpSarGacrgnUvbnÞúk tam TiskmøaMgkat;/ kmøaMgsgát; nigkmøaMgTajk¾eday k¾fillet weld manersIusþg;exSaysRmab;kmøaMgkat; ehIyvaEtg EtRtUv)aneKsnμt;fadac;edaysarkmøaMgenH. kardac;RtUv)ansnμt;ekItmantambøg;Edl kat;tam throat rbs;TwkbnSar. sRmab; fillet weld EdlbegáIteLIgCamYy shielded metal arc

process, throat CaRb EvgEkgBIRCugEKm b¤ root rbs;TwkbnSareTAGIub:Uetnus nigmantémøesμ I 707.0 dgénTMhMTwkbnSar. ¬Effective throad thickness sRmab;TwkbnSarEdl)anBI arc welding process manTMhMFMCag. dUcenH kñúgesovePAenH eyIgsnμt;eRbI shielded metal arc welding process¦. dUcenHsRmab;RbEvg L Edlrg bnÞúk P / kugRtaMgkmøaMgkat;eRKaHfñak;KW

LwPfv ××

=707.0

Edl w CaTTwgTwkbnSar

RbsinebIeKeRbI weld ultimate shearing stress/ WF enAkñúgsmIkarenH eKGacsresr

nominal load capacity rbs;TwkbnSardUcxageRkam³ Wn FLwR ×××= 707.0

ehIy nominal design strength KW Wn FLwR φφ ×××= 707.0 ¬&>@@¦



ersIusþg;rbs; fillet weld GaRs½yeTAnwgkareRbIR)as; weld metal EdlCaGnuKmn_eTAnwg RbePT electrode. ersIusþg;rbs; electrode RtUv)ankMNt;Ca ultimate tensile strength rbs;vaCamYy nwgersIusþg; 60, 70, 80, 90, 100, nig ksi120 b¤ 415, 480, 550, 620, 690, nig MPa830 sRmab; shielded metal arc welding process. nimitþsBaØasRmab;kMNt; electrod KWGkSr E Edlbnþ edayelxBIrxÞg; b¤bIxÞg;EdlbgðajBIersIusþg;rbs;vaCa ksi . edaysarEtersIusþg;CalkçN³dMbUg Edl

design engineer ykcitþTukdak; CaTUeTAGkSrBIrxÞg;cugeRkayRtUv)anbgðajeday XX ehIykMNt; smÁal;køayCa XXE70 b¤ 70E EdlbgðajBI electrode CamYy ultimate tensile strength ksi70 . eKKYreRCIserIs electrode [RtUvKñaCamYynwg base metal. sRmab; grade rbs;EdkEdleRbIR)as;TUeTA eKBicarNaEt electrode BIrRbePTb:ueNÑaHKW³ eRbI electrode XXE70 CamYynwgEdkEdlman yield strength tUcCag ksi60 eRbI electrode XXE80 CamYynwgEdkEdlman yied strength ksi60 b¤ ksi65 nimitþsBaØasRmab; electrode nigkarpþl;[rbs; AISC Specification EdledaHRsayCamYy nwgTwkbnSarRtUv)andkRsg;ecjBI Structural Welding Code rbs; American Welding Society

(AWS, 1996). eKGacrk)annUvlkçxNÐEdlminmanEcgenAkñúg AISC Specification enAkñúg AWS

Code. Design strength rbs;TwkbnSarRtUv)anbgðajenAkñúg AISC Table J2.5. Ultimate shearing

stress WF enAkñúg fillet weld es μInwg 6.0 dgén tensile strength rbs; weld metal EdlRtUv)ansM Kal;eday EXXF . dUcenH design stress KW WFφ Edl 75.0=φ nig EXXW FF 60.0= . sRmab; electrode FmμtaTaMgBIr design strengths (stresses) RtUv)anbgðajdUcxageRkam³ ( )[ ] ksiFXXE W 5.317060.075.0:70 ==φ ( )[ ] ksiFXXE W 36806.075.0:80 ==φ tRmUvkarbEnßmKWfakmøaMgkat;TTwgemKuNenAelI base metal minKYrbegáIt stress FMCag BMFφ Edl

BMFφ Ca nominal shear strength rbs;smÖar³EdlRtUvP¢ab;. dUcenHbnÞúkemKuNsRmab;tMNRtUv)an kMNt;Rtwm shear subject to metal base of area×= BMn FR φφ AISC J5, “Connecting elements” [ shear yielding strength Ca nRφ Edl



90.0=φ ygn FAR 6.0= (AISC Equation J5-3) nig gA CaRkLaépÞEdlrgkmøaMgkat;TTwg. dUcenH shear strength rbs; base metal CasresrCa yyBM FFF 54.0)6.0(90.0 ==φ dUcenH enAeBlEdlbnÞúksßitenAkñúgTisdUcG½kSrbs;TwkbnSar eKRtUveFVIkarGegát base metal edayeRbI TMnak;TMngénsmIkar &>@#. eKGacBnül;BItRmUvkarenHedayRtYtBinitükartP¢ab; bracket edaykar pSar EdlbgðajenAkñúgrUbTI 7>38. edaysn μt;fa bnÞúksßitenAEk,rcugEdlpSaredayeyIgGacecal cMNakp©it. RbsinebITWkbnSarTaMgBIrmanTMhMdUcKña design strength rbs;TwkbnSarmçag²kñúgRbEvg ÉktþaGacRtUv)anrkBIsmIkar &>@@ Ca WFw φ××707.0 b:uEnþBIsmIkar &>@#/ ersIusþg;rbs; bracket plate Tb;nwgkmøaMgkat;kñúgmYyÉktþaRbEvgKW BMFt φ× Cak;Esþg TwkbnSaminGacTb;Tl;nwgbnÞúkeRcIndUc base metal ¬kñúgkrNIenHvaCa bracket¦eT. eKdac; xatRtUvEteFVIkarGegátenHenAeBlEdl base metal rgnUvkmøaMgkat;TTwg. kñúgkrNIkartP¢ab;edaykarpSarCaeRcIn eTaHbICakarviPaKkþI karKNnakþI vamanPaBgayRsYl EdleKykersIusþg;kñúgmYyÉktþaRbEvgrbs;karpSar EdlGacCaersIusþg;rbs;TwkbnSar b¤CaersIusþg;rbs; base metal EdlmYyNatUcCagmksikSa. viFIenHnwgRtUv)anbgðajenAkñúg]TahrN_xageRkam.

]TahrN_ 7>12³ eKeRbIEdkbnÞHCaGgát;rgkarTajedayP¢ab;eTAnwg gusset pate dUcbgðajenAkñúgrUbTI 7>39. karpSarCaRbePT fillet welds .16/3 in EdleFVIeLIgCamYynwg electrode XXE70 . EpñkEdl



RtUvP¢ab;CaRbePTEdk 36A . snμt;faersIusþg;Tajrbs;Ggát;RKb;RKan; cUrkMNt; design strength rbs; tMNpSar.

dMeNaHRsay³ edaysarkarpSarmanlkçN³sIuemRTIeFobnwgG½kSrbs;Ggát; EpñknImYy²rbs;TwkbnSar nwgrgnUvkmøaMgEdlEbgEckes μ I. manEtRbEvgsrubrbs;TwkbnSar CamYynwgkmøaMgGnuvtþpÁÜbkat;tamTI RbCMuTm¶n;rbs;TwkbnSar ¬edayminKitcMNakp©ittictYc¦/ TItaMg nigTisedArbs;TwkbnSarnImYy²minTak; TgeT. ersIusþg;rbs; weld metal sRmab; electrode KW 70E ksiFW 5.31=φ ( ) ./176.45.31

163707.0707.0 inkipsFw W =⎟⎠⎞

⎜⎝⎛=×× φ

RtYtBinitü ersIusþg;rbs; base metal ¬kRmas;tUcCageKlub¦. BIwsmIkar &>@#/ shear subject to area×= BMn FR φφ

( ) ./86.4413654.054.0 inkipstFtF yBM =⎟⎠⎞

⎜⎝⎛==×= φ

ersIusþg;rbs;TwkbnSarlub. sRmab;kartP¢ab; ( ) kipsininkipsRn 4.33.44./176.4 =+×=φ cemøIy³ ersIusþg;rbs;tMNKW kips4.33 ]TahrN_ 7>13³ RbePTtMNEdleRbIenAkñúg]TahrN_ 7>12 RtUvTb;nwgkmøaMgemKuN kips40 . etI eKRtUvkarRbEvgTwkbnSarsrub RbePT filet weld .16/3 in EdleRbI electrode XXE70 b:unñan?



dMeNaHRsay³ ersIusþg;rbs;TwkbnSarkñúgmYyÉktþaRbEvgEdl)anBI]TahrN_TI 7>12 KW ./176.4 inkipsRn =φ RbEvgsrubEdlRtUvkarKW .58.9

176.440 in=

cemøIy³ RbEvgsrubKW .10in EdlRtUvKñanwg .5in sRmab;mçag².

karKNnakartP¢ab;edaykarpSarTamTarnUvkarBicarNanUv TMhMTwkbnSarGb,brma nigGtibrma nigRbEvgTwkbnSar. tRmUvkarTaMgenHsRmab; fillet welds RtUv)anbgðajenAkñúg AISC J2.2b

ehIyRtUv)an segçbdUcxageRkam³ TMhMGb,brma TMhMGb,brmaEdlGnuBaØatCaGnuKmn_eTAnwgkRmas;rbs;EpñkEdlRtUvP¢ab;Rkas;CageK ehIy RtUv)an[enAkñúg AISC Tabel J2.4. TMhMGtibrma tambeNþayRCugEKRmbs;Ggát;EdlmankRmas;tUcCag mmin 5.6.4/1 = TMhM fillet weld Gtibrmaes μ InwgkRmas;rbs;Ggát;enaH. sRmab;Ggát;EdlRkas;CagenH TMhMGtibrmaKW int 16/1− b¤

mmt 2− Edl t CaTMhMrbs;Ggát;. RbEvgGb,brma RbEvgGb,brmaGnuBaØatsRmab; fillet weld KWbYndgTMhMTwkbnSar. karkMNt;enHmintwgEtgeT b;uEnþRbsinebIminGacpþl;RbEvgTwkbnSarenH)an eKGaceRbIRbEvgxøICagenH)an RbsinebI effective size

rbs;TwkbnSarRtUv)aneKykesμ InwgmYyPaKbYnénRbEvfTwkbnSar. kartP¢ab;RbePTEdl)anbgðajenA kñúgrUbTI 7>40 EdldUcKñanwg]TahrN_BImun CakrNIBiesssRmab; shear lag sRmab;kartP¢ab;eday TwkbnSar Edl)anerobrab;enAkñúgCMBUkTI 3. AISC B3 )anbgðajfaRbEvgTwkbnSarenAkñúgkrNIenHmin RtUvtUcCagcm¶ayrvagTwkbnSareT KW WL ≥ .



End returns enAeBlEdlTwkbnSarlatsn§wgdl;kac;RCug vaRtUvEtbnþCMuvijRCugenaH dUcbgðajenAkñúgrUbTI 7>41. mUlehtusRmab;karbnþ EdleKehAfa end return KWCakarkarBarkugRtaMgRbmUlpþúM (stress

concentration) nigFanafaTMhMTwkbnSarRtUv)anrkSaelIRbEvgeBjrbs;TwkbnSar. End return KYrEt manRbEvgy:agtices μ IBIrdgTMhMTwkbnSar. RbEvgrbs; end return GacRtUv)anKitbBa©ÚleTAkñúgkar KNna load capacity b¤k¾eKGacecalva)an. CaTUeTAkarpSarEdlmanTMhMtUcmantémøefakCagkarpSarEdlmanTMhMFM. TMhMGtibrmaEdl eFVICamYynwgkarpSarmþgmanTMhMRbEhl .16/5 in ehIykarpSareRcIndgnwgbEnßmtémø. elIsBIenH sRmab; load capacity EdleKsÁal; eTaHbICaTwkbnSartUcbegáItRbEvgEvgCag EtTwkbnSarTMhMFMEdl begáItRbEvgxøInwgRtUvkarbrimaN weld metal eRcInCag.

]TahrN_TI 7>14³ r)arEdk 36A EdlmanTMhM .2/14 in× RtUv)aneRbICaGgát;rgkarTajedIm,ITb;Tl; nwg service dead load kips6 nig service live load kips18 . eKP¢ab;vaeTAnwg gusset plate Edlman kRmas; .8/3 in dUcEdlbgðajenAkñúgrUbTI 7>42. KNnakartP¢ab;edaypSar.

dMeNaHRsay³ enAkñúgkartP¢ab;enH base metal CaEdk 36A dUcenHeyIgRtUveRbI electrode XXE70 . edaysarEtRbEvgTwkbnSarminRtUv)ankMNt; dUcenHeyIgeRbITMhMGb,brmaGnuBaØat TMhMGb,brma .

163 in= (AISC Table J2.4)



sakl,g electrode XXE70 fillet weld .16/3 in . lT§PaBkñúgmYyÉktþaRbEvgKW ( ) ( ) ./176.45.31

163707.0707.0 inkipsFw W =⎟⎠⎞

⎜⎝⎛=φ

lT§PaBrbs; base metal KW ( ) ./29.7

833654.054.0 inkipstFy =⎟⎠⎞

⎜⎝⎛=

ersIusþg;rbs;TwkbnSartUcCag dUcenHeRbIvaedIm,IKNna. bnÞúkemKuN ( ) ( ) kipsLDPu 36186.162.16.12.1 =+=+= ehIy RbEvgEdlRtUvkar .62.8

176.436 in==

RbEvgGtibrma inin 62.875.01634 <=⎟⎠⎞

⎜⎝⎛= (OK)

sRmab; end return, RbEvgGb,brma .375.0

1632 in=⎟⎠⎞

⎜⎝⎛= yk .1in

sRmab;kartP¢ab;RbePTenH RbEvgrbs;TwkbnSarxagRtUvEtFMCagcm¶ayrvagTwkbnSar EdlkñúgkrNIenH KW es μ Inwg .4in . RbEvgTwkbnSarsrubrYmbBa©ÚlTaMg end return ( ) .62.8.10142 inin >=+ EdlRtUvkar cemøIy³ eRbI electrode XXE70 fillet weld .16/3 in CamYynwgRbEvg .10in dUcEdlbgðajenAkñúgrUb TI 7>43.

nimitþsBaØasRmab;karpSar karpSarRtUv)ankMNt;enAelI design drawing edaynimitþsBaØasþg;dar Edlpþl;nUvviFIgayRsYl sRmab;BN’naBItRmUvkarrbs;karpSar. PaBlMGitRtUv)an[enAkñúg Part 8 of the Manual, “Bolts,



Welds, and Connected Elements”(Volume II), ehIyminRtUv)anbgðajenATIenHGs;eT. enAkñúg esovePAenH eyIgpþl;EtkarENnaMy:agsegçbBInimitþsBaØabTdæansRmab; fillet welds dUcEdlbgðajenA kñúgrUbTI 7>44. nimitþsBaØaeKalKWExSedk (reference line) EdlrYmmanB½t’manBI RbePT/ TMhM nigRbEvgrbs; TwkbnSar rYmCamYynwgk,alRBYjEdlbgðajBITItaMgEdlRtUvpSar. RtIekaNEkgEdlmanRCugQrenA xageqVgRtUv)aneRbIedIm,Ibgðaj fillet weld. RbsinebIrUbRtIekaNenHenABIeRkam reference line kar pSarKWsßitenAxagrbs;k,alRBYj. EtpÞúymkvij ebIrUbRtIekaNenHsßitenAxagelI reference line vij enaHkarpSarRtUvsßitenAmçageTotrbs;kartP¢ab; EdlGac)aMg b¤min)aMgenAkñúgbøg;. elxenAelI reference line rab;BIeqVgmksþaM manTMhMTwkbnSar nigRbEvgTwkbnSar. vaKYrRtUv)andak;tamlMdab;Ebb enH. RbsinebITaMgxagmux nigxageRkayrbs;tMNEdlP¢ab;edaykarpSar B½t’manTaMgGs;RtUvEtbgðaj enAelI reference line TaMgelI nigeRkam. edIm,IkMNt;viFIsRsþEdlRtUveRbI b¤edIm,Ipþl;B½t’manbEnßm eK Gacdak;knÞúyRBYjenAxagcugrbs; reference line ehIykarkMNt;bgðajGacdak;enAEk,renaH. Rbsin ebIminmanB½t’manbEnßmeT knÞúyRBYjenaHRtUv)andkecj. cugeRkayrUbdgTg;CatiGacRtUv)andak;enA kEnøg Edl reference line kac;edIm,IbgðajfapSarenAkardæan.



]TahrNI 7>15³ bnÞHEdk 36A TMhM .84/3 in× RtUv)aneRbICaGgát;rgkarTajehIyRtUv)anP¢ab;eTAnwg gusset plate TMhM .8/3 in dUcbgðajenAkñúgrUbTI 7>45. RbEvgrbs;karP¢ab;minRtUvelIsBI .8in . KNna karpSaredIm,IbegáItkmøaMgTajeBjdl;Ggát;.

dMeNaHRsay³ design strength rbs;Ggát;QrelI gross area rbs;vaKW

( ) ( ) kipsAFP gynt 4.1948433690.090.0 =⎟⎠⎞

⎜⎝⎛==φ

bnÞab;mk KNna design strength rbs;Ggát;edayQrelI net area rbs;va. sRmab;kartP¢ab;Ggát; bnÞH RbsinebIkarpSarsßitenAEttamRCugxag enaH ge UAA = . EtRbsinebImankarpSartamTisTTwg enA xagcugGgát; enaH ge AA = . snμt;ykkrNITIBIr enaHeyIg)an ( ) ( ) kipsAFP euut 2618

435875.075.0 =⎟⎠⎞

⎜⎝⎛==φ

KNnasRmab;bnÞúkemKuN kips4.194 nigeRbI electrode 70E ksiFW 5.31=φ BI AISC Table J2.4 TMhMTwkbnSarGb,brmaKW .4/1 in . sakl,g fillet weld 70E TMhM .4/1 in ³ Design strength kñúgmYyÉktþaRbEvgrbs;TwkbnSar ( ) ./568.55.31

41707.0 inkips=⎟⎠⎞

⎜⎝⎛=

ersIusþg;rbs; base metal ( ) ./290.7833654.054.0 inkipstFy =⎟⎠⎞

⎜⎝⎛==

RbEvgTwkbnSarEdlRtUvkar .9.34568.5

4.194 in== tamsmμtikmμ RbEvgEdlGacpSar)anKW .24888 in=++ dUcenHeKminGaceRbITMhMTwkbnSar .4/1 in eT. RbsinebIRbEvgRtUv)ankMNt;Rtwm .24in enaHBIsmIkar &>@@ TMhMTwkbnSarEdlRtUvkarKW



( )( ) .364.05.3124707.0

4.194707.0

inFL

R

W

n ==×× φ

φ

sakl,g .8/3 in TMhMTwkbnSarGtibrma .

83.

1611

161

43 inin >=−= (OK)

RbEvgTwkbnSar .24.5.1834 inin <=⎟⎠⎞

⎜⎝⎛= (OK)

cemøIy³ eRbIkarpSardUcbgðajkñúgrUbTI 7>46.


T.Chhay 306 Eccentric Connections

VIII. tMNcakp©it Eccentric Connections

8>1> ]TahrN_sRmab;tMNcakp©it (Examples of Eccentric Connections) tMNcakp©itCatMNmYyEdlkmøaMgpÁÜbminkat;tamTIRbCMuTm¶n;rbs;eRKOgP¢ab; b¤TWkbnSar. Rbsin

ebItMNmanbøg;sIuemRTI eKeRbITIRbCMuTm¶n;rbs;RkLaépÞkmøaMgkat;rbs;eRKOgP¢ab; b¤TwkbnSarCacMNuc eKal (reference point) ehIycm¶ayEkgBIExSskm μrbs;kmøaMgeTATIRbCMuTm¶n;RtUv)aneKehAfa cMNak p©it. eTaHbICatMNCaeRcInGacrgnUvkmøaMgcakp©it EtkñúgkrNICaeRcIncMNakp©itTaMgenaHmantémøtUc EdlGacecal)an.

kartP¢ab; framed beam EdlbgðajenAkñúgrUbTI 8>1 a CaRbePTmYyéntMNcakp©it. kart P¢ab;enH eTaHCakñúgTRmg;tP¢ab;edayb‘ULúg b¤edaypSark¾eday vaRtUv)aneKeRbICaTUeTAsRmab;tP¢ab;Fñwm eTAssr. eTaHbICacMNakp©itkñúgtMNRbePTenHGacecal)ank¾eday EtvaRtUv)anykmkbgðajenATI enH. vamankartP¢ab;BIrepSgKñaKW kartP¢ab;BIEdkEkgeTAEdkFñwm nigkartP¢ab;EdkEkgeTAEdkssr. kartP¢ab;TaMgenHbgðajBItMNcakp©iteKalBIrRbePT³ tMNcMNakp©itEdlbegáItEtkmøaMgkat;TTwgenAkñúg eRKOgP¢ab; b¤TwkbnSar nigtMNcMNakp©itEdlbegáItTaMgkmøaMgkat;TTwg nigkmøaMgTaj.

RbsinebIeKBicarNaFñwm nigEdkEkgdac;edayELkBIssr dUcEdlbgðajenAkñúgrUbTI 8>1 b

enaHvabgðajy:agc,as;fa Rbtikm μ R eFVIGMeBIcMNakp©it e BITIRbCMuTm¶n;rbs;RkLaépÞrbs;eRKOgP¢ab;enA


tMNcakp©it 307 T.Chhay

kñúgRTnugFñwm. dUcenHeRKOgP¢ab;TaMgenHrgTaMgkmøaMgkat;TTwg nigm:Um:g;KU (couple) EdlsßitenAelI rbs;tMN ehIybegáItCakugRtaMgkmøaMgkat;rmYl (torsional shearing stress). RbsinebIssr nigEdkEkgRtUv)anpþac;ecjBIFñwm dUcbgðajenAkñúgrUbTI 8>3 c enaHeyIgeXIj y:agc,as;fa eRKOgP¢ab;enAkñúgsøabssrrgnRbtikmμ R EdlmanGMeBIenAcMNakp©it e BIbøg;rbs;eRKOg P¢ab; edaybegáIt couple dUcBImun. b:uEnþ kñúgkrNIenH bnÞúkminsßitenAkñúgbøg;rbs;eRKOgP¢ab; dUcenH couple eFVI[EpñkxagelIrbs;tMNrgkugRtaMgTaj ehIyEpñkxageRkamrgkugRtaMgsgát;. dUcenH eRKOg P¢ab;enAEpñkxagelIbMputrbs;tMNrgTaMgkmøaMgkat;TTwg nigkmøaMgTaj. eTaHbICa eyIgeRbIkartP¢ab;edayb‘ULúgenATIenHedIm,Ibgðajk¾eday k¾kartP¢ab;edaykarpSar Gacbgðajy:agsmBaØBIkarrgEtkmøaMgkat;TTwg b¤kmøaMgkat;TTwgrYmTaMgkmøaMgTaj.

RbtikmμbnÞúkemKuNGtibrmasRmab;tMN framed beam epSg²RtUv)an[enAkñúg Table 9-2 rhUtdl; 9-12 in Part 9 of the Manual, “Simple Shear and PR Moment Connections” (Volume

II). cMNap©itEdltUcEmnETnsRmab;tMNenHGacecal)an ehIyeKBicarNaEtkmøaMgkat;TTwgEt b:ueNÑaH. 8>2> tMNcMNakp©itedayb‘ULúg³ EtkmøaMgkat; (Eccentric Bolted Connections: Shear only)

rUbTI 8>2 EdlbgðajBI column bracket connection Ca]TahrN_BItMNedayb‘ULúgEdlrg kmøaMgkat;TTwgcakp©it. eKmanviFIBIrsRmab;edaHRsaybBaðaenH³ traditional elastic analysis ¬viPaK eGLasÞicburaN¦ nigviFIEdlmanlkçN³suRkitCag ¬b:uEnþsμ úKs μajCag¦ Ca ultimate strength

analysis ¬viPaKersIusþg;cugeRkay¦. viFITaMgBIrenHnwgRtUv)anbgðaj.



Elastic Analysis enAkñúgrUbTI 8>3 a, RkLaépÞkmøaMgkat;TTwgrbs;eRKOgP¢ab; nigbnÞúkRtUv)anbgðajdac;eday ELkBIssr nig bracket plate. eKGacdak;bnÞúkcMNakp©it P CamYynwgbnÞúkdUcKñaEdlmanGMeBIRtg; TIRbCMuTm¶n;rYmCamYynwg couple, PeM = Edl e CacMNakp©it. RbsinebIeyIgeFVIEbbenH bnÞúknwgman GMeBIcMp©it ehIyeKsn μt;faeRKOgP¢ab;nImYy²Tb;Tl;nUvcMENkbnÞúkes μ I²Kña KW nPpc /= Edl n CacMnYn eRKOgP¢ab;. kmøaMgeRKOgP¢ab;Edl)anBI couple Gacrk)anedaysn μt;fakugRtaMgkmøaMgkat;TTwgenAkñúg eRKOgP¢ab;CalT§plrbs; torsion énmuxkat;EdlekItBIRkLaépÞmuxkat;rbs;eRKOgP¢ab;. RbsinebI eyIgeFVIkarsnμt;EbbenH kugRtaMgkMMlaMgkat;enAkñúgeRKOgP¢ab;nImYy²GacRtUv)anrkBIrUbmnþkmøaMgrmYl

JMdfv = ¬*>!¦

Edl =d cm¶ayBITIRbCMuTm¶n;rbs;RkLaépÞeTAcMNucEdlkugRtaMgkMBugRtUv)ankMNt; =J m:Um:g;niclPaBb:UElrba;RkLaépÞeFobTIRbCMuTm¶n; ehIykugRtaMg vf EkgeTAnwg d . eTaHbICarUbmnþkmøaMgrmYlGnuvtþn_)anEtcMeBaHragsIuLaMg EteKeRbIva enATIenHedIm,IsnSMsMéc edaysar yielding stress mantémøFMCagkugRtaMgBitR)akd.

RbsinebIeKeRbIRTwsþIbTG½kSRsb (parallel-axis theorem) ehIyeKecalm:Um:g;niclPaBb:UElr

énRkLaépÞeFobG½kSTIRbCMuTm¶n;rbs;va enaHeKGackMNt; J sRmab;RkLaépÞsrubKW



22 dAAdJ ∑=∑= edayRKb;eRKOgP¢ab;manRkLaépÞ A dUcKña. enaHsmIkar *>! GacRtUv)ansresrCa 2dA

Mdfv∑

=

ehIykmøaMgkat;enAkñúgeRKOgP¢ab;nImYy²EdlekIteLIgeday couple KW

22 dMd

dAMdAAfP vm

∑=

∑==

dUcenHbgÁúMkmøaMgkat;TTwgTaMgBIrEdl)ankMNt;RtUv)anbUkbEnßmedaybBaÄredIm,ITTYl)ankmøaMgpÁÜb P dUcbgðajenAkñúgrUbTI 8>3 b EdleyIgykeRKOgP¢ab;enAxagsþaMEpñkxageRkameKbMputmkbgðaj. enA eBlEdleKkMNt;)ankmøaMgpÁÜbFMCageKbMput TMhMeRKOgP¢ab;k¾RtUv)aneRCIserIsedIm,ITb;Tl;kmøaMgenaH. eKminGaceFVIkarGegátedIm,IrkeRKOgP¢ab;EdleRKaHfñak;CaeKeT KWeKRtUveFVIkarKNnaCatémøelx. CaTUeTA vamanlkçN³gayRsYlCagkñúgkareFVIkarCamYynwgbgÁúMkmøaMgctuekaNEkg. sRmab; eRKOgP¢ab;nImYy² bgÁúMkmøaMgedk nigbgÁúMkmøaMgQrEdl)anBIkmøaMgkat;TTwgedaypÞal;KW

nP

p xcx = nig

nP

p ycy =

Edl xP nig yP CabgÁúMkmøaMgtamTis x nigTis y rbs;kmøaMgsrub P dUcEdl)anbgðajenAkñúgrUbTI 8>4. eKGacrkbgÁúMkmøaMgedk nigQrEdlekIteLIgedaycMNakp©itdUcxageRkam.

cm¶ayBITIRbCMuTm¶n;rbs;tMNeTAeRKOgP¢ab;nImYy²

( )222 yxd +∑=∑ Edl cMNucrYmrbs;RbB½n§kUGredaenKWCaTIRbCMuTm¶n;énRkLaépÞkmøaMgkat;rYmrbs;eRKOgP¢ab;. kmøaMgpÁÜb tamTis x rbs; mp KW³



( ) ( )22222 yxMy

yxMd

dy

dMd

dyp

dyp mmx

+∑=

+∑=

∑==

dUcenH ( )22 yxMxpmy+∑

=

ehIykmøaMgeRKOgP¢ab;srubKW ( ) ( )22

yx ppp ∑+∑= Edl mxcxx ppp +=∑ mycyy ppp +=∑ RbsinebI P ¬bnÞúkEdlGnuvtþeTAelItMN¦ CabnÞúkemKuN enaHkmøaMg p enAelIeRKOgP¢ab;Ca bnÞúkem KuNedIm,ITb;Tl;nwg shear nig bearing EdlCa design strength EdlRtUvkar. ]TahrN_ 8>1³ kMNt;kmøaMgrbs;eRKOgP¢ab;EdleRKaHfñak;enAkñúg bracket connection Edl)anbgðaj enAkñúgrUbTI 8>5.

dMeNaHRsay³ TIRbCMuTm¶n;rbs;RkumeRKOgP¢ab;GacRtUv)anrkedayeRbIG½kSedkkat;tameRkam nigeday GnuvtþeKalkarN_m:Um:g; ( ) ( ) ( ) .6

81128252 iny =

++=

bgÁúMkmøaMgQr nigkmøaMgedkKW ( ) ←== kipsPx 63.2250

51 nig ( ) ↓== kipsPy 72.4450

52



edayeyageTAtamrUbTI 8>6 a, eyIgGacKNnam:Um:g;rbs;bnÞúkeFobTIRbCMuTm¶n;³ ( ) ( ) kipsinM −=−−+= .7.48061436.2275.21272.44 ¬RsbRTnicnaLika¦

rUbTI 8>6 b bgðajBITisedArbs;bgÁúMkmøaMgb‘ULúg nigTMhMénbgÁúMkmøaMgb‘ULúgEdlRtUvKñaEdlekIteLIg edaym:Um:g;KUr (couple). edayeRbITisedATaMgenH nigTMhMEdlRtUvKñaCakarnaMpøÚvEdlkmøaMgTaMgenaH RtUv)anbUktamc,ab;RbelLÚRkam. eyIgGacsnñidæan)anfaeRKOgP¢ab;xagsþaMEpñkxageRkameKbMput nwgmankmøaMgpÁÜbFMCageKbMput. bgÁúMkmøaMgedk nigbBaÄrrbs;eRKOgP¢ab;nImYy²Edl)anBIkmøaMgcMp©itKW ←== kipspcx 795.2

836.22 nig ↓== kipspcy 590.5

872.44

sRmab; couple ( ) ( ) ( ) ( ) ( ) ( )[ ] 22222222 5.1925216275.28 inyx =++++=+∑



( )( )

←==+∑

= kipsyx

Mypmx 98.145.19267.480

22

( )( )

↓==+∑

= kipsyx

Mxpmy 867.65.19275.27.480

22

←=+=∑ kipspx 78.1798.14795.2 ↓=+=∑ kipsp y 46.12867.6590.5 ( ) ( ) kipsP 7.2146.1278.17 22 =+= ¬emIlrUbTI 8>6 c¦ cemøIy³ kmøaMgb‘ULúgEdleRKaHfñak;KW kips7.21 . karGegátBITMhM nigTisedArbs;bgÁúMkmøaMgedk nigbBaÄrbBa¢ak;fakarsnñidæanfaeRKOgP¢ab;Edl)aneRCIserIsBitCamaneRKaHfñak;Emn.

Ultimate Strength Analysis viFIEdlerobrab;BIxagmuxmanlkçN³gayRsYlkñúgkarGnuvtþ b:uEnþminsuRkit. kñúgkarviPaK KW )ansnñidæanfaTMnak;TMngbnÞúk-kMhUcRTg;RTayrbs;eRKOgP¢ab;manlkçN³smamaRt ¬CabnÞat;¦ ehIy fa yield stress minRtUvFM. karBiesaFn_bgðajfavaminEmnCakrNI ehIyfaeRKOgP¢ab;nImYy²minman shear yield stress BitR)akdeT. viFIsaRsþEdlBN’naenATIenHkMNt; ultimate strength rbs;tMN edayeRbITMnak;TMngminsmamaRtbnÞúk-kMhUcRTg;RTayEdlkMNt;edaykarBiesaFn_ sRmab;eRKOgP¢ab; nImYy². karsikSaedaykarBiesaFEdlraykarN_enAkñúg Crawford and Kulak (1971) edayeRbI b‘ULúgRbePT bearing 325A Ggát;p©it .4/3 in nigEdkbnÞH 36A b:uEnþlT§plGaceRbIsRmab;b‘ULúg

325A EdlmanTMhMepSg²CamYynwgEdkRbePTepSg²CamYynwglT§pllMeGogtictYc. viFIenHnwgpþl; nUvlT§pllMeGogenAeBleRbICamYyb‘ULúg slip-critical nigCamYyb‘ULúg 490A (AISC, 1994). kmøaMgb‘ULúgEdlRtUvnwgkMhUcRTg;RTay Δ KW ( )λμΔ−+= eRR ult 1

( ) 55.010174 Δ−= e ¬*>@¦ Edl =ultR kmøaMgkat;TTwgrbs;b‘ULúgenAeBldac; MPakips 33074 == =e eKalrbs;elakenEB 718.2= =μ emKuNkat;bnßy 10= =λ emKuNkat;bnßy 55.0=



Ultimate strength rbs;tMNKWQrelIkarsnμt;dUcxageRkam³ !> enAeBldac; RkumeRKOgP¢ab;vilCMuvij instantaneous center (IC).

@> kMhUcRTg;RTayrbs;ERKOgP¢ab;mYy²smamaRteTAnwgcm¶ayBI IC nwgeFVIGMeBIEkgeTAkaMén rgVil.

#> eKGacTTYl)anlT§PaBrbs;tMNenAeBlEdl ultimate strength rbs;eRKOgP¢ab;enAq¶aybM putBI IC. ¬rUbTI 7>8 bgðajBIkmøaMgb‘ULúgCakmøaMgTb;Tl;EdleFVIGMeBIRbqaMgnwgkmøaMg Gnuvtþn_¦.

$> EpñkEdlRtUvP¢ab;RtUvEtrwg. Cavi)akénkarsnμt;TIBIr kMhUcRTg;RTayrbs;eRKOgP¢ab;nImYy²KW

( )34.0max

maxmax r

rr

r=Δ=Δ

Edl =r cm¶ayBI IC eTAeKOgP¢ab; =maxr cm¶ayeTAeRKOgP¢ab;EdlenAq¶aybMput =Δmax kMhUcRTg;RTayrbs;eRKOgP¢ab;q¶aybMputenA ultimate .34.0 in= ¬EdlkMNt;eday karBiesaFn_¦

CamYynwg elastic analysis, vamanPaBgayRsYlCagkñúgkareFVIkarCamYynwgbgÁúMkmøaMgctuekaNEkg b¤ R

rxRy = b¤ R

ryRx =



Edl x nig y Cacm¶ayedk nigcm¶aybBaÄrBI instantaneous center eTAeRKOgP¢ab;. enAxN³eBl dac; lMnwgRtUv)anrkSa ehIysmIkarlMnwgbIxageRkamRtUv)anGnuvtþeTAelIRkumeRKOgP¢ab; ¬eyageTAelI rUbTI 8>7¦³ ( ) 0

1=−=∑ ∑

=x

m

nnxx PRF ¬*>#¦

( ) ( ) 01

=×−+= ∑=

m

nnnoIC RrerPM ¬*>$¦

ehIy ( ) 0=−∑=∑ ynym

y PRF ¬*>%¦ Edl Gnu)at n kMNt;nUveRKOgP¢ab;mYy² nig m CacMnYnsrubrbs;eRKOgP¢ab;. viFIsaRsþTUeTAKWsnμt;TI taMg instantaneous center bnÞab;mkkMNt;témøRtUvKñarbs; P EdlbMeBjsmIkarlMnwg. RbsinebI GBa©wgEmn TItaMgenHKWRtwmRtUv ehIy P CalT§PaBrbs;tMN. viFIsaRsþCak;lak;KWdUcxageRkam³ !> snμt;témøsRmab; or . @> edaHRsayrk P BIsmIkar *>$. #> CMnYs or nig P eTAkñúgsmIkar *># nig *>%.

$> RbsinebIsmIkarTaMgenaHRtUv)anbMeBjCamYynwgkRmitlMeGogEdlGacTTYlyk)an kar viPaKenHRtUv)anbBa©b;. EtebImindUecñaHeT eKRtUveFVIkareRCIserIstémøsakl,g or fμ I ehIy eKRtUveFVIkarKNnaeLIgvij.

sRmab;krNITUeTAénbnÞúkbBaÄr smIkar *># nwgRtUv)anbMeBjedays½VyRbvtþ. edIm,IPaBgay RsYl nigkMu[)at;bg;»PasPaB eyIgBicarNaEtkrNIenH. EteTaHbICamYykarsn μt;enH karKNna sRmab; trial problem CaeRcInmanlkçN³lM)ak EdlRtUvkarCMnYykMuBüÚT½rCacaM)ac;. Epñk (B) rbs; ]TahrN_ 8>2 RtUv)aneFVIkarCamYynwgCMnYyBI standard spreadsheet program sRmab; personal

computers. ]TahrN_ 8>2³ Bracket connection EdlbgðajenAkñúgrUbTI 8>8 RtUvRTkmøaMgemKuNcakp©it kips53 . tMNRtUv)anKNnaeday[manb‘ULúgBIrCYrQr EdlkñúgmYyCYr²manb‘ULúg 4 RKab; Etb‘ULúgmYyRKab; RtUv)andkecaledayKμanectna. RbsinebIeKeRbIb‘ULúg bearing-type 325A EdlmanGgát;p©it .8/7 in etItMNenHmanlkçN³RKb;RKan;b¤Gt;? snμt;faeFμjb‘ULúgsßitenAkñúgbøg;kat;. eRbIEdk 36A nigGnuvtþ nUvkarviPaKxageRkam³ (a) elastic analysis; (b) ultimate strength analysis.



dMeNaHRsay³ a. Elastic analysis. sRmab;RbB½n§kUGredaenEdlmanKl;enARtg;p©itrbs;b‘ULúgxag eRkamEpñkxageqVg ¬rUbTI 8>9¦ ( ) ( ) ( ) .857.3

7916232 iny =

++=

( ) .286.1733 inx ==

( ) ( ) ( ) ( ) ( ) ( ) ( ) 222222222 .29.82143.51143.22857.02857.32714.13286.14 inyx =+++++=+∑

.714.6286.153 ine =−+= ( ) kipsinPeM −=== .8.355714.653 ¬RsbRTnicnaLika¦ ↓== kipspcy 571.7

753 0=cxp

BITisedA nigTMhMEdlRtUvKñaEdlbgðajenAkñúgrUbTI 8>9 b‘ULúgeRkameKEpñkxagsþaMRtUv)ancat;TukfaCa b‘ULúgEdlmaneRKaHfñak;CageK ( )

( )←==

+∑= kips

yxMypmx 68.16

29.82857.38.355

22

( )( )

↓==+∑

= kipsyx

MxPmy 411.729.82

714.18.35522

kipspx 68.16=∑ kipsp y 98.14411.7571.7 =+=∑ ( ) ( ) kipsp 4.2298.1468.16 22 =+=



edIm,IkMNt; design strength rbs;b‘ULúgrg bearing eRbIGgát;p©itrn§ .

1615

161

87

161 indh =+=+=

sRmab;rn§EdlenAEk,rRCugEKmCageK eRbI .2inLe = enaH .513.1

216/152

2inhLL ec =−=−=

.75.18722 ind =⎟⎠⎞

⎜⎝⎛=

eday dLc 2< bearing strength KW ( ) ( )( )( )( ) boltkipstFLR ucn /4.3658455.0531.12.175.02.1 === φφ sRmab;rn§epSgeTot eRbI .3ins = enaH dinhsLc 2.062.2

16153 >=−=−=

dUcenH ( ) ( ) ( )( ) boltkipsdtFR un /56.4158455.0874.275.04.2 =⎟⎠⎞

⎜⎝⎛== φφ

témø bearing TaMgBIrFMCagkmøaMgkñúgmYyb‘ULúg dUcenH bearing strength KWRKb;RKan;. sRmab; shear ( ) 2

2.6013.0

48/7 inAb ==

π ( )( ) kipskipsAFR bvn 4.226.216013.04875.0 <=== φφ (N.G.) cemøIy³ tMNminbMeBjlkçxNÐeday elastic analysis.



b. eyIgedaHRsaytamviFI ultimate strength analysis CamYynwgCMnYyrbs; standard spreadsheet

software. lT§plrbs;témøsakl,gcugeRkayrbs; .57104.1 inro = RtUv)an[enAkñúgtarag 8>1. RbB½n§kUGredaen nigelxerogb‘ULúgRtUv)anbgðajenAkñúgtarag 8>10. tarag 8>1

eKalenARtg; b‘ULúgelx !

eKalenARtg; IC eRKOg

P¢ab; 'x 'y x y

r Δ R rR Ry

1 0.000 0.000 0.285 -3.857 3.868 0.255 70.774 273.731 5.221

2 3.000 0.000 3.285 -3.857 5.067 0.334 72.553 367.598 47.045

3 0.000 3.000 0.285 -0.857 0.903 0.060 47.649 43.046 15.050

4 3.000 3.000 3.285 -0.857 3.395 0.224 69.563 236.188 67.310

5 0.000 6.000 0.285 2.143 2.162 0.143 63.631 137.555 8.398

6 3.000 6.000 3.285 2.143 3.922 0.259 70.891 278.061 59.377

7 0.000 9.000 0.285 5.143 5.151 0.340 72.631 374.107 4.023

srub 1710.287 206.424



BIsmIkar *>$ ( ) rRerP o ∑=+ kips

errRP

o424.206

71429.657104.129.1710

=+

=+

∑=

Edl e RtUv)anyk 5 xÞg;eRkayex,ósedIm,IsuRkitPaBx<s;. BIsmIkar *>% 00.0424.206424.206 =−=−∑=∑ PRF yy bnÞúkEdlGnuvtþminmnabgÁúMkmøaMgedk dUcenHsmIkar *># RtUv)anbMeBjedaysV½yRbvtþ. bnÞúk kips424.206 EdleTIbnwg)ankMNt;Ca failure load sRmab;kartP¢ab; ehIyRtUv)anQr enAelIeKalkarN_EdleRKOgP¢ab;EdleRKaHfñak;eTAdl; ultimate load capacity. RbsinebIbnÞúkdac; rbs;tMNRtUv)anKuNedaypleFob fasterner design strength elI fasterner ultimate strength

kips74 (Crawford nig Kulak, 1971), eyIgnwgTTYl)anlT§PaBrbs;tMN. BI a. design strength rbs;b‘ULúgmYy ¬EdlQrelI shear¦ KW kips6.21 . bnÞúkemKuNGtibrma ( ) kipskips 531.6074/6.21206 >== (OK) cemøIy³ kartP¢ab;manlkçN³RKb;RKan;eday ultimate strength analysis. Table 8-18 dl; 8-25 enAkñúg Part 8 of the Manual (Volume II) pþl;[emKuNsRmab;viPaK b¤KNnaKMrUFm μtaénRkumb‘ULúgEdlrgnUvbnÞúkcakp©it. sRmab;kartMeobb‘ULúgnImYy²Edl)anBicarNa taragTaMgenaHpþl;nUvtémø C EdlCapleFob connection failure load elI fasterner ultimate

strength. edImI,TTYl)anbnÞúktMNEdlmansuvtßiPaB témøefrenHRtUv)anKuNeday design strength rbs;eRKOgP¢ab;EdleRbI. sRmab;bnÞúkcakp©itminRtUv)anbBa©ÚleTAkñúgtaragTaMgenHeT dUcenH eKGac eRbI elastic method EdlCaviFImansuvtßiPaB. BitNas; kmμviFIkMuBüÚT½r b¤ spreadsheet software k¾RtUv )aneRbIedIm,IKNna ultimate strength anlysis. ]TahrN_ 8>3³ eRbItaragenAkñúg Part 8 of the Manual edIm,IkMNt; factored load capacity uP Edl QrelI bolt shear sRmab;tMNEdlbgðajenAkñúgrUbTI 8>11. b‘ULúg bearing-type 325A Ggát;p©it

.4/3 in edayeF μjsßitenAkñúgbøg;kat;. b‘ULúgrgnUv single shear.



design strength rbs;b‘ULúgGgát;p©it .4/3 in Edlrg single shear KW ( ) ( )( ) kipsAr bn 90.154418.04875.048 === φφ eday nu rPC φ/= / ( ) kipsrCP nu 3.2490.1553.1 === φ cemøIy³ lT§PaBbnÞúkemKuNGtibrma (maximum factored load capacity) rbs;tMNKW kips3.24 . 8>3> tMNcMNakp©itedayb‘ULúg³ kmøaMgkat;bUknwgkmøaMgTaj

Eccentric Bolted Connections: Shear Plus Tension sRmab;kartP¢ab;EdleKeRbI tee stub bracket dUckñúgrUbTI 8>12 bnÞúkcMNakp©itbegáIt couple EdlGacbegáInkmøaMgTajenAkñúgCYrxagelIrbs;eRKOgP¢ab; ehIykat;bnßykugRtaMgTajenAkñúgCYrxag eRkam. RbsinebIeRKOgP¢ab;Cab‘ULúgEdlK μankugRtaMgTajedIm b‘ULúgxagelInwgRtUv)andak;[rgkug RtaMgTaj ehIyb‘ULúgxageRkamnwgminrg\T§iBl. edayminKitBIRbePTrbs;eRKOgP¢ab; b‘ULúgnImYy² nwgrgnUvcMENkkmøaMgkat;es μI²Kña.



RbsinebIeRKOgP¢ab;Cab‘ULúgersIusþg;x<s;EdlrgeRbkugRtaMg épÞb:Hrvagsøabssr nigsøab bracket nwgrgkarsgát;esμI munnwgkmøaMgxageRkAGnuvtþmk. Bearing pressure nwges μ InwgkmøaMgTaj b‘ULúgsrubEdlEckedayépÞb:H. edaysarbnÞúk P Gnuvtþbnþicmþg² kmøaMgsgát;enAxagelInwgRtUv)an kat;bnßy ehIykmøaMgsgát;enAxageRkamnwgekIneLIg dUcbgðajenAkñúgrUbTI 8>13 a. enAeBlEdlkM laMgsgát;enAxagelIRtUv)anrMsayGs;rlIg bgÁúMkmøaMgnwgRtUv)anbMEbk ehIy couple Pe nwgRtUv)an Tb;Tl;edaykmøaMgb‘ULúgTaj ehIykmøaMgsgát;enAelIépÞb:HEdlenAsl; dUcEdlbgðajenAkñúgrUbTI 8>13 b. enAeBlEdlkmøaMgxiteTArk ultimate load kmøaMgenAkñúgb‘ULúgnwgxiteTACit ultimate

tensile strength rbs;va. viFIEdlsamBaØ nigmansuvtßiPaBRtUv)aneRbIenATIenH. eKsnμt;G½kSNWtrbs;tMNkat;tamTIRbCMu Tm¶n;rbs;RkLaépÞb‘ULúg. bU‘LúgEdlsßitenABIxagelIG½kSenHrgkmøaMgTaj ehIyb‘ULúgEdlenABIxag eRkamG½kSenHRtUv)ansnμt;fargkmøaMgsgát; dUcbgðajenAkñúgrUbTI 8>13 c. b‘ULúgnImYy²RtUv)ansnμt; faTTYl)antémø ultimate utr . edaysarEtmanb‘ULúgBIrRKab;enARKb;nIv:U ¬rUbTI 8>13 c¦ kmøaMgnI-mYy²RtUv)anbgðaj utr2 . kmøaMgpÁÜbénkmøaMgTaj nigkmøaMgsgát;Ca couple Edles μ Inwgm:Um:g;Tb;rbs; tMN. m:Um:g; couple GacRtUv)anrkedayeFVIplbUkm:Um:g;énkmøaMgb‘ULúgeFobG½kSNamYyEdlgayRsYl dUcCaG½kSNWt. enAeBlEdlm:Um:g;Tb;RtUv)andak;[esμ Im:Um:g;Gnuvtþn_ eKGacrkkmøaMgTajb‘ULúg utr EdlminsÁal;BIsmIkarEdlTTYl)an. ¬viFIenHRsedogKñanwg Case II in Part 8 of the Manual,

Volume II).



]TahrN_ 8>4³ tMN beam-to-column RtUv)anbegáIteLIgeday structural tee dUcbgðajenAkñúgrUbTI 8>14. eKeRbIb‘ULúg fully tightened bearing-type 325A Ggát;p©it .4/3 in cMnYn 8 RKab;edIm,IP¢ab; søabrbs; tee eTAnwgsøabssr. cUrGegátPaBRKb;RKan;rbs;tMN ¬tee-to-column connecvtion¦ Rb sinebIvargbnÞúkemKuN kips88 enAcMNakp©it .3in . snμt;faeFμjb‘ULúgsßitenAkñúgbøg;kat;. EdkTaMg Gs;Ca 36A .

dMeNaHRsay³ shear/bearing load sRmab;b‘ULúgmYyKW kips118/88 = . sRmab; bearing design

strength eRbIGgát;p©itRbehag .

1613

161

43

161 indh =+=+=

sRmab;RCugEdlenAEk,rRCugEKmCageKbMput yk .5.1 inLe = . enaH .094.1

216/135.1

2inhLL ec =−=−=

.5.14322 ind =⎟⎠⎞

⎜⎝⎛=

edaysar dLc 2< / ( ) ( )( )( )( ) kipskipstFLR ucn 1198.3158560.0094.12.175.02.1 >=== φφ (OK) sRmab;RbehagepSgeTotyk .3ins = . enaH dinhsLc 2.188.2

16133 >=−=−=

dUcenH ( ) ( ) ( )( ) kipskipsdtFR un 1185.4358560.0434.275.04.2 >=⎟⎠⎞

⎜⎝⎛== φφ (OK)



tMNmanlkçN³RKb;RKan;sRmab; bearing. sRmab; shear design strength ( ) 2

24418.0

44/3 inAb ==

π ( )( ) kipsAFR bvn 90.154418.04875.0 === φφ KNnakmøaMgTajsRmab;b‘ULúgmYy nwgbnÞab;mkRtYtBinitü tension-shear interaction. edaysarPaB sIuemRTI TIRbCMuTm¶n;sßitenAkm<s;Bak;kNþal. rUbTI 8>15 bgðajRkLaépÞb‘ULúg nigkarEbgEckkmøaMg Tajb‘ULúg. m:Um:g;rbs; resisting couple RtUv)anrkedayeFVIplbUkm:Um:g;eFobG½kSNWt³ ( ) ututNA rrM 245.45.15.15.42 =+++=∑ m:Um:g;EdlGnuvtþKW ( ) kipsinePM uu −=== .264388 dak;m:Um:g;Tb; nigm:Um:g;Gnuvtþn_[es μ IKña eyIg)an 26424 =utr b¤ kipsrut 11= Tensile design strength KW ( )( ) kipsAFR btn 82.294418.09075.0 === φφ RtYtBinitü RCSC Equation LRFD 4.2 BI bolt specification (RCSC, 1994) CamYynwg

kipsrP utu 11== nig =uV bolt shear force kips11=

( ) ( ) 0.1615.09.15

1182.29

11 2222

<=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

vn

u

tn

uRV

RP

φφ (OK)

cemøIy³ tMNKWRKb;RKan;



enAeBlEdlb‘ULúgenAkñúgtMN slip-critical rgkarTaj slip-critical strength CaFm μtaRtUv)an kat;bnßyedayemKuNEdlpþl;[eday AISC Equation A-J3-2 ¬emIl Epñk 7>9¦. mUlehtuKWfa clamping effect nigkmøaMgkkitRtUv)ankat;bnßy. b:uEnþenAkñúgtMNEdleTIbnwgBicarNa vamankmøaMg sgát;bEnßmenAkñúgEpñkxageRkamrbs;tMNEdlbegáInkmøaMgkkit EdlvaTUTat;nwgkarkat;bnßyenAkñúg EpñkxageRkamrbs;tMN. sRmab;mUlehtuenH slip-critical strength minKYrRtUv)ankat;bnßyenAkñúgRb ePTtMNenHeT. 8>4> tMNcMNakp©itedaypSar³ EtkmøaMgkat;

Eccentric Welded Connections: Shear only eKviPaKtMNcMNakp©itedaypSartamviFIdUcKñasRmab;tMNedayb‘ULúg elIkElgRtg;kmøaMgkñúg eRKOgP¢ab;mYy²RtUv)anCMnYsedaykmøaMgkñúgRbEvgTwkbnSarÉktþa. dUckñúgkrNIEdltMNcMNakp©it edayb‘ULúgrgkmøaMgkat; tMNedaypSarrgkmøaMgkat;GacRtUv)anGegátedayviFI elastic method b¤ ultimate strength method. Elastic method bnÞúkenAelI bracket EdlbgðajenAkñúgrUbTI 8>16 a GacnwgRtUv)anBicarNa[eGVIGMeBIenA kñúgbøg;énTwkbnSar EdlCabøg;rbs; throat. RbsinebIeyIgsn μt;EbbenH bnÞúknwgRtUv)anTb;edayRkLa épÞTwkbnSarEdlbgðajenAkñúgrUb 8>16 b. b:uEnþ karKNnamanlkçN³samBaØ RbsinebIeKeRbI throat mYyÉktþa. bnÞab;mkbnÞúkEdlKNna)anRtUvKuNnwg 707.0 CamYynwgTMhMrbs;TwkbnSaedIm,ITTYl)an bnÞúkBitR)akd.



bnÞúkcMNakp©itenAkñúgbøg;TwkbnSarEdleFVI[TwkbnSarrgTaMgkmøaMgkat;pÞal; (direct shear)

nigkmøaMgkat;edayrmYl (torsional shear). edaysarFatunImYy²rbs;TwkbnSarTb;Tl;nwgcMENk es μ Irbs; direct shear enaH direct shear stress KW

LPf =1

Edl L CaRbEvgsrubrbs;TwkbnSar ehIyesμ InwgRkLaépÞkmøaMgkat;edayKitCaelx edaysareKsnμt; TMhM throat esμ InwgmYyÉktþa. RbsinebIeKeRbIkMub:Usg;Ekg

LP

f xx =1 nig

LP

f yy =1

Edl xP nig yP CabgÁúMkmøaMgtamTis x nig y . kugRtaMgkmøaMgkat;EdlekIteLIgedaysar couple RtUv)aneKrkCamYynwgrUbmnþkmøaMgrmYl

JMdf =2

Edl =d cm¶ayBITIRbCMuTm¶n;rbs;RkLaépÞkmøaMgkat;eTAcMNucEdlkugRtaMgkMBugRtUv)anKNna =J m:Um:g;niclPaBb:UElrrbs;RkLaépÞenaH rUbTI 8>17 bgðajBIkugRtaMgTaMgenHenARtg;kac;RCugxagelIEpñkxageRkamrbs;TwkbnSar. tamkMub:Usg; Ekg

JMyf x =2 nig

JMxf y =2

Edl ( ) ∫ ∫∫∫ +=+=+==A A xyAA

IIdAydAxdAyxdArJ 22222

Edl xI nig yI Cam:Um:g;niclPaBrbs;RkLaépÞkmøaMgkat;. enAeBlEdlbgÁúMkmøaMgTaMgGs;RtUv)ankM Nt; eyIgGacbUkbgÁúMkmøaMgedIm,ITTYl)ankugRtaMgkmøaMgkat;srubenARtg;cMNucEdleyIgcg;dwg b¤ ( ) ( )22

yxv fff ∑+∑=



dUcKñanwgtMNedayb‘ULúg CaTUeTATItaMgeRKaHfñak;sRmab;kugRtaMgpÁÜbGacRtUv)ankMNt;BIkarsegátelI témø nigTisedArbs;bgÁúM direct shear nig torsional shearing stress. edaysareKeRbITwkbnSarkñúgmYyÉktþa karKNnaTIRbCMuTm¶n; nigm:Um:g;niclPaBKWmanlkçN³Ca ExSbnÞat;. enAkñúgesovePAenH eyIgKitGgát;TwkbnSarCaGgát;ExSEdleyIgsnμt;eTARbEvgdUcKñanwgRCug EKmrbs;EpñkEdlRtUvP¢ab;EdlenAEk,rva. elIsBIenH eyIgecalm:Um:g;niclPaBrbs;Ggát;ExSeFobeTA nwgG½kSEdlRtYtKñaCamYynwgExS. ]TahrN_ 8>5³ kMNt;TMhMrbs;TwkbnSarEdlRtUvkarsRmab;tMN bracket enAkñúgrUbTI 8>18. bnÞúk

kips60 CabnÞúkemKuN. eKeRbIEdk 36A sRmab;ssr nig bracket.

dMeNaHRsay³ eKGacCMnYsbnÞúkcakp©itedaybnÞúkcMp©it nig couple dUcbgðajenAkñúgrUbTI 8>18. Direct shearing stress KitCa ./ inkips KWdUcKñasRmab;RKb;Ggát;TwkbnSar ehIyesμ Inwg



./143.22860

812860

1 inkipsf y ==++

= munnwgKNnabgÁúMkmøaMgrmYlrbs; shearing stress, eKRtUvkMNt;TItaMgrbs;TIRbCMuTm¶n;rbs;RkLaépÞ kmøaMgkat;. BIeKalkarN_m:Um:g;CamYynwgplbUkm:Um:g;eFobG½kS y / ( ) ( )( )24828 =x b¤ .286.2 inx = cMNakp©it e KW .71.15286.2810 in=−+ ehIym:Um:g;rmYlKW ( ) kipsinPeM −=== .6.94271.1560

RbsinebIeKecalm:Um:g;niclPaBrbs;TwkbnSartamTisedknImYy²eFobG½kSTIRbCMuTm¶n;rbs;va enaH m:Um:g;niclPaBénRkLaépÞsrubeFobnwgG½kSTIRbCMuTm¶n;tamTisedkKW ( )( ) ( )( ) 423 .0.720682121

121 inI x =+=

dUcKña ( )( ) ( ) ( ) 4223 .0.195286.212286.248811212 inI y =+⎥⎦

⎤⎢⎣⎡ −+=

ehIy 40.9150.1950.720 inIIJ yx =+=+= rUbTI 8>18 bgðajTisedArbs;bgÁúMkugRtaMgTaMgBIrenAkac;RCugrbs;tMNnImYy². tamkarsegát/ kac; RCugxagelIEpñkxagsþaM b¤kac;RCugxageRkamEpñkxagsþaMGacRtUv)anKitCaTItaMgEdlmaneRKaHfñak;. Rb sinebIeKeRCIserIskac;RCugxageRkamEpñkxagsþaM enaH ( ) ./181.6

0.91566.942

2 inkipsJ

Myf x ===

( ) ./886.50.915

286.286.9422 inkips

JM

f xy =

−==

( ) ( ) ./13.10886.5143.2181.6 22 inkipsfv =++= RtYtBinitüersIusþg;rbs; base metal. BIsmIkar &>@! shear subject to area×= BMn FR φφ

( ) ⎟⎠⎞

⎜⎝⎛==×=1693654.054.0 tFtF yBMφ

./13.10./94.10 inkipsinkips >= (OK) BIsmIkar &>@0 weld strength KW Wn FLwR φφ ×××= 707.0 Electrode EdlRtUvKñasRmab;Edk 36A KW 70E / CamYynwg ksiFW 5.31=φ . dUcenHTMhMTwkbnSarEdl RtUvkarKW



( )( ) .455.05.310.1707.0

13.10707.0

inFL

Rw

W

n ===φ

φ

cemøIy³ eRbI fillet weld .2/1 in CamYynwg electrode 70E . Ultimate Strength Analysis eKGacKNna Eccentric welded shear connection edayeRbI elastic method y:agsuvtßiPaB b:uEnþemKuNsuvtßiPaBGacFMCagGVIEdlRtUvkar ehIyGacERbRbYlBItMNmYyeTAtMNmYy (Bultler, Pal,

and Kulak, 1920). karviPaKRbePTenHmanKuNvibtþixøHdUc elastic method sRmab; eccentric bolted

connections, edayrYbbBa©ÚlTaMgkarsnμt;faTMnak;TMngrvag bnÞúk-kMhUcRTg;RTay sRmab;karpSar. Rb PBepSgeTotrbs;kMhusKWkarsnμt;faersIusþg;rbs;TwkbnSarminGaRs½ynwgTisedArbs;bnÞúkEdlGnuvtþ.

Ultimat strength procedure RtUv)anbgðajenAkñúg Part 8 of the Manual (Volume II) ehIyRtUv)an segçbenATIenH. vaQrelIkarsikSaRsavRCavrbs; Butler et al. (1972) nig Timler (1984) ehIyviFI EdlesÞIrEtdUcKñaEdlbegáIteLIgsRmab; eccentric bolted connections eday Crawford and Kulak

(1971). CMnYs[karBicarNaelIeRKOgP¢ab;mYy² eyIgKitTwkbnSarEdlCab;CaGgát;TwkbnSardac;² Edl pÁúMP¢ab;Kña. enAeBldac; bnÞúkEdlGnuvtþmkelItMNRtUv)anTb;edaykmøaMgenAkñúgFatunImYy² CamYynwg kmøaMgEdleFVIGMeBIEkgeTAnwgkaMEdlbegáIteLIgBI instantaneous center of rotation eTATIRbCMuTm¶n; rbs;Ggát;TwkbnSar dUcbgðajenAkñúgrUbTI 8>19. KMnitkñúgkarKNnaenHKWRsedogKñanwgKMnitEdleRbI sRmab;eRKOgP¢ab;. b:uEnþ karkMNt;kMhUcRTg;RTayGtibrmarbs;Ggát;TwkbnSar nigkarkMNt;kmøaMgkñúg énGgát;TwkbnSarnImYy²enAeBlEdldac;KWBi)ak. edIm,IkMNt;FatuEdlmaneRKaHfñak; eKRtUvkMNt;pl eFob r/maxΔ sRmab;FatunImYy²/ Edl ( ) ww 17.06087.1 65.0

max ≤+=Δ −θ =θ mMurvagkmøaMgTb; nigG½kSrbs;Ggát;TwkbnSar ¬emIlrUbTI 8>19¦ =w TMhMTwkbnSar =r cm¶ayBI IC eTATIRbCMuTm¶n;rbs;Ggát;TwkbnSar



FatuEdlmanpleFobtUcCageKKWCaFatuEdleTAdl; ultimate capacity muneK. bnÞab;mkkMhUcRTg; RTayrbs;FatudéTeTotRtUv)ankMNt;eday max

maxΔ=Δ

rr

Edl =r kaMsRmab;Fatu

rrΔ

=Δ

max

max sRmab;FatuEdleRKaHfñak;

eKGackMNt;kmøaMgTb;sRmab;FatunImYy²BI ( ) ( )[ ] 3.05.1 9.09.1sin50.00.160.0 ppFR EXX −+= θ Edl =EXXF weld electrode tensil strength

maxΔΔ

=p

¬mindUckrNItMNedayb‘ULúgEdl R CaGnuKmn_eTAnwg θ ¦. karKNnaBImunKWQrelIkarsnμt;TItaMg rbs; instantaneous center of rotation. RbsinebIvaCaTItaMgBitR)akd smIkarlMnwgnwgRtUv)anbMeBj. karKNnabnþeTotKWRsedogKñanwgtMNedayb‘ULúg. !> KNna load capacity BIsmIkar 0=∑ ICM

Ed;l IC Ca instantaneous center. @> RbsinebIsmIkarlMnwgkmøaMgBIrRtUv)anbMeBj enaHTItaMg instantaneous center Edl)an

snμt; nigbnÞúkEdl)anrkenAkñúgCMhanmYyBitCaRtwmRtUv EtebImindUecñaHeT eKRtUvsnμt;TI taMgfμI ehIyeFVIkarKNnasareLIgvij.



vabgðajy:agc,as;nUv)aBcaM)ac;kñúgkareRbIR)as;kmμviFIkMuBüÚT½r. dMeNaHRsayedaykMuBüÚT½r sRmab;;TRmg;Fm μtaCaeRcInsRmab; eccentric welded shear connection RtUv)an[enAkñúgtaragEdl manenAkñúg Part 8 of the Manual. Table 8-38 rhUtdl; 8-45 [lT§PaBbnÞúkemKuN (factored load

capacity) sRmab;karbnSMGgát;TwkbnSartamTisedk nigTisbBaÄrFmμtaCaeRcInedayQrelI ultimate

strength analysis. taragTaMgenHGacRtUv)aneRbIsRmab;karKNna b¤karviPaK nwgerobrab;nUvsßanPaB CaeRcInEdlvisVkrGacnwgCYbRbTH. sRmab;tMNTaMgLayNaEdlmin)anerobrab;enAkñúgtarageKGac eRbI elastic methoid. ]TahrN_ 8>6³ kMNt;TMhMTwkbnSarEdlcaM)ac;sRmab;kartP¢ab;enAkñúg]TahrN_ 8>5 edayQrelIkar BicarNa ultimate strength. cUreRbItaragsRmab; eccentrically load weld group Edl[enAkñúg Part 8 of the Manual. dMeNaHRsay³ TwkbnSarrbs;]TahrN_ 8>5 CaRbePTdUcKñaeTAnwgrUbEdlbgðajenAkñúg Tabl;e 8-42

(angle = o0 )/ ehIykardak;bnÞúkk¾dUcKña. eKRtUvkartémøefrxageRkamsRmab;bBa©ÚleTAkñúgtarag³ 3.1

127.15====

le

lala

67.0128===

lklk

edayeFVI interpolation enAkñúg Table 8-42 sRmab; 3.1=a 14.1=C sRmab; 6.0=k ehIy 30.1=C sRmab; 7.0=k

enaHsRmab; 67.0=k eyIgTTYl)an 25.1=C sRmab; electrode XXE70 / 0.11 =C témø D EdlcaM)ac;KW ( )( ) 0.4

120.125.160

1===

lCCP

D u

dUcenHTMhMTwkbnSarEdlcaM)ac;KW ( ) 25.00.4

161

= ¬TMhMTwkbnSarEdlRtUvkarenAkñúg]TahrN_ 8>5 KW 455.0 cemøIy³ eRbI electrode 70E / fillet weld .4/1 in



karpþl;[CaBiesssRmab;Ggát;rgbnÞúktamG½kS Special Provision for Axially Loaded Members enAeBlEdlGgát;eRKOgbgÁúMrgbnÞúktamG½kS kugRtaMgRtUv)anBRgayes μ IenAelImuxkat; ehIy kmøaMgpÁÜbRtUv)anBicarNafaeFVIGMeBItamG½kSTIRbCMuTm¶n; EdlvaCaG½kSEvgkat;tamTIRbCMuTm¶n;. sRmab; Ggát;EdlrgbnÞúkcMp©itenAxagcugrbs;va kmøaMgTb;pÁÜbEdlpþl;[edaytMNk¾RtUveFVIGMeBItamG½kSenHEdr. RbsinebIGgát;enHmanmuxkat;sIuemRTI lT§plGacRtUv)ansMercedaykarpSar b¤P¢ab;b‘ULúgedaysIuemRTI. RbsinebIGgát;manmuxkat;minsIuemRTI dUcCamuxkat;EdkEkgDub (double-angle section) enAkñúgrUbTI 8>20 karpSar b¤karP¢ab;b‘ULúgedaysIuemRTIeFVI[tMNenaHCatMNrgbnÞúkcakp©it CamYynwg couple Te dUcbgðajenAkñúgrUbTI 8>20 b.

AISC J1.8 GnuBaØat[ecalcMNakp©itenHsRmab;Ggát;rgkmøaMgsþaTic. enAeBlEdlGgát;rg fatigue EdlbNþalmkBIPaBRcMdEdlénkardak;bnÞúk b¤PaBmanGt;rbs;kugRtaMg cMNakp©itRtUvEtyk mkBicarNa b¤k¾minykmkBicarNaedaysarkartP¢ab;edaykarpSar b¤edayb‘ULúgEdlmanlkçN³sm Rsb . ¬CakarBit eTaHbIdMeNaHRsayGacRtUv)aneKeRbIsRmab;EtGgát;EdlrgEtkmøaMgsþaTick¾eday¦. eKGackMNt;karP¢ab;enHedayGnuvtþsmIkarlMnwgkmøaMg nigm:Um:g;. sRmab;tMNEdlpSarEdlbgðajenA kñúgrUbTI 8>21 smIkardMbUgGacRtUv)anTTYledayplbUkm:Um:g;eFobTwkbnSartamTisedkxageRkam³



02 313

32 =−−=∑ LPL

PTcM L

eKedaHRsaysmIkarenHedIm,Irk 1P EdlCakmøaMgTb;caM)ac;enAkñúgTwkbnSartamTisedkxagelI. bnÞab;mkeKGacCMnYstémøenHeTAkñúgsmIkarlMnwgkmøaMgxageRkam³

0321 =−−−=∑ PPPTF eKGacedaHRsaysmIkarenHedIm,Irktémø 2P EdlCakmøaMgTb;caM)ac;enAkñúgTwkbnSartamTis

edkxageRkam. sRmab;RKb;TMhMrbs;TwkbnSar eKGacedaHRsayrkRbEvg 1L nig 2L . dMeNIrkaredaH RsayRtUv)anbgðajenAkñúg]TahrN_ 8>7 EdleKsÁal;Ca balancing the weld. ]TahrN_ 8>7³ Ggát;rgkarTajEdlpSMeLIgeday double-angle section, 2/1352 ××L EdleKdak; eCIgEvgrbs;vaTl;xñgKña. EdkEkgRtUv)anP¢ab;eTAnwg gusset plate kRmas; .8/3 in . EdkTaMgGs;Ca

36A . KNnatMNedaykarpSar edayeFVIkarkat;bnßycMNakp©itedIm,ITb;nwg tensil capacity eBj rbs;Ggát;. dMeNaHRsay³ Load capacity rbs;Ggát;edayQrelI gross section KW ( )( ) kipsAFP gynt 0.2435.73690.090.0 ===φ Load capacity EdlQrelI net seactionRtUvkartémørbs; U . eKminsÁal;RbEvgTwkbnSar dUcenHeKminGacKNna U BI AISC Equation B3-2 )aneT. edayeRbI témømFüm 85.0 eKTTYl)an³ ( ) 2.375.65.7085 inUAA ge ===



( )( ) kipskipsAFP eunt 0.2433.277375.65875.075.0 >===φ Yeilding rbs; gross section CasßanPaBkMNt;EdlykmksikSa dUcenH kipsPnt 0.243=φ . sRmab;EdkEkgmYy bnÞúkEdlRtUvTb;KW kips5.121

20.243=

Electrode EdlRtUvKñanwgEdk 36A KW XXE70 / ehIy TMhMTwkbnSarGb,brma .

163 in= (AISC Table J2.4)

TMhMGtibrma .167

161

21 in=−= (AISC J2.2b)

sakl,g electrode 70E fillet weld .16/5 in ³ lT§PaBenAkñúgRbEvg .1in ( )WFw φ707.0=

( )5.31165707.0 ⎟⎠⎞

⎜⎝⎛=

./960.6 inkips= lT§PaBrbs; base metal rgkmøaMgkat; ( ) ( )yBM FtFt 54.0== φ

( )( )3654.083⎟⎠⎞

⎜⎝⎛=

./29.7 inkips= edayersIusþg;rbs;TwkbnSartUcCageK dUcenHeRbIersIusþg;rbs;TwkbnSar ./960.6 inkips .

eyagtamrUbTI 8>22. lT§PaBrbs;TwkbnSarenAxagcugrbs;EdkEkgKW ( ) kipsP 80.345960.63 ==

( ) ( ) 052580.3425.35.121 12 =−⎟⎠⎞

⎜⎝⎛−=∑ PM L



kipsP 58.611 = 080.3458.615.121 2 =−−−=∑ PF / kipsP 12.252 =

.85.8960.6

58.61960.61

1 inP

L === yk .9in .61.3

960.612.25

2 inL == yk .4in cemøIy³ eRbIkarpSaredUcbgðajenAkñúgrUbTI 8>23

8>5> tMNcMNakp©itedaypSar³ kmøaMgkat; nigkmøaMgTaj

Eccentric Welded Connections: Shear and Tension tMNcMNakp©itCaeRcIn CaBiesskartP¢ab; beam-to-column TwkbnSarrgkmøaMgTaj nigkmøaMg kat;. tMNEbbenHBIrRbePTRtUv)anbgðajenAkñúgrUbTI 8>24.

Seated beam connection pSMeLIgedayEdkEkgEdlmanRbEvgxøIRtUv)aneRbICaeFñIr (shelf) edIm,I RTFñwm. TwkbnSarEdlP¢ab;EdkEkgenHeTAssrRtUvTb;nwgm:Um:g;EdlekIteLIgedayRbtikmμcakp©it k¾dUc direct shear Edl)anBIRbtikmμrbs;Fñwm. EdkEkgEdlP¢ab;enAxagelIrbs;søabFñwmpþl;nUv torsional

stability eTA[Fñwm Etvamin)anCYyRTRbtikm μeT. eKGacP¢ab;vaeTAnwgRTnugrbs;FñwmCMnYs[karP¢ab; eTAnwgsøabrbs;Fñwm)an. beam-to-angle connection GacRtUv)aneFVIeLIgedaykarpSar b¤b‘ULúg ehIy vaminRTnUvbnÞúkKNnaNaeT.

Framed beam connection ¬manlkçN³FmμtaCageK¦ EdlmanEdkEkgbBaÄrpSarP¢ab;eTAnwg ssr ehIyrgnUvRbePTbnÞúkdUckrNI seated beam connection. Epñkrbs;kartP¢ab; beam-to-angle k¾CaRbePTcakp©it b:uEnþbnÞúkenAkñúgbøg;énkmøaMgkat;TTwg dUcenHvaminmankmøaMgTajeT. TaMg seated

connection nig framed connection GacRtUv)anP¢ab;edayb‘ULúg.



enAkñúgRbePTnImYy²Edl)anerobrab;xagelI TWkbnSarbBaÄrenAelIsøabssrrgbnÞúkdUcbgðajenA

kñúgrUbTI 8>25. dUcKñaCamYynwgtMNedayb‘ULúgenAkñúgrUbTI 8>3 bnÞúkcakp©it P nig couple PeM = . kugRtaMgkmøaMgkat;KW

APfv =

Edl A CaRkLaépÞ throat srubrbs;TwkbnSar. eKGacKNnakugRtaMgkmøaMgTajGtibrmaBI flexure formula

I

Mcft = Edl I Cam:Um:g;niclPaBeFobG½kSTIRbCMuTm¶n;rbs;RkLaépÞEdlpSMeLIgedayRkLaépÞ throat

srubrbs;TwkbnSar nig c Cacm¶ayBIG½kSTIRbCMuTm¶n;eTAcMNucq¶abMputrbs;RCugEdlrgkarTaj. eKGac rkkugRtaMgkmøaMgpÁÜbGtibrmaedayeFVIplbUkviuTr½kMub:Usg;TaMgBIrenH enaHeK)an

22tvr fff +=

sRmab;xñat kips nig .in / kugRtaMgenHnwgRtUv)anKitCa 2/ inkips . RbsinebIkñúgkarKNnaenH eK eRbITMhM throat Éktþa enaHeKGacsMEdgtémøenAHCa ./ inkips . RbsinebI rf RtUv)ankMNt;BIbnÞúkem KuN eKGaceRbobeFobvaCamYynwg design strength rbs;TwkbnSarénRbEvgÉktþa. eTAHbICaviFIKNna RtUv)ansnμt;eFVIkarCalkçN³eGLasÞick¾eday k¾vamanlkçN³suvtßiPaBCamYynwg LRFD context Edr.



]TahrN_ 8>8³ eKeRbI 2/146 ××L enAkñúg seated beam connection dUcbgðajenAkñúgrUbTI 8>26. vaRtUvRTnUvbnÞúkemKuNRbtikmμ kips22 . EdkTaMgGs;Ca 36A ehIyeKeRbI electrode XXE70 . etI eKRtUvkarTMhMTwkbnSar fillet weld b:unμansRmab;tP¢ab;eTAnwgsøabssr?

dMeNaHRsay³ dUckñúg]TahrN_KNnaBImun/ eKeRbITMhM throat ÉktþasRmab;KNna. eTaHbICakarpSar enHRtUvkar end return k¾eday edIm,IsRmYlkñúgkarKNna eKnwgecalvasRmab;karKNnaxageRkam. enARKb;krNI eKGac)a:n;s μanRbEvgrbs;vaenARtg;cMNucenH edaysareKminTan;)ankMNt;TMhMTwkbnSar. edaysarmanKMlatBIssr .4/3 in FñwmRtUv)anRTeday .25.3 in elIRbEvg .4in éneCIgrbs; EdkEkg. RbsinebIeKsnμt;[kmøaMgRbtikmμeFVIGMeBIRtg;cMNuckNþalrbs;RbEvgEdlb:H enaHcMNak p©iteFobnwgTwkbnSarKW .375.2

225.375.0 ine =+=



ehIym:Um:g;Kw ( ) kipsinPeM −=== .25.52375.222

sRmab;rUbragénkarpSarEdlsnμt;enAkñúgrUbTI 8>27 ( )( ) 4

3.36

12612 inI == / .3

26 inc ==

( ) ./354.436

325.52 inkipsI

Mcft === ( )( ) ./833.1

61222 inkips

APfv ===

( ) ( ) ./724.4833.1354.4 2222 inkipsfff vtr =+=+= eKGacrkTMhMTwkbnSarEdlcaM)ac; w eday[ rf es μ IeTAnwglT§PaBTwkbnSarkñúgmYyÉktþaRbEvg ( )Wr Fwf φ707.0= ( )5.31707.0724.4 w= / .212.0 inw = BI AISC Table J2.4, TMhMTwkbnSarGb,brma .

41 in= ¬edayQrelITMhMsøabrbs;ssr .8/5 in

BI AISC J2.2b, TMhMGtibrma .

167

161

21 in=−=

RtYtBinitülT§PaBkmøaMgkat;TTwgrbs; base metal: Applied direct shear ./833.1 inkipsfv == Shear capacity of angle leg ( ) ( ) ( )( )3654.0

2154.0 === yBM FtFt φ



./833.1./72.9 inkipsinkips >= (OK)

cemøIy³ eRbI electrode XXE70 / fillet weld .4/1 in .

eyIgecalnUv end returns enAkñúg]TahrN_ 8>8 b:uEnþeKGacbBa©ÚlvaedaykareFVIkarKNna

elIkTIBIrCamYynwg end return EdlmanRbEvgBIrdgTMhMTwkbnSarEdl)anrkeXIjenAkñúgkarKNna elIkTImYy. ¬CMhanbENßmenHminRtUv)anGnuvtþenAkñúg]TahrN_enHeTedaysarTMhMTwkbnSarGb,-brmaRKb;RKan;sRmab;karKNna¦. End return RtUv)anykmkniyayenAkñúg]TahrN_ 8>9.

]TahrN_ 8>9³ rUbTI 8>28 bgðajBI framed beam connection edaypSar. Edk framing angle Ca

2/134 ××L ehIyssrCa 7212×W . EdkTaMgGs;CaRbePT 36A ehIyeKeRbI electrode XXE70 edIm,IbegáIt fillet weld .8/3 in . kMNt;kmøaMgRbtikmμemKuNrbs;FñwmEdlkMNt;edayTwk

bnSarenAelIsøabssr.

dMeNaHRsay³ eKsn μt;kmøaMgRbtikm μrbs;FñwmeFVIGMeBIkat;tamTIRbCMuTm¶n;rbs;TwkbnSarén framing

angle. dUcenH cMNakp©itrbs;kmøaMgeFobnwgTwkbnSarenARtg;søabssrCacm¶ayBITIRbCMuTm¶n;eTAsøab ssr. sRmab;TMhM throat mYyÉktþa nigTwkbnSarEdlbgðajenAkñúgrUbTI 8>29 a

( )( )( ) .1689.0

5.223225.15.22 inx =

+= nig .831.21689.03 ine =−=



m:Um:g;enAelITwkbnSarEdlenAelIsøabssrKW kipsinRM −== .831.2Re Edl R CaRbtikmμrbs;FñwmKitCa kips BITMhMEdl[enAkñúgrUbTI 8>29 b/ lkçN³rbs;TwkbnSarenAelIsøabssr ( ) .63.15

75.0321632 iny =

+=

( ) ( ) ( ) 4223

.291863.1575.063.15163212321 inI =+−+=

sRmab;TwkbnSarTaMgBIr ( ) 4.583629182 inI == ( ) ./007582.0

583663.15831.2 inRkipsR

IMcft ===

( ) ./01527.075.0322

inRkipsRARfv =

+==

( ) ( ) ./01705.001527.0007582.0 22 inRkipsRRfr =+=

yk ( )WFwR φ707.001705.0 = ykKNnarktémø R ( )5.31

83707.00175.0 ⎟⎠⎞

⎜⎝⎛=R / kipsR 8.489=

RtYtBinitülT§PaBkmøaMgkat;TTwgrbs; base metal ¬kRmas;rbs;EdkEkglub¦ ( ) ( ) ( )( ) ./72.93654.05.054.0 inkipsFtFt yBM ===φ Direct shear RtUv)anTb;Kw



( ) ./72.9./48.775.3228.489 inkipsinkips <= (OK)

cemøIy³ kmøaMgRbtikmμFñwmemKuNGtibrma kips490= 8>6> tMNTb;m:Um:g; (Moment-Resisting Connection) enARKb; beam-to-column connection nig beam-to-beam connection TaMgGs; vaEtgman karTb;m:Um:g;xøH eTaHbICakarKNnatMNenaHCatMNsamBaØ b¤k¾tMNEdlKμanm:Um:g;k¾eday. müa:gvijeTot eKBi)akkñúgkareFVI[man perfectly frictionless pin or hinge ehIytMNCaeRcInEdlRtUv)anKNna CatMNEdldac;edayKμanm:Um:g;. dUcKña eKk¾Bi)akkñúgkareFVI[man perfectly rigid joint EdlGac manlT§PaBepÞr moment capacity rbs;Ggát;mYyeTAGgát;mYyeTotEdr. dUcenH eTaHbICa framed nig

seated beam connections EdlbgðajkñúgrUbTI 8>24 k¾GacCatMNrwgxøH EdlvaGacbBa¢Únm:Um:g;tictYc RbsinebI connecting angle man flexible RKb;RKan;. dUcEdl)ankt;cMNaMBIxagelI bnÞúkcakp©iteFob eTAnwgb‘ULúg b¤TwkbnSarKWtUcNas; ehIyEdlCaTUeTARtUv)anecal. AISC Specification kMNt;kartP¢ab;enHCaBIrRbePT enAkñúg Section A2.2, “Types of Comstruction.”

Type FR – Fully Restrained (Rigid, or Continuous, Framing). eRKOgbgÁúMEdlman moment-resistingg joint GacepÞrm:Um:g;EdlGgát;GacTb;)an edaymineFVI[Ggát;enaHmanmMurgVil enARtg;tMNenaH. RbsinebIeRKagRtUv)anKNnaCa rigid frame dUcenHtMNRtUv)anKNnaCa moment

connection. Type PR – Partially Restrained (semirigid Framing). eRKagRbePTenHCa eRKagEdl RtUv)anKNnaedayQrelIkarsÁal;brimaNTb; (restraint) cenøaHrvagtMNsamBaØ nigtMNrwg. CaTUeTA moment restraint sßitenAcenøaH %20 eTA %90 rbs; member moment capacity. bBaðacMbgrbs; eRKagEdlmantMNRbePTenHKWTamTarnUvkarviPaKeRKagd¾saMjauMedaysarvtþmanrbs; partial joint

restraint. tRmUvkarcaM)ac; sRmab;tMNRbePTenHKWExSekag m:Um:g;-mMurgVil. RbsinebIeKecal partial restraint eKGaccat;TukFñwmCaFñwmTRmsamBaØEdlminman moment

restraint enARtg;tMN. Framed and seated beam connections sßitenAkñúgRbePTenH. CaTUeTAtMN EdlepÞr member capacity ticCag %20 RtUv)ancat;TukCatMNsamBaØ.



TRmFñwmEdlRtUv)anKNnaenA kñúgkrNIenH eBlxøHRtUv)aneKehAfa shear connection EdlmanEt kmøaMgRbtikmμ b¤kmøaMgkat;enAxag cugEdlRtUv)anbBa¢Ún. eRKagEdlman shear connection RtUv)anBRgwgenAkñúgbøg;rbs;eRKagedaysarvaK μan “frame

action”edIm,IeFVI[man lateral stability. cRmwg (bracing) TaMgenHmaneRcInTRmg; GacCa diagonal

bracing members, shear wall, or lateral support BIeRKagEdlenACab;. m:Um:g;EdlekItBIbnÞúkxag ¬CaTUeTAKW xül; nigrBa¢ÜydI¦ RtUv)anykmkKitkñúgkarKNnasRmab;kareRCIserIs beam-to-column connections. sRmab;viFIenH eKsn μt;tMN[eFVIkarCatMNsamBaØedIm,ITb;Tl;nwgbnÞúkefr nigbnÞúk Gefr ¬bnÞúkTMnaj gravity load¦ nigCa moment connection CamYynwglT§PaBEdlmankMNt;kñúgkar Tb;Tl;m:Um:g;xül;. RbsinebIeKKNnaFñwmCaRbePTTRmsamBaØ m:Um:g;bnÞúkTMnajGtibrmaGac over-

estimated ehIyFñwmGac overdesigned. b:uEnþkñúgkrNICaeRcIn m:Um:g;xül;GacmantémøtUc. RbsinebI eKeRbItMNsamBaØ Specification TamTar[eKarBnUvlkçxNÐxageRkam³

!> eTaHbICaFñwm ¬rt¦ minRtUv)anRTedayTRmsamBaØk¾eday k¾vaRtUvEtRTbnÞúkTMnajtamEtva GaceFVI)an.

@> tMN nigGgát;EdlRtUv)anP¢ab; ¬Fñwm nigssr¦ RtUvmanlT§PaBGacTb;m:Um:g;xül;)an. #> tMNRtUvman inelastic rotational capacity RKb;RKan;EdleRKOgP¢ab; b¤TwkbnSarnwgmin

RtUv)an overload eRkambnSMénbnÞúkTMnaj nigbnÞúkxül;. enAkñúgsovePAenH eyIgBicarNaEttMNBIrRbePTKW³ tMNsamBaØ (simple connection) Edl KNnasRmab;bnÞúkTMnaj ¬CamYynwg lateral frame stability Edlpþl;[eday positive bracing

system¦ nigtMNrwg (rigid connection) EdlKNnasRmab; moment capacity rbs;FñwmFMCag %90 . eyIg)anBicarNa simple connection enAkñúg framed nig seated beam connections rYcehIy dUcenH eyIgnwgRtUvkarykcitþTukdak;eTAelI rigid connectionsvijmþg. ]TahrN_FmμtaCaeRcInEdleRbI moment connection RtUv)anbgðajenAkñúgrUbTI 8>30. Ca TUeTA karepÞrm:Um:g;PaKeRcInRtUv)anbBa¢ÚntamsøabFñwm ehIy moment capacity k¾RtUv)aneLIg. tMN enAkñúgrUbTI 8>30 a bgðajBIKMnitenH. EdkbnÞHEdlP¢ab;RTnugFñwmeTAssrKWRtUv)anpSarP¢ab;eTAnwg ssrenAeragCag nigRtUv)ancab;b‘ULúgeTAnwgFñwmenAkardæan. CamYynwgkarerobcMEbbenH FñwmRtUv)an Gacdak;enAelITItaMgy:agRsYleday[søabGacRtUv)anpSarP¢ab;eTAnwgssrenAkardæan. Plate

connection RtUv)anKNnaedIm,ITb;Tl;EtkmøaMgkat; nigTTYlRbtikm μrbs;Fñwm. Complete penetra-



tion groove welds P¢ab;søabFñwmeTAssr nigGacepÞrm:Um:g;esμInwg moment capacity rbs;søabFñwm. vanwgrYmKñaCamYy moment capacity rbs;FñwmPaKeRcIn b:uEnþbrimaNrbs;karTb;RtUv)anpþl;[ eday plate connection. ¬edaysar strain harderning full plastic moment capacity rbs;FñwmGac RtUv)anbegáIteLIgtamry³søab¦. kareFVIkartP¢ab;søabTamTarfaEpñkd¾tUcrbs;RTnugFñwmRtUv)andk ecjehIy “backing bar” RtUv)aneRbIenAelI søabmYyedIm,IGnuBaØat[karpSarTaMgGs;eFVIeLIgBIelI. enAeBlEdlkarpSarBIxagelIRtCak; vanwgrYjCaTUeTARbEhl .8/1 in . bMlas;TItamTisbeNþayEdl TTYl)anRtUv)anykmkKitsRmab;eRbIR)as; slotted bolt hole nigedayrwtbNþwgb‘ULúgeRkayeBlTwk bnSarRtUv)anRtCak;. tMNRbePTenH eRbI column stiffenders EdlminRtUvkarCaTUeTAeT ¬emIlEpñk 8>7¦. Moment connection rbs;rUbTI 8>30 a k¾RtUv)anbgðaj recommended connection design

practice: RKb;eBlTaMgGs; karpSarKYrEtRtUv)aneFVIenAkñúgeragCag ehIykarcab;b‘ULúgKYreFVIenAkardæan. karpSarenAeragCagmantémøefakCag niggayRsYlkñúgkarRtYtBinitü. sRmab; beam-to-column moment connections Ggát;CaEpñkrbs; plane frame ehIyRtUv)an dak;dUcbgðajenAkñúgrUbTI 8>30 a EdlRTnugenAkñúgbøg;rbs;eRKagEdlkarBt;rbs;Ggát;nimYy²eFobeTA nwgG½kSemrbs;va. enAeBlEdlFñwmRtUv)anP¢ab;eTAnwgRTnugrbs;ssrCaCagsøabrbs;ssr ¬Ca-]TahrN_ enAkñúgeRKaglMhr¦ eKeRbItMNdUcEdlbgðajenAkñúgrUbTI 8>30 b. tMNenHRsedogKñaeTA nwgGVIEdlbgðajenAkñúgrUbTI 8>30 a b:uEnþTamTarnUvkareRbI column stiffener edIm,IeFVIkartP¢ab;eTAnwg søabFñwm.

eTaHbICatMNEdlbgðajenAkñúgrUbTI 8>30 a CatMNsamBaØk¾eday k¾kartMeLIgrbs;faTamTar nUvkRmitGt;»ntUcEdr. RbsinebIFñwmtUcCagkarrMBwgTukcenøaHrvagssr nigsøabFñwmGacbgáPaBlM)ak kñúgkarpSar enAeBlxøHeKeRbI backing bar. Three-plate connection EdlbgðajenAkñúgrUbTI 8>30 c minman handicap eT ehIyvamanGtßRbeyaCn_bEnßmEdlRtUv)anP¢ab;edayb‘ULúgy:agl¥enAkardæan. Flange plate nig web plate RtUv)anpSarenAkñúgeragCageTAnwgsøabssr nigcab;b‘ULúgeTAFñwmRtUv)an eFVIenAkardæan. edIm,Ipþl;[sRmab;karERbRbYlenAkñúgkm<s;Fñwm cm¶ayrvag flange plates RtUv)aneFVI eLIgFMCagkm<s;Fmμtarbs;Fñwm b:uEnþRbEhl .8/3 in . KMlatenHRtUv)anbMeBjenAsøabxagelIkñúgeBl dMeLIgCamYy shims/ Edl thin strip rbs;EdkedayRtUv)aneRbIsRmab;EktRmUvkarP¢ab;enARtg;tMN. Shim GacCaRbePTmYykñúgcMeNamBIrRbePTKW conventional shim nig finger shim EdlGacs‘k



eRkayeBlb‘ULúgRtUv)anP¢ab; dUcbgðajenAkñúgrUbTI 8>30 d. enAkñúgtMbn;EdlmantMbn;rBa¢ÜyFM tMN EdlbgðajenAkñúgrUbTI 8>30 a RtUvkarkarKNnaBiess (FEMA, 1995).

]TahrN_ 8>10 bgðajBIkarKNnarbs; three-plate moment connect edayrYmbBa©ÚlTaMg

tRmUvkarsRmab;kartP¢ab;Ggát; Edlmanerobrab;eday AISC J5. ]TahrN_ 8>10³ KNna three-plate moment connection rbs;RbePTEdl)anbgðajrUbTI 8>31 sRmab;kartP¢ab;Fñwm 5021×W eTAsøabrbs;ssr 9914×W . snμt;Fñwm set-back .2/1 in . karviPaK eRKagbgðajfatMNRtUvEtepÞrm:Um:g;bnÞúkemKuN kipsft −.210 nigkmøaMgkat;emKuN kips33 . RKb;bnÞH EdkEdlpSareTAnwgssrCamYynwg electrode XXE70 nigkarP¢ab;b‘ULúgeTAFñwmCamYynwg bearing-

type bolts 325A . EdkTaMgGs;CaRbePTEdk 36A . dMeNaHRsay³ sRmab; web plate ¬edayecalcMNakp©it¦ sakl,gb‘ULúgGgát;p©it .4/3 in . snμt;fa eFμjsßitenAkñúgbøg;kmøaMgkat;. lT§PaBkmøaMgkat;TTwgrbs;b‘ULúgKW ( )( ) kipsAF bv 90.154418.04875.0 ==φ cMnYnb‘ULúgEdlRtUvkar 08.2

90.1533

==



sakl,gb‘ULúg 3 RKab; nigkMNt;kRmas;bnÞHEdlTamTarsRmab; bearing. eRbIKMlat nigcm¶ay eTARCugEKmenAkñúgrUbTI 8>32 a ehIyGgát;p©itrn§KW .

1613

161

43

161 indh =+=+=

sRmab;RbehagEdlenAEk,rRCugEKmbMput .094.1

216/135.1

2inhLL ec =−=−=

.5.14322 ind =⎟⎠⎞

⎜⎝⎛=

edaysar dLc 2< / bearing strength KW ( ) ( )( ) ( ) bolttkipsttFLR ucn /11.5758094.12.175.02.1 === φφ

sRmab;RbehagdéT dinhsLc 2.188.2

16133 >=−=−=



dUcenH ( ) ( ) ( ) bolttkipstdtFR un /03.7858434.275.04.2 =⎟⎠⎞

⎜⎝⎛== φφ

edIm,IrkkRmas;EdlRtUvkardak; total bearing strength es μ Inwg applied load: ( ) 3330.78211.57 =+ tt b¤ .154.0 int = sRmab;RTnugFñwm (beam web) .154.0.380.0 inintw >= edIm,IkMNt;kRmas;bnÞHEdkEdlRtUvkarsRmab;kmøaMgkat; cUrBicarNamuxkat;bBaÄrkat;tambnÞHEdk. BI AISC J5, “Connecting Elements,” [ ]ygn FAR 60.090.0=φ (AISC Equation J5-3)

( )( )[ ]36960.090.033 t= .189.0 int = ¬lub¦ dUcenHyk .4/1 int = sRmab;kartP¢ab; shear plate eTAnwgsøabssr TMhM fillet weld Gb,brmaKW .4/1 in . ¬edayQrelI EpñkEdlRtUvP¢ab;EdlmankRmas;Rkas;Cag TMhM fillet weld Gb,brmaKW .16/5 in b:uEnþvaminRtUvkarFM CagkRmas;rbs;EpñkEdlRtUvP¢ab;EdlesþIgCageT¦. enaH lT§PaBkñúgmYyÉktþaRbEvg ( ) ( )5.31

41707.0707.0 ⎟⎠⎞

⎜⎝⎛== WFw φ

./568.5 inkips= lT§PaBkmøaMgkat;TTwgrbs; base metal KW ( ) ( )( ) ./86.43654.0

4154.0 inkipsFtFt yBM ===φ ¬lub¦

dUcenHRbEvgEdlcaM)ac;rbs; fillet weld .4/1 in KW .79.6

86.433 in=

karpSarCab;KñaenAelIRCugmçagrbs;bnÞHGacRKb;RKan; b:uEnþCaTUeTAeKRtUvpSarsgxag ehIyRtUv)anGnuvtþ enATIenH. TTwgGb,brmarbs;bnÞHEdkGacRtUv)ankMNt;BIkarBicarNacm¶ayeTARCugEKm. bnÞúkEdlRtUv )anRT ¬Rbtikm μFñwm¦ KWmanTisbBaÄr dUcenHcm¶ayeTARCugEKmcaM)ac;eKarBtamtRmUvkarrbs; AISC

Table J3.4. RbsinebIeyIgsnμt;RCugEKmCa sheared edge cm¶ayeTARCugEKmGb,brmaKW .1 41 in .

CamYynwg beam setback .2/1 in nigcm¶ayeTARCugEKm .1 21 in dUcEdl)anbgðajenAkñúgrUbTI

8>32 b TTwgrbs;bnÞHEdkKW



( ) .5.35.125.0 in=+ ykbnÞHEdkTMhM 41

213 ×

sRmab; flange plates, rkkmøaMgRtg;épÞb:HrvagsøabFñwm nigbnÞHEdk. BIrUbTI 8>33

HdM = nig ( ) kips

dMH 0.121

83.2012210

=== sakl,gb‘ULúg 325A Ggát;p©it .4/3 in . ¬edaysarb‘ULúgGgát;p©it .4/3 in RtUv)aneRCIserIssRmab; shear connection dUcenHeyIgsakl,gTMhMb‘ULúgdUcKña¦. RbsinebIkmøaMgkat;TTwgb‘ULúglub cMnYnb‘U LúgEdlRtUvkarKW .

1613

161

43

161 indh =+=+=

sRmab;RbehagEdlenAEk,rRCugEKmCageK .094.1

216/135.1

2inhLL ec =−=−=

( ) .5.14/322 ind == edaysar dLc 2< / bearing strength KW ( ) ( )( ) ( ) bolttkipsttFLR ucn /11.5758094.12.175.02.1 === φφ sRmab;RbehagepSgeTot dinhsLc 2.188.2

16133 >=−=−=

dUcenH ( ) ( ) ( ) bolttkipstdtFR un /30.7858434.275.04.2 =⎟⎠⎞

⎜⎝⎛== φφ

edIm,IrkkRmas;EdlRtUvkar dak; total bearing strength [es μI applied load:

( ) ( ) 0.12130.78611.572 =+ tt b¤ .207.0 int = Flange plate TaMgBIrnwgRtUv)anKNnaCa tension connecting elements. ¬ebIeTaHbICabnÞHEdkmYyrgkmøaMgsgát;k¾eday kartP¢ab;lMGitecalnUvbBaðasißrPaBTaMgGs;¦.



eKnwgkMNt;muxkat;Gb,brmaEdlRtUvkarsRmab;kugRtaMgTajenAelI gross nig net area. BI AISC Equation J5-1, ( )ygn FAR 90.0=φ gA EdlRtUvkar ( )

2.735.33690.00.121

90.090.0in

FH

FR

yy

n ====φ

BI AISC Equation J5-2, unn FAR 75.0=φ nA EdlRtUvkar ( )

2.782.05875.00.121

75.075.0in

FH

FR

uu

n ====φ

sakl,gTTwgrbs;bnÞHEdk .5.6 inwg = ¬es μ IeTAnwgTTwgsøabrbs;Fñwm¦. kMNt;kRmas;caM)ac;edIm,I bMeBjtRmUvkar requirement. 2.735.35.6 intAg == b¤ .575.0 int = KNnakRmas;EdlcaM)ac;edIm,IbMeBjtRmUvkar net area ( ) ttdwttwA holegnn 750.4

8725.6 =⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=∑−==

yk 2.782.2750.4 int = b¤ .586.0 int = ¬lub¦ kRmas;k¾RtUvFMCagGVIEdlTamTarsRmab; bearing dUcenHvaRtUvCakRmas;Gb,brmaEdlGacTTYlyk )an. sakl,gbnÞH 8

52

16 × . bnÞHenHCa tension connecting element dUcenH net area rbs;vamin GacelIsBI gA85.0 enAkñúgkarKNna (AISC J5.2): 2.969.2

8725.6

85 inAn =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=

( )( ) 22 .969.2.453.35.6625.085.085.0 ininAg >== (OK) ykbnÞH 8

52

16 × Epñkrbs;RkLaépÞsøabrbs;FñwmnwgRtUv)an)at;bg;edaysarRbehagrbs;b‘ULúg nig moment capacity RtUv)ankat;bnßy. AISC B10 GnuBaØatkarkat;bnßyenHedIm,I[ecalenAeBl fgyfnu AFAF 90.075.0 ≥ (AISC Equation B10-1) Edl =fgA gross flange area

( ) 2.494.3535.0530.6 intb ff ==⋅= =fnA net flange area



( ) 2.557.2872530.6535.0 indbt hff =⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=∑−=

edayeRbI AISC Equation B10-1 eyIgTTYl)an ( )( ) kipsAF fnu 2.111557.25875.075.0 == ( )( ) kipskipsAF fgy 2.1112.113494.3369.09.0 >== edaysar AISC Equation B10-1 minRKb;RKan; flexural KYrRtUvQrelIRkLaépÞsøabRbsiT§PaB (effective flange area) fn

y

ufe A

FF

A65

=

( ) 2.433.3557.23658

65 in=⎟

⎠⎞

⎜⎝⎛= (AISC Equation B10-3)

RkLaépÞenHminxusKñay:agxøaMgBI actual gross flange are 2.494.3 in dUcenH flexural strength eday minRtUvEkERb. cemøIy³ eRbItMNEdlbgðajenAkñúgrUbTI 8>34 ¬tRmUvkar column stiffener nwgRtUv)anBicarNaenAkñúg Epñk 8>7¦*

* rUbTI 8>34 k¾bgðajBInimitþsBaØasMrab; bevel groove weld, edayeRbIenATIenHsMrab; beam flange plate-to-column connection



8>7> Column Stiffeners and other Reinforcement m:Um:g;PaKeRcInEdl)anepÞrBIFñwmeTAssrenAkñúgtMNrwgmanTRmg;Ca couple EdlpSMeLIgeday kmøaMgTaj nigkmøaMgsgát;EdlmanenAkñúgsøabrbs;Fñwm. karGnuvtþn_kmøaMgcMNucEdlmantémøFMGac TamTarkarBRgwgssr. sRmab;m:Um:g;GviC¢manEdldUckrNICamYybnÞúkTMnaj kmøaMgTaMgenHmanTisedA dUcbgðajenAkñúgrUbTI 8>35 CamYynwgsøabxagelIbMputrbs;FñwmEdlbBa¢ÚnkmøaMgTajeTAssr ehIy søabxageRkamEdlbBa¢ÚnkmøaMgsgát;. kmøaMgTaMgBIrRtUvbBa¢ÚneTARTnugssrCamYynwgkmøaMgsgát;EdlmaneRKaHfñak;Cagedaysar stability problem. kmøaMgTajenAxagelIGacrMxansøabssr ¬rUbTI 8>35 c¦ EdlbegáItbnÞúkbEnßm eTAelIkartP¢ab;edaypSarénsøabssreTAsøabFñwm. RbePTeRKOgBRgwg (stiffener) Edl)anbgðaj )anBRgwgsøabssr. dUc)aneXIjy:agc,as; stiffener RtUv)anpSarP¢ab;eTAnwgRTnug nigsøab. Rbsin ebIm:Um:g;EdlGnuvtþminpøas;bþÚrTisedA stiffener EdlTb;Tl;nwgkmøaMgsgát; ¬stiffener xageRkam¦ min RtUvkarkarpSareT. AISC Specification Requirements

tRmUvkarrbs; AISC sRmab;karBRgwgRTnugssrRtUv)anerobrab;enAkñúg Chapter K, “strength

Design Considerations.”. sRmab;EpñkCaeRcIn karpþl;[enHQrenAelIkarviPaKedayRTwsþIEdlRtUv )anEkERbedIm,I[RtUvnwglT§plrbs;karBiesaF. RbsinebIbnÞúkemKuNGnuvtþn_EdlRtUv)anepÞreday søabFñwm b¤ flange plate FMCag design strength nRφ sRmab;RKb;sßanPaBkMNt;Edl)anBicarNaTaMg Gs; enaHeKRtUvEteRbI stiffener.

edIm,IeCosvag local bending failure rbs;søabssr kmøaMgTajBIsøabFñwmdac;xatminRtUv FMCag ( )yffn FtR 225.6φφ = (AISC Equation K1-1)

Edl 90.0=φ

=ft kRmas;rbs;søabssr

=yfF yield stress rbs;søabssr sRmab;sßanPaBkMNt;rbs; local web yielding rgkugRtaMgsgát;



( )[ ]wywn tFNkR += 5φφ (AISC Equaton K1-2) b¤ enAeBlEdlbnÞúkRtUv)anGnuvtþedaycm¶ayBIcugrbs;Ggát;Edlesμ Ikm<s;rbs;Ggát; ( )[ ]wywn tFNkR += 5.2φφ (AISC Equation K1-3) Edl 0.1=φ =k cm¶ayBIépÞsøabxageRkArbs;ssreTAeCIgrbs; fillet EdlenAelIRTnug =N RbEvgrbs;bnÞúkGnuvtþn_=kRmas;rbs;søabFñwm b¤ flange plate =ywF yield stress rbs;RTnugssr =wt kRmas;rbs;RTnugssr eyIgk¾eRbI AISC Eqution K1-2 nig K1-3 in Section 5.13 edIm,IGegát web yielding enAkñúgFñwmEdl rgbnÞúkcMcMNuc. edIm,IkarBar web crippling enAeBlEdlbnÞúksgát;RtUv)anbBa¢ÚneTAEtsøabmYy dUckñúgkrNI ssrxageRkAEdlmanP¢ab;CamYyFñwmEtmçag enaHbnÞúkGnuvtþn_minRtUvFMCag design strength Edl[ daysmIkarmYykñúgcMeNamsmIkarxageRkam. ¬eyIgk¾Føab;)anerobrab;BI web crippling enAkñúg web

crippling enAkñúgEpñkTI 5>13¦ enAeBlEdlbnÞúkRtUv)anGnuvtþenAcm¶ayy:agtic 2/d BIcugrbs;ssr

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 31135φφ (AISC Equation K1-4)

Edl 75.0=φ =d km<s;srubrbs;ssr RbsinebIbnÞúkRtUv)anGnuvtþenAcugrbs;ssr

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 3168φφ sRmab; 2.0≤

dN

(AISC Equation K1-5b)

b¤ w

fyw

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+=

5.12 2.04168φφ sRmab; 2.0>

dN

(AISC Equation K1-5b)



kmøaMgsgát; backling rbs;RTnugRtUv)anGegátenAeBlEdlbnÞúkRtUv)anbBa¢ÚneTAsøabssr TaMgBIr. bnÞúkEbbenHnwgekItmanenAssrxagkñμúgCamYynwgFñwmEdlP¢ab;eTAssrTaMgsgxag. Design

strength sRmab;sßanPaBkMNt;enHKW

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

h

FtR

ywwn

34100φφ (AISC Equation K1-8)

Edl 90.0=φ =h km<s;RTnugssrBIeCIgrbs; fillet eTAeCIgrbs; fillet ¬rUbTI 8>36¦ RbsinebIkartP¢ab;enAEk,rcugrbs;ssr ¬EdlRbsinebIbnÞúkRtUv)anGnuvtþenAcm¶ay 2/d BI cug¦ ersIsþg;Edl[eday AISC Equation K1-8 KYrRtUv)ankat;bnßyBak;kNþal. niyayedaysegçb edIm,IGegátPaBcaM)ac;sRmab; column stiffener eKRtUvRtYtBinitüsßanPaBkM Nt;bIdUcxageRkam³ !> Local flang bending (AISC Equation K1-1) @> Loacl web yielding (AISC Equation K1-2 or K1-3)

#> Web crippling b¤kmøaMgsgát; buckling rbs;RTnug. ¬RbsinebIkmøaMgsgát;RtUv)anGnuvtþ eTAelIsøabEtmYy eKRtUvRtYtBinitü web crippling [AISC Equation K1-4 b¤ K1-5]. RbsinebIkmøaMg sgát;RtUv)anGnuvtþeTAelIsøabTaMgBIr eKRtUvRtYtBinitü compressive buckling rbs;RTnug [AISC

Equation K1-8]¦.



RbsinebI stiffener EdlRtUvkareday AISC Equation K1-2 sRmab; local web yielding,

eKGacrkRkLaépÞmuxkat;EdlRtUvkarsRmab; stiffener dUcxageRkam. snμt;faeKGacTTYl)an design

strength bEnßmBIRkLaépÞrbs; stiffener stA Edl yield. dUcenHBI AISC Equation K1-2. ( )[ ]yststwywn FAtFNkR ++= 5φφ Edl ystF Ca yield stress rbs; stiffener. dak;[GgÁxagsþaMrbs;smIkarenHesμ InwgbnÞúkGnuvtþn_Edl smÁal;eday bfP nigedaHRsaysRmab; stA eKTTYl)an ( )

yst

wywbfst F

tFNkPA

+−=

5/φ ( )

yst

wywbbfF

tFtkP +−=

5 ¬*>^¦

Edl 0.1=φ nig bt KWkRmas;rbs;søabssr b¤ flange plate. smIkar 8>6 k¾GacRtUv)aneRbIedIm,IRtYt Binitü local buckling yielding strength rbs;ssr. edaHRsayrk stA RbsinebITTYl)anlT§pl GviC¢man eKnwgminRtUvkar stiffener sRmab;sßanPaBenHeT. RbsinebIeKRtUvkar stifferner AISC K1-9 [nUvTMhMsmamaRtrbs;vadUcxageRkam³

TTwgrbs; stiffener bUknwgkRmas;Bak;kNþalrbs;RTnugssrRtUvFMCagb¤esμ InwgmYyPaKbIén TTwgrbs;søabFñwm b¤ flange plate EdlbBa¢ÚnkmøaMgeTAssr b¤BIrUbTI 8>37

32bw btb ≥+ dUcenH

23wb tbb −≥

kRmas;rbs; stiffener dac;xatRtUvEtFMCagb¤es μ InwgBak;kNþalkRmas;rbs;søabFñwm b¤ flange plate b¤

2b

sttt ≥

pleFobTTwgelIkRmas;RtUvEt

yst Ftb 250≤ ¬xñat IS¦

yst Ftb 95≤ ¬xñat US¦

eKRtUvkar Full-depth stiffener sRmab;krNI compression buckling b:uEnþeKGnuBaØat[eRbI half-depth stiffener sRmab;sßanPaBkMNt;epSgeTot. dUcenHeKRtUvkar full-depth stiffener EtenA eBlEdlFñwmRtUv)anP¢ab;eTAnwgssrTaMgsgxag.



sRmab;RKb;sßanPaBkMNt;TaMgGs; karsMerckñúgkarpSar stiffener P¢ab;eTAsøabKWQr elIlkçxNÐxageRkam³

enAelIxagEdlrgkmøaMgTaj eKRtUvpSar stiffener P¢ab;eTAnwgRTnug nigsøab. enAelIxagEdlrgkmøaMgsgát; stiffener RKan;EtRtUvkardak;EGbnwgsøabEtb:ueNÑaH EteKk¾Gac

pSarvaP¢ab;eTAnwgsøab. Part 3 of the Manual, “Column Design,” mantémøefrEdlRtUv)anerobCataragEdlGaceFVI

karkMNt;karcaM)ac;sRmab; stiffener. kareRbIR)as;rbs;vaRtUv)anbgðajenAkñúg]TahrN_EdlmanenA kñúg “General Notes” EtminRtUv)anbgðajenATIenHeT.

kmøaMgkat;enAkñúgRTnugssr Shear in the Column Web

karepÞrm:Um:g;EdlmantémøFMeTAssrGacbegáItkugRtaMgkmøaMgkat;FMenAkñúgRTnugssrenAkñúgRBM Ednrbs;tMN. ]TahrN_ tMbn; ABCD enAkñúgrUbTI 8>38. eBlxøH eKehAtMbn;enHCa panel zone. Net moment RtUv)anKit dUcenHRbsinebIFñwmRtUv)antP¢ab;eTARCugTaMgsgxagrbs;ssr plbUkBiC-KNiténm:Um:g;begáIt web shear enH. RbsinebIkmøaMgsøabFñwmRtUv)ansnμt;[eFVIGMeBIenAcm¶ay bd95.0 BIKña Edl bd Cakm<s;Fñwm enaHkmøaMg søabnImYy²GacRtUv)anykCa

bdMMH

95.021 +=

RbsinebIkmøaMgkat;ssrenAEk,r panel Ca uV ehIymanTisedAdUcbgðaj kmøaMgkat;TTwgsrub enAkñúg panel KW u

bu V

dMMVHP −

+=−=

95.021 ¬*>&¦



Web shear strength RtUv)an[enAkñúg AISC K1.7 Ca vRφ Edl 90.0=φ ehIy vR Ca GnuKmn_ eTAnwgbnÞúktamG½kSenAkñúgssr. enAeBlEdl yu PP 4.0≤

wcyv tdFR 60.0= (AISC Equation K1-9)

enAeBlEdl yu PP 4.0> /

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

y

uwcyv P

PtdFR 4.160.0 (ASIC Equation K1-10)

Edl =uP bnÞúktamG½kSenAkñúgssr =yP axial yield strength rbs;ssr yAF= =A RkLaépÞmuxkat;rbs;ssr edayrYmbBa©ÚlTaMgeRKOgBRgwg ¬]TahrN_/ doubler plates¦ =cd TMhMssrtamTisFñwmsrub =wt kRmas;RTnugssr edayrYmbBa©ÚlTaMgbnÞHEdkEdlBRgwg =yF yield stress rbs;RTnugssr

RbsinebIRTnugssrman shear strength minRKb;RKan; eKRtUvBRgwgva. eKGaceRbI double plate

EdlmankRmas;RKb;RKan;edIm,IpSarP¢ab;eTAnwgRTnug b¤ diagonal stiffener mYyKUr. kñúgkarGnuvtþeK eRcIneRbI stiffener Cag.



AISC K1.7 k¾)anpþl;nUvsmIkaredIm,IenAeBlEdleKBicarNaBI frame stabality EdlrYmbBa©Úl TaMgkMhUcRTg;RTayrbs; panel zone. vaminRtUv)anerobrab;enATIenHeT. ]TahrN_ 8>11³ kMNt;faetItMNén]TahrN_ 8>10 RtUvkar stiffener b¤k¾ column web reinforce-

ment. snμt;fa 0=uV nig 4.0/ =yu PP . dMeNaHRsay³ BI]TahrN_ 8>10 flange force RtUv)anykes μ Inwg kipsHPbf 0.121== RtYtBinitü local flange bending CamYynwg AISC Equation K1-1:

( )yffn FtR 225.6φφ = ( ) ( )[ ] kipskips 12112336780.025.690.0 2 >== (OK)

RtYtBinitü local web yielding CamYynwg AISC Equation K1-2: ( )[ ]wywn tFNkR += 5φφ

( ) ( )( ) kipskips 121136485.03685438.150.1 >=⎥⎦⎤

⎢⎣⎡ += (OK)

RtYtBinitü web crippling CamYynwg AISC Equation K1-4:

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 31135φφ

( )( ) ( )485.0780.036

780.0485.0

16.148/531485.013575.0

5.12

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛+=

kipskips 121193 >= (OK)

cemøIy³ eKminRtUvkar column stiffener eT. sRmab;kmøaMgkat;TTwgeNAkñúgRTnugssr BIsmIkar *>& nigedayecalkRmas;rbs; shim enA kñúgkarKNnark bd kmøaMgkat;TTwgemKuNenAkñúg column web panel zone KW ( )

ub

VdMMP −

+=

95.021 ( )

( )[ ] kips12008/5283.2095.0

12210=−

+=

edaysar yu PP 4.0= eRbI AISC Equation K1-9: ( )( )( ) kipstdFR wcyv 3.148485.016.143660.060.0 ===



Design strength KW ( ) kipskipsRv 1201343.14890.0 >==φ (OK) cemøIy³ eKminRtUvkar column web reinforcement eT. ]TarhrN_ 8>12³ rUbTI 8>39 bgðajBI beam-to-column connection EdlepÞrm:Um:g;emKuN

kipsft −142 . m:Um:g;enHekIteLIgedaysarbnÞúkTMnagefr nigGefr. eKeRbIEdkRbePT 36A nig electrode 70E . cUreFVIkarGegát colum stiffener nigtRmUvkar web panel-zone reinforcement. snμt;fa 0=uV nig yu PP 4.0< . dMeNaHRsay³ flange force KW ( ) kips

tdMP

bbbf 07.98

525.090.1712142

=−

=−

=

edIm,IRtYtBinitü flange bending eKeRbI AISC Equation K1-1: ( )yffn FtR 225.6φφ =

( ) ( )[ ] kipskips 07.9850.6336560.025.690.0 2 <== (N.G.) dUcenH eKRtUvkar stiffener edIm,IkarBar loacla flange bending. edIm,IRtYtBinitü local web yielding eKeRbIsmIkar 8>6 CMnYs[kareRbI AISC Equation K1-2: ( )

yst

wywbbfst F

tFtkPA

+−=

5 ( )[ ]( )( ) 2.6236.0

3636.036525.0062.1507.98 in=

+−=

edaysar stA viC¢man dUcenHeKRtUvkar stiffener mYyKUrEdlman combined cross-sectional area

y:agtic 2.623.0 in . RtYtBinitü web crippling strength edayeRbI AISC Equation K1-4:

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 31135φφ

( )( ) ( )360.0560.0365.1

560.0360.0

25.8525.03136.013575.0 2

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛+=

kipskips 07.989.107 >= (OK)

eKeRCIserIsTMhM stiffener edayQrelIlkçxNÐEdlpþl;[eday AISC Section K1-9,

ehIybnÞab;mkeKRtUvRtYtBinitüRkLaépÞmuxkat;EdlTTYl)an.



TTwgGb,brmaKW .825.1

2360.0

3015.6

23in

tbb wf =−=−≥ RbsinebIeKminGnuBaØat[bnøay stiffener eTAhYsRCugrbs;søabssr TTwgGtibrmaKW

.855.32

360.007.8 inb =−

≤ kRmas;Gb,brmaKW

.2625.02525.0

2in

tb == sakl,g 16/53× ³

22 6236.0.875.1stiffeners21653 ininAst >=×⎟⎠⎞

⎜⎝⎛= (OK)

RtYtBinitüpleFobTTwgelIkRmas; (width-thickness ratio)

6.916/53

==sttb

6.98.1536

9595>==

yF (OK)



edaysarEtkartP¢ab;enHmanEtmçag dUcenHeKminRtUvkar full-depth stiffeners eT. dUcenH .125.4

225.8

2ind

== yk .4 21 in

cemøIy³ eRbIEdkTMhM 21416/53 ×× cMnYn 2 bnÞH. ¬kat;RcwbRCugEkgxagkñúgrbs;bnÞHEdkedIm,IeCos

vag fillet enARtg;kEnøgEdlsøab nigRTnugrbs;ssrCYbKña. kat;RcwbedaymMu o45 sRmab;TMhM .8/5 in ¦.

KNnaTwkbnSarsRmab;P¢ab; stiffener eTARTnugssr TMhMGb,brma .

163 in= (AISC Table J2.4, edayQrelIkRmas;RTnug)

TMhMcaM)ac;sRmab;ersIusþg;KW ( )WFL

wφ707.0

stiffenerby resisted force=

BIsmIkar *>^ kmøaMgEdlRtUvTb;eday stiffener KW ( ) wywbbfystst tFtkPFA +−= 5

( )[ ]( )( ) kips45.22360.036525.0062.1507.98 =+−= RbEvgEdlGacpSarP¢ab; stiffener eTAnwgRTnugssrKW .5.15stiffeners2sids2

855.4 inL =××⎟⎠⎞

⎜⎝⎛ −= ¬emIlrUbTI 8>40¦

( )( ) .163.0650.0

5.315.15707.045.22 ininw <== TMhMGb,brma

ersIusþg;kmøaMgkat;rbs; base metal KW ( ) ./075.6

1653654.054.0 inkipstFtFR styBMn =⎟⎠⎞

⎜⎝⎛===φφ

nig ersIusþg;TwkbnSarcaM)ac; ¬sRmab; stiffener mYy¦ ( )( )( )25.31707.00650.0= ./075.6./09.2 inkipsinkips <= (OK)

cemøIy³ yk filler weld .16/3 in . KNnaTwkbnSarsMrba;P¢ab; stiffener eTAnwgsøabssr TMhMGb,brma .

41 in= (AISC Table J2.4, edayQrelIkRmas;søab)

lT§PaBTwkbnSarkñúg ( ) ./538.55.3141707.0.1 inkipsin =⎟⎠⎞

⎜⎝⎛=

./6075.054.0 inkipstF sty =< (OK)



RbEvgEdlmansRmab; ( )( ) .5.922853 in=⎟⎠⎞

⎜⎝⎛ −=

TMhMcaM)ac;sRmab;ersIusþg;KW ( ) ( )( ) .

41.106.0

5.315.9707.045.22

707.0stiffenerby resisted force inin

FLw

W<===

φ

cemøIy³ yk fillet weld .4/1 in . ¬m:Um:g;Gnuvtþn_EdlekIteLIgedaybnÞúkTMnaj ehIyEdlminGac bþÚrTisedAGnuvtþn_)an dUcenHeKGacdak; stiffener Pa¢b;eTAnwgsøabssr Edl stiffener enHTb;søabrg karsgát;rbs;FñwmedaymincaM)ac;pSar b:uEnþkrNIenHmin)anniyayenATIenHeT¦. RtYtBinitüRTnugssrsRmab;kmøaMgkat;TTwg. BIsmIkar *>& ( ) ( )

( ) kipsVdMMP u

b2.1000

90.1795.012142

95.021 =−=−

+=

BI AISC Equation K1-9

( )( )( ) kipstdFR wcyv 15.64360.025.83660.060.0 === Design strength KW

( ) kipskipsRv 5.10074.5715.6490.0 <==φ (N.G.) eRbI AISC Equation edIm,IrkkRmas;RTnugEdlRtUvakar. edaHRsayrk wt edayKuNPaKyk nigPaKEbgeday φ

=wt required doubler plate thickness

.265.0360.0625.0 in=−= sakl,g .16/5 intd = . TwkbnSarRtUvmanTMhM[RtUvKñanwgersIusþg;kmøaMgkat;énkRmas;caM)ac;

rbs; doubler plate. yk



( )WdBM FwtF φφ 707.0= b¤ ( )

( )( )( ) .231.0

5.31707.0265.03654.0

707.0in

FtFwW

dBM ===φ

φ

yk .4/1 inw = BI AISC J2.2b, TMhMTwkbnSarGtibrmaKW .

41

61

165

161 intd =−=− (OK)

cemøIy³ double plate .16/5 in nig fillet weld in4/1 eRbI diagonal stiffener

eRbI full-depth horizontal stiffeners dUcbgðajenAkñúgrUbTI 8>41 ¬RKan;EtCaCMerIs¦.

kmøaMgkat;TTwgEdlTb;eday web reinforcement KW kips46.4274.572.100 =− . RbsinebIkmøaMg enHRtUv)anKitCakMub:Usg;kmøaMgtamG½kSedk P enAkñúg stiffener kipsP 46.42cos =θ Edl o

c

bdd 26.65

25.890.17tantan 11 =⎟

⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛= −−θ

( ) kipsP o 5.10126.65tan

46.42==

yk ( ) kipsAFAR stystn 5.101369.0 === φφ bnÞab;mk ( )

2.13.3369.05.101 inAst ==

eRbI stiffener BIr/ 16/93× enAsgxagRTnug



stA Edlpþl;[ ( ) 22 .13.3.38.316932 inin >=⎟⎠⎞

⎜⎝⎛= EdlRtUvkar (OK)

RtYtBinitüpleFobTTwgelIkRmas; (width-thickness ratrio): 8.15

36953.5

16/93

=<==sttb (OK)

KNnaTwkbnSar. RbEvgrbs; diagonal stiffener nImYy²KW ( ) .7.19

26.65cos25.8

cosin

do

c ==θ

RbsinebIeKpSarenAelIépÞTaMgsgxagrbs; stiffener enaHRbEvgTwkbnSarKW ( ) .8.7847.19 inL == TMhMTwkbnSarEdlcaM)ac;sRmab;ersIusþg;KW ( ) ( )( ) .058.0

5.318.78707.05.101

707.0in

FLPw

W===

φ

eRbITMhMGb,brma .4/1 in (AISC Table J2.4) edaysarTMhMEdlcaM)ac;sRmab;ersIusþg;mantémøtUc eyIgnwgGegátemIllT§PaBkñúgkareRbITwknSarEdl minCab;Kña. BI AISC J2.2b

RbEvgGb,brma .0.14144 inw =⎟⎠⎞

⎜⎝⎛== b:uEnþvaminRtUvtUcCag .5.1 in ¬ .5.1 in lub¦

lT§PaB nigKMlatrbs;RkuménTwkbnSarbYnKW ( ) ( ) ( ) ( )( ) kipsFwL w 41.335.315.1

41707.04707.04 =⎟⎠⎞

⎜⎝⎛=φ

lT§PaBEdlcaM)ac;kñúg ./152.57.195.101.1 inkipsin ==

KMlatEdlcaM)ac;rbs;TwkbnSar .48.6152.5

41.33 in== shear capacity of base metal ( )( ) ./00.7360.03654.054.0 inkipstF wy ===

lT§PaBrbs;TwkbnSar ( ) ( )5.3141707.0707.0 ⎟⎠⎞

⎜⎝⎛== WFw φ

./00.7./57.5 inkipsinkips <= (OK)

cemøIy³ eRbITwkbnSarminCab;Kña .1.4/1 21 inin × EdlmanKMlatBImYyeTAmYy .6in KitBIG½kS enAelIépÞ

nImYy²rbs; diagonal stiffener. dUcEdl)anbgðajBImun eKniymeRbIdiagonal stiffener Cag doubler plate b:uEnþsRmab;lkçN³ esdækic©eKKYrEteRbIvaCamYynwgmuxkat;ssrFM. témøBlkmμCamYynwg doubler plate nig stiffener TaMg



Gs;GacnwgbEnßmtémøeRcIneTAelIsMPar³sRmab;ssrmuxkat;FM. 8>8> End Plate Connection End plate connection Ca beam-to-column nig beam-to-beam connection Edlmankar eBjniym ehIyRtUv)aneKeRbIcab;taMgBIBak;kNþalTsvtSr_qñaM 1950 mkemøH. rUbTI 8>42 bgðajBI end plate connection BIrRbePTKW³ tMNsamBaØ b¤tMNrgEtkmøaMgkat; (Type PR construction) nig tMNrwg b¤tMNTb;m:Um:g; (Type FR construction). Rigid connection k¾RtUv)anehA mü:ageTotfa extended end plate connection. eKalkarN_rbs;RbePTTaMgBIrKW bnÞHEdkEdlRtUv)anpSarP¢ab;enA xagcugrbs;FñwmRtUv)ancab;P¢ab;eTAnwgssr b¤Fñwmedayb‘ULúg. tMNenHRtUvkarb‘ULúgticCagkartP¢ab; epSgeTotEdlGaceFVI[kardMeLIgelOn. sRmab;tMNsamBaØ eKRtUvykcitþTukdak;kñúgkareFVI[manlkçN³ flexible RKb;RKan;edIm,IeFVI [FñwmmanmMurgVilenAxagcug. eKGacTTYl)an flexibility enH RbsinebIbnÞHEdkmanTMhMtUc nigesþIg ebIeRbobeFobCamYynwg tMNRbePT fully restrained. Manual of Steel Construction, in Part 9,

“Simple Shear Connections,” )anENnaMfa kRmas;RtUvsßitenAcenøaH .4/1 in nig .8/3 in edIm,I TTYl)an flexibility. EpñkenHrbs; Manual k¾bgðajBIeKalkarN_ENnaM nig]TaheN_EdlrYmman reaction capacities sRmab;bnSMCaeRcInénbnÞHEdk nigb‘ULúg.

karKNna moment-resisting end plate connections RtUvkarkarkMNt;kRmas;bnÞH TMhMTwk bnSar nigkarlMGitBIb‘ULúgCaedIm. karKNnaBITwkbnSar nigb‘ULúgCakarGnuvtþn_nUv traditional

analysis procedures. b:uEnþ karKNna kRmas;bnÞHKWQrelIlT§plrbs;karBiesaF nig statistical

research (Krishnamuthy, 1978). EpñkrgkarTajrbs;tMNKWmaneRKaHfñak; Éb‘ULúgenAEpñkrgkar sgát;mannaTICaGñkrkSatMN[enARtg;G½kS. RbsinebImanm:Um:g;sgxag eKRtUvKNnaEpñkrgkar TajTaMgsgxag. viFITUeTAKWxageRkam³

!> kMNt;kmøaMgenAkñúgsøabrgkarTajrbs;Fñwm @> eRCIserIsb‘ULúgEdlcaM)ac;edIm,ITb;Tl;nwgkmøaMgenH nigteRmobva[manlkçN³sIuemRTI

eFobnwgsøabrgkarTaj. RbsinebIm:Um:g;sßitenAsgxag eKRtUveFVIkartMerobdUcKñaenAelIEpñk rgkarsgát;Edr. b‘ULúgRtUvEtmancMnYnRKb;RKan;edIm,ITb;Tl;nwgkmøaMgkat;TTwgEdl)anmk BIRbtikm μFñwm.



#> cat;TukEpñkrbs;søabFñwm nigbnÞHEdkEdlenAek,reFVIkarCa tee-shape EdlrgbnÞúkTajEdl GnuvtþeTAelIRTnugrbs;va dUcbgðajenAkñúgrUbTI 8>43.

$> eRCIserIsTTwg nigkRmas;rbs;søab tee enHedIm,IbMeBjtRmUvkar flexural dUcKñanwgviFI KNna tee hanger ¬emIlEpñk 7>8¦.

%> RtYtBinitükmøaMgkat;enAkñúgbnÞHEdk. ^> KNnaTwkbnSar. Manual of Steel Construction (Volume II), bgðajbIviFIsaRsþKNnalMGitCamYynwg]Ta-

hrN_enAkñúg Part 10, “Fully Restrained (FR) Moment Connection”. viFIsaRsþkñúgkarKNnarbs; vaRsedogKñanwgGVIEdl)anerobrab;xagelIedaymankarEksRmYlxøH eBlxøHeKehAvafa Split-tee

method (Krishnamurthy, 1978). GVIEdlxusKña KWCMhanTI $ sRmab;karKNnam:Um:g;Bt;enAkñúgbnÞH Edk. Traditional analysis KitbBa©ÚlTaMg prying forces EdlmanniyayenAkñúgEpñkTI 7>8. sRmab; viFIKNnanaeBlbc©úb,nñ kareRCIserIsb‘ULúg nigkRmas;bnÞHEdkminGaRs½ynwgkarBIcarNaBI prying

action eT. karKNnam:Um:g;KWQrelIkarsikSa statistical analysis of finite element Edlmankar bBa¢ak;edaykareFVIBiesaFn_. CMhandMbUgenAkñúgviFIsaRsþKNnaKW KNnakmøaMgenAkñúgsøab gkarTaj rbs;Fñwm.



f

uuf td

MP

−=

bnÞab;mk eKeRCIserIsb‘ULúgedIm,ITb;nwgkmøaMgTajenH ehIyeKtMerobvaCaBIrCYr[manlkçN³ sIuemRTIeFobnwgsøabrgkarTajrbs;Fñwm. eKRtUvbEnßmb‘ULúgy:agticBIrenARtg;søabrgkarsgát;sRmab; tRmUvkarrbs;RbtikmμFñwm. cMnYnb‘ULúgEdlRtUvkaredIm,ITb;Tl;nwgRbtikm μFñwmnwgQrelI shear capacity b¤k¾ slip-critical capacity rbs;b‘ULúg EdlGaRs½ynwgRbePTrbs;tMN. RbsinebItMNCa bearing-

type eKRtUvRtYtBinitüGnþrkmμénkmøaMgkat; nigkmøaMgTajenAkñúgb‘ULúg. eKmincaM)ac;eFVIkarGegátenH sRmab; clip-critcal connection.

m:Um:g;GtibrmaenAkñúg split –tee nwgekItmanenARtg; “load line”, muxkat; 1-1 EdlbgðajenA kñúgrUbTI 8>43 KW



sFMt 1= Edl =1F kmøaMgkat;TTwg

2ufP

=

=s cm¶ayBI load line eTAcMNucrbt; 2ep

= wdpp bfe 707.025.0 −−= BIrUbTI 8>43/ fp Cacm¶ayBIG½kSb‘ULúgeTAsøabFñwm EdlCaTUeTAes μnwgGgát;p©itb‘ULúg .2/1 indb + ehIy w CaTMhMTwkbnSar. eKehA fp Cacm¶ayb‘ULúg (bolt distance) ehIy ep Cacm¶ayb‘ULúg RbsiT§PaB (effective bolt distance b¤ effective span). m:Um:g; tM EdlRtUv)anbMElgedayemKuN

mα edIm,ITTYl)anm:Um:g;RbsiT§PaB euM tmeu MM α= Edl ( ) ( ) 4/13/1 // bewfbam dpAACC=α =aC cMnYnefrEdlTak;TgeTAnwglkçN³rbs;smÖar³rbs;b‘ULúg nigbnÞHEdk. pfb bbC /= =fb TTwgrbs;søabFñwm

=pb TTwgrbs; end plate [Krishnamurthy (1978) )anENnaMnUvTTwgRbsiT§PaBGtibrma pf twb ++ 2 Edl pt CakRmas;rbs; end plate. Manual ENnaMTTwgCak;Esþg

Gtibrma .1inb f + ] =fA RkLaépÞsøabFñwm =wA RkLaépÞRTnugFñwmEdlenAcenøaH fillet cMnYnefr aC CaGnuKmn_EtnwglkçN³rbs;smÖar³ ehIyRtUv)anerobCataragsRmab;cMNat;fñak; TUeTArbs; structural steel nig b‘ULúgersIusþg;x<s;. taragenHRtUv)anbgðajenAkñúg Table 10-1 enAkñúg Part 10 én Manual. Table 10-2 [nUvtémø wf AA / sRmab;rUbragFñwmEdlRtUv)aneRbICaTUeTA. enA eBlEdleKKNnam:Um:g; euM rYcehIy eKGacdak;va[es μ Inwg design strength enaHeKnwgGacrk kRmas;bnÞHEdkGtibrma prept EdlcaM)ac;. sRmab;muxkat;ctuekaNEkgEdlekageFobnwgG½kStUc (minor axis) enaH design strength KW



ypp

ybpbnb Ftb

ZFMM req

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛===

490.0

2

φφφ

eday[smIkarenHes μ Inwgm:Um:g;emKuN eKTTYl)ankRmas;bnÞHEdk

euypp

MFtb

pre =⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

490.0

2

dUcenH yp

eup Fb

Mt req 90.0

4=

eKGacP¢ab;søabrgkarTajrbs;FñwmeTAnwgbnÞHEdkeday full penetration groove weld b¤k¾ eday filler weld EdlpSarBT§½CMuvijsøabTaMgGs;. kmøaMgenAkñúgsøabTaMgGs;RtUv)anbegáItenAelIEpñk rgkarTaj. eKKYrpSarRTnugenAépÞsgçagCamYynwg fillet welds EdlmanlT§PaBTb;Tl;nwgRbtikmμFñwm. eKRtUveKarBnUveKalkarN_ENnaMbEnßmxageRkamedIm,IbMeBjkarsnμt;sRmab;GnuvtþnUvviFIKNnaxagelI.

!> TaMgbnÞHEdk nigEdkFñwmRtUvman yield stress dUcKñaKw yF @> Ggát;p©itb‘ULúg bd minRtUvFMCag mmin 38.1 2

1 = #> b‘ULúgRtUvEtrgkarTajEdleKarBtam AISC Table J3.1. $> cm¶ayRCugEKmbBaÄrKYrmantémøRbEhl bd4

31 b:uEnþminKYrtUcCag bd211

]TahrN_ 8>13³ KNna end plate connection sRmab;Fñwm 3518×W . tMNenHRtUvmanlT§PaBkñúg karbBa¢Únm:Um:g;emKuN kipsft −173 nigkmøaMgkat;TTwgemKuN kips34 . eRbIEdk 36A / electrode

XXE70 nig slip-critical bolts 325A . dMeNaHRsay³ kmøaMgsøabKW ( ) kips

tdM

Pf

uuf 2.120

425.07.1712173

=−

=−

=

sakl,gb‘ULúgBIrCYrEdlkñúgmYyCYrmanBIrRKab;enAsøabxagelI nigb‘ULúgBIrRKab;enAsøabxageRka Edl b‘ULúgTaMgGs;manR)aMmYyRKab;. Design strength rgkmøaMgTajsRmab;b‘ULúgmYyRKab;KW bn AR )90(75.0=φ ehIyRkLaépÞmuxkat;EdlcaM)ac;sRmab;b‘ULúgmYyKW ( ) ( )

2.445.09075.0

4/2.1209075.0

Requiredin

RA n

b ===φ



cemøIy³ eRbIb‘ULúg 325A Ggát;p©it .8/7 in ¬ 2.6013.0 inAb = ¦ eKGackMNt;kmøaMgkat;GtibrmaEdlRTedaytMNBIkarBicarNa slip-critical strength rbs;b‘ULúg ¬EdlnwgmantémøtUcCag shear strength¦. sRmab;b‘ULúgR)aMmYyRKab; ( ) ( )( )( )( )( ) kipskipsNNTR sbmstr 343.87163933.013.10.113.1 >=== μφφ (OK) ¬eKmindwgkRmas;rbs;søabssr ehIyeKminTan;sÁal;kRmas;rbs; end plate dUcenHeKminGaceFVIkar Gegát bearing strength enAeBlenH)aneT. b:uEnþ enAeBlEdlRKb;EpñkEdlRtUvtP¢ab;TaMgGs; RtUv)anKNna enaHeKGacRtYtBinitü bearing strength¦. edaysarvaCa slip-critical connection enaHeKminRtUvkar RtYtBiniüGnþrkm μénkmøaMgkat; nigkmøaMgTajeT. cemøIy³ eRbIbU‘LúgR)aMmYy EdlbYnRtUv)antMerobsIuemRTIKñaeFobnwgsøabrgkarTaj nigBIreTotsßitenA Rtg;søabrgkarsgát;. sRmab; flange weld RbEvgEdlGacpSar)anKW ( ) ( ) .55.1230.0425.020.6222 inttbL wff =−+=−+= TMhMTwkbnSarEdlRtUvkarKW ( ) ( )( ) .4301.0

5.3155.12707.02.120

707.0in

FLP

ww

uf ===φ

eTaHbICaeKminTan;sÁal;kRmas;rbs; end plate k¾eday k¾TMhMTwkbnSarGb,brmaEdl)anBI AISC

Table J2.4 minEdlFMCag .16/5 in dUcenH .43.0 in EdlRtUvkarsRmab;ersIusþg;nwgmantémøFMCag. cemøIy³ eRbI fillet weld .16/7 in sRmab; end plate/ yk .375.1500.0875.0

21 indp bf =+=+=

wdpp bfe 707.025.0 −−= ( ) .8470.0

167707.0875.025.0375.1 in=⎟⎠⎞

⎜⎝⎛−−=

sRmab;TTwgbnÞHEdk/ yk .00.7100.61 inbb fq =+=+= bnÞab;mk kipsin

pPsFM euf

t −=⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛== .45.25

28470.0

22.120

221 36.1=aC (Table 10-1, Part 10 of the Manula)



9258.000.700.6

===q

fb b

bC

504.0=w

fAA (Table 10-2, Part 10 of the Manual)

4/13/1

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

b

e

w

fbam d

pAA

CCα

( )( ) ( ) 9939.0875.0/8470.0504.09258.036.1 4/13/1 == ( ) kipsinMM tmeu −=== .29.2545.259939.0α ( )

( )( ) .668.03600.790.0

29.25490.04 in

FbMt

yp

eupreq ===

cemøIy³ ykkRmas;bnÞHEdk .4/3 in TTwgbnÞHEdkRbsiT§PaBGtibrmaEdlENnaMeday Krishnamurthy (1978) KW 00.7.62.7

43

167200.62 >=+⎟⎠⎞

⎜⎝⎛+=++ intwb pf (OK)

RtYtBinitükmøaMgkat;. kmøaMgkat;enAkñúgbnÞHEdkKW kips

PF uf 1.60

22.120

21 === BI AISC J5, ersIusþg;kmøaMgkat;KW (shear strength) KW ( ) ( ) ( ) kipskipsFAR ygn 1.6010236

43760.090.060.090.0 >=⎟⎠⎞

⎜⎝⎛ ×==φ (OK)

edIm,ITTYl)an shear strength rbs;RTnugdUcKña ersIusþg;TwkbnSarEdlcaM)ac; ¬TwkbnSarBIrCYrEdlenA sgçagRTnug¦ KW ./819.5

7.17103 inkips

dVnv ==

φ TMhMTwkbnSarEdlRtUvkar ( ) .131.0

5.31707.02/819.5 inw ==

kMNt;TMhMTwkbnSarEdlcaM)ac;edIm,ITb;Tl;nwgkarBt;enAkñúgRTnug. enAeBlEdlm:Um:g;Bt;eFVIkardl;m:U m:g;)øasÞic kugRtaMgenAkñúgRTnuges μInwg yield stress yF ehIybnÞúkkñúgmYyÉktþaRbEvgrbs;TwkbnSarKW ( ) ( )( ) ./720.9300.03690.01 inkipstF wyb ==××φ bnÞúkkñúgmYyÉktþarbs;TwkbnSarmYyCYrKW ./86.42/72.9 inkips= ehIyTMhMTwkbnSarEdlRtUvkarKW



( ) .131.0.2182.05.31707.0

860.4 ininw >==

TMhMTwkbnSarGb,brmaKW .4/1 in (AISC Table J2.4, edayQrelIkRmas;rbs;bnÞHEdk). cemøIy³ eRbI fillet weld .4/1 in ¬karKNnaRtUv)ansegçbenAkñúgrUbTI 8>44¦

Column Web Stiffener Consideration

eKbegáIt AISC Equation K1-2 EdlkarBar web yeilding rbs;ssrenAkñúgtMN beam-to-

column connection enAeBlEdleKeRbI end plates. smIkarenHKWQrelIkarkMNt;kugRtaMgenAelImux kat;rbs;RTnugEdlbegáIteLIgedaykRmas;rbs;va nigRbEvg ktb 5+ dUcbgðajenAkñúgrUbTI 8>45 b. eKnwgTTYl)anRkLaépÞFMCag enAeBlEdlbnÞúkRtUv)anbBa¢Úntamry³ end plate. RbsinebIeKKitTwk bnSar beam flange-to-plate nigbnÞúkRtUv)ansnμt;EckedayCRmal 1:1 tamry³bnÞHEdk RbEvgRTnug EdlrgbnÞúknwgesμ Inwg ktwt pb 522 +++ . edayQrelIkarsikSaRsavRCavedaykarBiesaF (Hendrick

and Murray, 1984) tYr k5 GacRtUv)anCMnYseday k6 Edlpþl;lT§plenAkñúgsmIkarxageRkamsRmab; yielding strength rbs;RTnug³ ( )[ ]wywpbn tFtwtkR 226 +++=φφ Edl =w TMhMTwkbnSar



elIsBIenH eKRtUveFVIkarGegátBI local flange bending ning web stability (web crippling b¤ compression buckling). Part 10 of the Manual maneKalkarN_ENnaMBIkarKit local flange

bending.

8>9> esckþIsnñidæan (Concluding Remarks) enAkñúgeyIgsgát;F¶n;elIkarKNna nigkarviPaKBIb‘ULúg nigTwkbnSareRcInCag connection

fitting dUcCa framing angle nig beam seats. kñúgkrNICaeRcIn karpþl;[sRmab; bearing enAkñúg tMNedayb‘ULúg nig base metal/ nigsRmab;kmøaMgkat;enAkñúgtMNedayTwkbnSar nwgFananUvPaBRKb; RKan;rbs;ersIusþg;rbs;EpñkTaMgenH. b:uEnþeBlxøH eKRtUvkarGegátkmøaMgkat;bEnßm. enAeBlxøHeTot eK RtUvEtBicarNaBI direct tensiion nigm:Um:g;Bt;. Flexibility rbs;tMNCakarBicarNad¾sMxan;mYyeTot. sRmab; shear connection (simple

framing), EpñkEdlP¢ab;RtUvman flexible RKb;RKan;edIm,IGnuBaØat[tMNvileRkamGMeBIrbs;kmøaMg. b:uEnþ tMNRbePT FR (rigid connections) KYrEtrwgRKb;RKan;EdlmMurgVilrbs;Ggát;EdlRtUv)anP¢ab;GacrkSa nUvtémøGb,brma. CMBUkenHRKan;EtENnaMBIkarKNnatMNenAkñúgeRKOgbgÁúMEdkEtb:ueNÑaH edaymin)anniyaylMGit Gs;esckþIeT. Blodgett (1966) KWCaRbPBB½t’mand¾manRbeyaCn_EdlniyaylMGitBItMNedaypSar.

eTaHbICavaRtUv)ane)aHBum<yUrbnþicEmn Etvapþl;nUvkarENnaMEdlmanRbeyaCn_CaeRcIn. dUcKña Detailing for Stell Construction (AISC, 1983) CaRbPaBEdlmanB½t’manEdlmanGtßRbeyaCn_ sRmab;GñkKNna nigGñklMGitkartP¢ab;.


T.Chhay 370 Composite Construction

IX. eRKOgbgÁúMsmas Composite Construction

9>1> esckþIepþIm (Introduction) eRKOgbgÁúMsmasCaeRKOgbgÁúMsMNg;EdlGgát;rbs;vapÁúMeLIgedaysmÖar³BIrRbePTKW EdkeRKag nigebtugGarem:. niyay[xøIGgát;eRKOgbgÁúMsmaspSMeLIgedaysmÖar³BIr b¤eRcInRbePT. eRKOgbgÁúM smasRtUv)anerobrab;enAkñúg AISC Chapter I, “Composite Members.”. Fñwmsmas (composite beam) GacmaneRcInTRmg;. FñwmsmasBIdMbUgRtUv)ancak;bgáb;kñúgeb tugdUcbgðajenAkñúgrUbTI 9>1 a. vaCaCeRmIsmYyenAeBlEdleKRtUvkarkarBareRKOgbgÁúMEdkBIePøIg (fireproofing) ehIymUlehtumYyeTotKWeKGacKitBIkarcUlrYmrbs;ersIusþg;ebtugeTAkúñgersIusþg;rbs; Fñwm. naeBlbc©úb,nñenH eKmanviFIkarBarePøIgEdlmanlkçN³esdækic© nigTm¶n;Rsal dUcenHeKkRmcak; bgáb;eRKOgbgÁúMEdkkñúgebtugeToteT. eKGacTTYl)an composite behavior edayP¢ab;FñwmEdkeTAnwg kRmalebtugEdlvaRTEdleFVI[EpñkTaMgBIreFVIkarCamYyKña. enAkñúgRbB½n§kRmal b¤RbB½n§dMbUl Epñk rbs;kRmalxNÐeFVIGMeBICamYynwgFñwmEdkedIm,IbegáItCaFñwmsmasEdlman rolled steel shape EdlenA BIelIsøabxagelICasøabebtug ¬rUbTI 9>1 b¦. kareFVIkarrYmKñaenHGacRbRBwtþeTA)anRbsinebIeKkarBarkarrGiltamTisedk (horizontal

slippage) rvageRKOgbgÁúMTaMgBIr. eKGaceFVIdUcenH)an RbsinebIkmøaMgkat;tamTisedkenARtg;épÞb:H RtUv)ankarBaredayeRKOgsRmab;P¢ab;EdleK[eQμaHfa shear connectors. eKOgsRmab;P¢ab;enHGac Ca headed studs, spiral reinforcing steel b¤CaEdkrag channel shape tUc²RbEvgxøIRtUv)anpSar P¢ab;eTAnwgsøabxagelIrbs;EdkFñwmeTAtamKMlatkMNt; edIm,Ipþl;nUvkarpSarP¢ab;CalkçN³emkanictam ry³TMBk;enAkñúgebtugEdlrwgmaM ¬rUbTI 9>1 c¦. Stud CaRbePT shear connector EdleKniymeRbICag eK eKGaceRbIvaelIsBImYyedImenARtg;TItaMgEtmYy RbsinebIsøabFñwmmanTMhMTUlayRKb;RKan; ¬vaGa Rs½ynwgKMlatGnuBaØatEdlmanniyayenAkñúgkfaxNÐ 9>4¦. mUlehtumYyénPaBeBjniymrbs; shear stud KWPaBgayRsYlkñúgkardMeLIgrbs;va. eKRtUvkarcMnYn shear connector RKb;RKan;edIm,IeFVI[FñwmeTACaFñwmsmaseBjelj (fully

composite beam). cMnYn shear conncter EdlticCagtRmUvkarnwgeFVI[ekItmanPaBrGilxøHrvag eRKOgbgÁúMEdk nigebtug FñwmEbbenHeK[eQμaHfa FñwmsmasedayEpñk (partially composite).


eRKOgbgÁúMsmas 371 T.Chhay

Partially composite beam ¬EdlCak;Esþgman\T§iBlCag fully composite beam¦ RtUv)anbkRsay enAkñúgEpñkTI 9>7.

eRKOgbgÁúMsmasenAkñúgGKarPaKeRcInRtUv)anbegáIteLIgedaykRmalEdk (stell deck) EdleFVI CaBum<sRmab;ebtugkRmal ehIyRtUv)anminRtUv)anykecjeRkayeBlebtugrwgmaM. kRmalEdkk¾cUl rYmenAkñúgersIusþg;rbs;kRmal EteyIgmin)anBicarNaBIkarKNnakRmalEdkenATIenHeT. eKGaceRbI kRmalEdkpñt;EdlrnUtmanTisEkg b¤RsbnwgTisrbs;Fñwm. enAkñúgRbB½n§kRmalFmμta rnUtEtgEtEkg eTAnwgFñwmkRmal ehIyRsbeTAnwgrtEdlRTva. eKpSar Shear stud P¢ab;eTAnwgFñwmEdktamcenøaHrnUt dUcenHKMlatrbs; stud tambeNþayFñwmRtUv)ankMNt;edaycMnYnpñt;rbs;rnUt. rUbTI 9>2 bgðajBI kRmalxNÐEdlbegáIteLIgedaykRmalEdkEdlrnUtEkgeTAnwgFñwm. s<an highway PaKeRcInEdleRbIFñwmEdkCaFñwmsmas ehIyCaerOy²FñwmsmasCaCeRmIsEdl



manlkçN³esdækic©sRmab;sMNg;GaKar. eTaHbICaeKGaceRbI rolled steel beam EdlmanrUbragtUc Cag manTm¶n;RsalCagenAkñúgeRKOgbgÁúMsmask¾eday k¾ GtßRbeyaCn_rbs;vaRtUv)ankat;bnßyeday sartémøbEnßmén shear connector. eTaHbICay:agdUcenHk¾eday k¾GtßRbeyaCn_epSgeTotrbs;vaGac eFVI[eRKOgbgÁúMsmasmankarTak;TajEdr. eKGaceRbIFñwmEdlrak;Cag ehIyPaBdabrbs;vanwgtUcCag eRKOgbgÁúMFmμta (conventional noncomposite construction).

kugRtaMgeGLasÞicenAkñúgFñwmsmas Elastic Stresses in Compostie Beams eTaHbICa design strength rbs;FñwmsmasCaTUeTAQrelIlkçxNÐenAkar)ak;k¾eday k¾karyl; dwgBIkareFVIkarCamYynwgbnÞúkeFVIkar (service load) mansar³sMxan;sRmab;mUlehtuCaeRcIn. eKEtgEt eFVIkarGegátPaBdabrbs;eRKOgbgÁúMeRkamGMeBIrbs; service load ehIyenAkñúgkrNIxøH design strength

KWQrelIsßanPaBkMNt;én yield dMbUg. eKGacKNnakugRtaMgrgkarBt; (flexural stress) nigkugRtaMgrgkarkat; (shearing stress) enA kñúgFñwmrbs; homogeneous material BIrUbmnþ

IMcfb = nig

ItVQfv =

b:uEnþ edaysarFñwmsmasminEMmnCa homogeneous material dUcenHrUbmnþTaMgenHKμann½y. edIm,IGaceRbIrUbmnþTaMgenH)an eKRtUvbMElgmuxkat;rbs;ebtug[eTACamuxkat;Edk. viFisaRsþenH tRmUv[ strain rbs;EdkEdl)anRbDiteLIgBIebtugmantémødUcKñanwg strain rbs;EdkBitR)akd. rUbTI 9>3 bgðajBIkMNat;rbs;FñwmsmasCamYynwgdüaRkam stress nig strain. RbsinebIkRmalxNÐ RtUv)anP¢ab;y:agl¥eTAnwg rolled steel shape enaH strain RtUvEtmanragdUcGVIEdl)anbgðaj EdlRsb eTAnwg small displacement theory Edl)anniyayfa muxkat;EdlmanlkçN³erobes μ ImuneBlrgkar Bt;enAEtrkSalkçN³erobes μ IeRkayeBlrgkarBt;. b:uEnþ karBRgaykugRtaMgCalkçN³smamaRt



(linear stress distribution) Edl)anbgðajmann½yEtcMeBaHFñwmTaMgLayNaEdlRtUv)ansnμt;faCa homogeneous material. dMbUg eKRtUvtRmUv[ strain enAkñúgebtugRtg;RKb;cMNucTaMgGs;esμ Inwg strain enAkñúgEdkCMnYsenARKb;cMNucenaH sc εε = b¤

s

s

c

cEf

Ef

=

nig ccc

ss nff

EEf == ¬(>!¦

Edl =cE m:UDuleGLasÞicrbs;ebtug ==

c

sEE

n pleFobm:UDul

AISC I2.2 [m:UDuleGLasÞicebs;ebtug*

ccc fwE '5.1= (US)

( ) ccc fwE '103.1 35.1 −⋅= (SI)

Edl =cw Tm¶n;maDrbs;ebtug =cf ' ersIusþg;rgkarsgát;rbs;ebtugenA @*éf¶

Tm¶n; normal-weight concrete mantémøRbEhl 33 /2320/145 mkgftlb = eKGacbkRsaysmIkar (>! dUcxageRkam³ eKRtUvkarebtug n 2.in edIm,ITb;Tl;nwgkmøaMgdUcKña EdlEdk 2.1in GacTb;)an. edIm,IkMNt;RkLaépÞrbs;EdkEdlnwgTb;Tl;nwgkmøaMgdUcKñaEdlebtugGac eFVI)an eKRtUvEckRkLaépÞebtugeday n . mann½yfaCMnYs cA eday nAc / . lT§plEdlTTYl)an CaRkLaépÞbMElg (transformed area). BicarNamuxkat;smasEdlbgðajenAkñúgrUbTI 9>4 a ¬karkMNt;TTwgsøabRbsiT§PaB b enA eBlEdlFñwmCaEpñkrbs;RbB½n§kRmalnwgENnaMenAxagmux¦. edIm,IbMElgRkLaépÞebtug cA [eTACa RkLaépÞEdk eyIgRtUvEckvanwg n . viFId¾gayRsYlKWeKRtUvEckTTwgeday n ehIyrkSakRmas;[enA dEdl. kareFVIdUcenHeKTTYl)an homogeneous steel section dUcbgðajkñúgrUbTI 9>4b. edIm,IKNna kugRtaMg eyIgRtUvrkTItaMgG½kSNWtrbs;rUbragsmas ehIyKNnam:Um:g;niclPaBEdlRtUvKña. bnÞab;mk eyIgGacKNna bending stresses CamYynwg flexural formula. enAEpñkxagelIbMputrbs;srésEdk

* The ACI Building Code (ACI, 1995) [témørbs; ( ) ccc fwE '335.1= KitCa psi b¤ ( ) ccc fwE '043.05.1= KitCa

2/ mmN



tr

tst I

Myf =

enAEpñkxageRkambMputrbs;Edk

tr

bsb I

Myf =

Edl =M m:Um:g;Bt;Gnuvtþn_ =stI m:Um:g;niclPaBeFobG½kSNWt ¬dUcKñanwgG½kSTIRbCMuTm¶n;rbs; homogeneous section¦ =ty cm¶ayBIG½kSNWteTAEpñkxagelIbMputrbs;Edk =by cm¶ayBIG½kSNWteTAEpñkxageRkambMputrbs;Edk eKGackMNt;kugRtaMgenAkñúgebtugtamviFIdUcKña b:uEnþedaysarsmÖar³EdleyIgKitCaEdk enaHlT§pl tUvEcknwg n ¬emIlsmIkar (>!¦ dUcenHeK)an témøGtibrmarbs;

trc nI

yMf =

Edl y Cacm¶ayBIG½kSNWteTATItaMgx<s;bMputrbs;ebtug. dMeNIrkarKNnaenHmann½ysRmab;Etm:Um:g;Bt;viC¢man EdlkmøaMgsgát;enAxagelIeRBaHeKmin KitersIusþg;rgkarTajrbs;ebtug. ]TahrN_ 9>1³ FñwmsmasmYypSMeLIgedayEdk 36A manrag 3616×W CamYynwgkRmalebtug kRmas; .5in nigTTwg .87in enABIxagelIFñwm. ersIusþg;rbs;ebtugKW psif c 4000' = . kMNt;kugRtaMg GtibrmaenAkñúgEdk nigebtugEdlekItBIm:Um:g;Bt;viC¢man klipsft −160 .



dMeNaHRsay³ ksifwE ccc 34954145' 5.15.1 === 3.8

349529000

===c

sEEn yk 8=n

edaysarEtm:UDuleGLasÞicrbs;ebtugCatémøRbhak;RbEhl dUcenHeyIgGacyktémø n CatémøKt; ehIyvanwgpþl;nUvPaBsuRkitRKb;RKan;. dUcenH .88.10

887 in

nb

== rUbTI 9>5 bgðajBI transformed section.

eKGackMNt;TItaMgrbs;G½kSNWtedayGnuvtþeKalkarN_m:Um:g;CamYynwgG½kSrbs;m:Um:g;enAEpñk xagelIbMputrbs;kRmal. karKNnaRtUv)ansegçbenAkñúgtarag 9>1 ehIycm¶ayBITItaMgx<s;bMputrbs; kRmaleTATIRbCMuTm¶n;KW .202.4

00.651.273 in

AAyy ==

∑∑

= edayGnuvtþRTwsþIbTG½kSRsb nigedayerobCataragénkarKNnaenAkñúgtarag 9>2 eyIgTTYl)anm:Um:g; niclPaBrbs; transformed section KW



4.1526inItr = kugRtaMgenATItaMgx<s;bMputrbs;EdkKW .7980.000.5202.4 intyyt −=−=−= Edl t CakRmas;rbs;kRmal ( )( ) ksi

LMy

ftr

tst 00.1

15267980.012160

=×

== ¬rgkarTaj¦

tarag 9>1 eRKOgbgÁúM A y Ay

ebtug 54.40 2.50 136.0

3616×W 10.6 12.93 137.1

65.00 273.1

tarag 9>21

eRKOgbgÁúM A y I d 2AdI + ebtug 54.40 2.50 113.3 1.702 270.9

3616×W 10.6 12.93 448 8.728 1255

1525.9

¬TItaMgx<s;bMputrbs;EdksßitenABIxageRkamG½kSNWt dUcenH stf CakugRtaMTaj¦ kugRtaMgenATItaMgeRkambMputrbs;Edk³ .66.16202.486.155 inydtyb =−+=−+= ( )( ) ksi

IMyf

tr

bsb 0.21

152666.1612160

=×

== ¬rgkarTaj¦

kugRtaMgenATItaMgx<s;bMputrbs;rbs;ebtugKW ( )( ) ksi

nIyMf

trc 661.0

15268202.412160

=××

==

RbsinebIeKsn μt;ebtugminmanersIusþg;Tb;karTaj enaHebtuEdlsßitenABIeRkamG½kSNWtminRtUv)anyk mkKiteT. enaHragFrNImaRtrbs; transformed section xusBIragFrNImaRtedImEdl)ansn μt;. edIm,I



TTYl)anlT§plsuRkit eKRtUveFVIkarKNnaTItaMgG½kSNWteLIgvijedayQrelIragFrNImaRtf μ IenH. eyagtamrUbTI 9>6 nigtarag 9>3 eyIgGacKNnaTItaMgf μIrbs;G½kSNWtdUcxageRkam³

6.1088.101.13744.5 2

++

=∑∑

=y

yAAyy

( ) 1.13744.56.1088.10 2+=+ yyy

01.1376.1044.5 =−+ yy .140.4 iny = m:Um:g;niclPaBrbs;RkLaépÞsmasEdleFVIeLIgvijenHKW ( )( ) ( ) 423 .1524140.493.126.10448140.488.10

31 inItr =−++=

tarag 9>3

eRKOgbgÁúM A y Ay ebtug y88.10 2/y 244.5 y

3616×W 10.6 12.93 137.1

ehIykugRtaMgKW ( )( ) ksifst 08.1

1524140.4512160

=−×

= ¬rgkarTaj¦ ( )( ) ksifsb 1.21

1524140.486.15512160

=−+×

= ¬rgkarTaj¦ ( )( )

( ) ksifc 652.015248

140.412160=

×=

PaBxusKñarvagkarviPaKTaMgBIrGacecal)an ehIykarKNnaTItaMgG½kSNWteLIgvijminmanRbeyaCn_eT.



cemøIy³ kugRtaMgGtibrmaenAkñúgEdkKW kugRtaMgrgkarTaj ksi1.21 ehIykugRtaMgGtibrmaenAkñúgeb tugKW kugRtaMgrgkarsgát; ksi652.0 . ersIusþg;Tb;nwgkarBt; Flexural strength enAkñugkrNICaeRcIn eKnwgTTYl)an nomial flecural strength enAeBlEdlmuxkat;EdkTaMg mUl yield ehIyebtugEbkedaysarkmøaMgsgát;. karEbgEckkugRtaMgEdlRtUvKñaenAelImuxkat;smas RtUv)aneKehAfa karEbgEcgkugRtaMg)aøsÞic (plastic stress distribution). AISC Specification [nUv design strength sRmab;m:Um:g;Bt;viC¢manCa nbMφ EdlRtUv)ankMNt;dUcxageRkam³ !> sRmab;rUbragEdlman compact web ( yw Fth /640/ ≤ sRmab; US b¤

yw Fth /1680/ ≤ sRmab; SI) emKuNersIusþg; 85.0=bφ ehIy nM RtUv)anTTYlBI plastic stress

distribution. @> sRmab;rUbragEdlman noncompact web ( yw Fth /640/ > sRmab; US b¤

yw Fth /1680/ > sRmab; SI) 9.0=bφ ehIy nM RtUv)anTTYlBI elastic stress distribution Edl RtUvKñanwg yilding dMbUgrbs;Edk. rUbragTaMgGs;EdlmanenAkñúgtaragrbs; Manual Ca compact web dUcenHeKRtUveRbIlkçxNÐ TImYysRmab;karedaHRsayFñwmsmas elIkElgEt built-up steel shapes. enAkñúgCMBUkenHeyIg niyayEt compact shape b:ueNÑaH. enAeBlEdlFñwmsmaseTAdl;sßanPaBkMNt;)aøsÞic eKEbgEckkugRtaMgtamviFImYykñúgcMeNam viFIbIEdlbgðajenAkñúgrUbTI 9>7. kugRtaMgebtugRtUv)anbgðajCakugRtaMgsgát;BRgayes μ I cf '85.0 EdlbnøayBITItaMgx<s;bMputrbs;kRmaleTACMerAEdlGactUcCag b¤es μ InwgkRmas;kRmalsrub. karEbg EckenHKW Whitney equivalent stress distribution EdlkugRtaMgpÁÜbRtUvKñanwgkugRtaMgpÁÜbrbs;karEbg EckkugRtaMgBitR)akd (ACI, 1995). rUbTI 9>7 a bgðajBIkarEbgEckEdlRtUvKñanwg full tensil

yielding rbs;Edk nigkugRtaMgsgát;edayEpñkrbs;ebtug CamYynwgG½kSNWt)aøsÞic (PNA) enAkñúg kRmalxNÐ. edayersIusþg;Tajrbs;ebtugmantémøtUc ehIyvamintUv)aneKKitkñúgkarKNnaeTenaH K μankugRtaMgNa RtUv)anbgðajenAkEnøgEdlkugRtaMgTajmanGMeBIelIebtug. lkçxNÐenHeKeRbICaTUeTA enAeBlEdlva man shear connectors RKb;RKan;edIm,ITb;Tl;nwgkarrGil KWedIm,IFananUvkareFVIkarCa



eRKOgbgÁúMsmas. kñúgrUbTI 9>7 b bøúkkugRtaMgebtugRtUv)anbnøayeBj kRmas;rbs;kRmal ehIy

PNA sßitenAkñúgsøabrbs;FñwmEdk. dUcenHEpñkrbs;søabnwgrgkugRtaMgsgát; edIm,IbegáInkmøaMgsgát; enAkñúgkRmalxNÐ. rUbTI 9>7 c bgðajBIlT§PaBTIbI Edl PNAsßitenAkñúgRTnug. cMNaMfa sRmab; krNITaMgbIenH eKmincaM)ac;bnøaybøúkkugRtaMgebtugeBjkRmas;kRmaleT. kñúgkrNInImYy²EdlbgðajenAkñúgrUbTI 9>7 eyIgGacrk nominal moment capacity eday KNnam:Um:g; couple EdlekIteLIgedaykmøaMgTajpÁÜb nigkmøaMgsgát;pÁÜb. eyIgGacTTYlva)aneday eFVIplbUkm:Um:g;rbs;kmøaMgpÁÜbeFobnwgcMNucgayRsYlNamYy. edaysarkartP¢ab;rbs;FñwmEdkeTAnwg kRmalebtug vaminmanbBaðaCamYynwg lateral torsional buckling enAeBlEdlebtugrwgmaM ehIyeK TTYl)an composite action. edIm,IkMNt;faetIeKRtUvykkrNINamkeRbI eKRtUvKNnakmøaMgsgát;pÁÜbNaEdltUcCageKkñúgcM eNam !> ys FA @> cc Af '85.0 #> nQ∑ Edl =sA RkLaépÞmuxkat;rbs;EdkFñwm =cA RkLaépÞrbs;ebtug tb= ¬emIlrUbTI 9>7¦ =∑ nQ ersIiusþg;kmøaMgkat;srubrbs; shear connector lT§PaBnImYy²bgðajBIkmøaMgkat;tamTisedkenARtg;épÞb:HrvagEdk nigebtug. enAeBlEdllT§PaBTI mYylub eKeRbIEdkTaMgmUl ehIyeKGnuvtþkarEbgEcgkugRtaMgrbs;rUbTI 9>7 a. lT§PaBTIBIrRtUvKñanwg ebtugEdllub ehIy PNA sßitenAkñúgEdk ¬rUbTI 9>7 b b¤ c¦. krNITIbIlubEtenAeBlEdleKeRbI shear connector ticCagtRmUvkarsRmab; full composite behavior EdleFVI[ekItman partial

composite behavior. eTaHbICa partial composite action GacekItmanCamYynwgkRmalxNÐtan; b¤kM ralxNÐEdlekItBI steel deck k¾eday k¾vaRtUv)anykmkniyayenAkñúgkfaxNÐ 9>7/ “Composite

Beams with Formed Steel Deck”.



]TahrN_ 9>2³ KNna design strength rbs;Fñwmsmasrbs;]TahrN_ 9>1. snμt;faeKman shear

connector RKb;RKan;sRmab; full composite behavior. dMeNaHRsay³ kMNt;kmøaMgsgát; C enAkñúgebtug ¬kmøaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦. edaysarvaCa full composite action kmøaMgEdlmantémøtUcCagKW ys FA nig

cc Af '85.0 ³ ( ) kipsFA ys 6.381366.10 == ( )( ) kipsAf cc 1479875485.0'85.0 =×=



kmøaMgsgát;enAkñúgEdklub kipsC 6.381= . enHmann½yfaeKminRtUvkarkRmas;TaMgmUlrbs;ebtugedIm,IbegáItkmøaMgsgát;EdlRtUvkareT. eKTTYl)an karEbgEckkugRtaMgenAkñúgrUbTI 9>8.

eKk¾GacKNnakmøaMgsgát;rYmdUcxageRkam abfC c'85.0= enaHeyIg)an ( )( ) .290.1

87485.06.381

'85.0in

bfCa

c===

kmøaMg C nwgsßitenAelITIRbCMuTm¶n;rbs;RkLaépÞrgkarsgát;enAkm<s; 2/a BITItaMgx<s;bMput rbs;kRmalxNÐ. kmøaMgTajpÁÜb T ¬es μInwg C ¦ nwgsßitenATIRbCMuTm¶n;rbs;RkLaépÞEdk. ékXñas; rbs; couple RtUv)anbegáIteLIgeday C nig T KW .28.12

2290.15

286.15

22inatdy =−+=−+=

Nominal strength KWm:Um:g; couple b¤ ( ) kipsftkipsinTyCyM n −===== 5.390.468628.126.381 ehIy design strength KW ( ) kipsftM nb −== 3325.39085.0φ cemøIy³ design strength kipsft −= 332



enAeBlEdlvaman full composite behavior ]TahrN_ 9>2 CaKMrUsRmab;lkçxNÐenH. karvi PaKsRmab;krNI PNA EdlmanTItaMgsßitenAkñúgmuxkat;EdknwgRtUv)anrk enAeBlEdleKdwgfavaCa partial composite action. 9>2> karsagsg;edaymankarTb; nigedayminmankarTb;

Shored Versus Unshored Construction Tal;EtebtugrwgmaM nwgvaTTYl)annUv design strength rbs;va ¬y:agtic %75 énersIusþg;sgát; enA 28 éf¶ cf ' ¦ enaHmanminmankareFVIkarCasmas (composite behavior) eT ehIyTm¶n;rbs;kRmal dac;xatRtUv)anRTedaymeFüa)ayepSg². enAeBlEdlebtugrwgmaM vaGaceFVIkarCaeRKOgbgÁúMsmas ehIykmøaMgGnuvtþn_bnþbnÞab;RtUv)anTb;Tl;edayFñwmsmas. RbsinebIFñwmEdkRtUv)anRTedaycnÞl; RKb;RKan;tambeNþayRbEvgrbs;vamunnwgebtugRtUv)ancak; Tm¶n;rbs;ebtugRss;nwgRtUvRTedaycnÞl; beNþaHGasnñeRcInCagedayEdkFñwm. enAeBlEdlebtugrwgmaM cnÞl;beNþaHGasnñRtUv)anruHerIecj ehIyTm¶n;rbs;kRmalxNÐk¾dUcCabnÞúkbEnßmnwgRtUvRTedayFñwmsmas. b:uEnþRbsinebIeKmineRbIcnÞl; rolled steel shape minRtwmEtRTTm¶n;pÞal;rbs;vab:ueNÑaHeT b:uEnþvaRtUvRTTm¶n;rbs;kRmalxNÐ nigBum< kñúgeBlebtugeFVIkarrwgmaM. enAeBlEdleKTTYl)an composite behavior bnÞúkbEnßmTaMgbnÞúkefr nigbnÞúkGefrnwgRtUvRTedayFñwmsmas. eyIgnwgBicarNalkçxNÐxusKñaedaylMGitdUcxageRkam. K μancnÞl;³ muneBlebtugrwgmaM Unshored: Before Concrete cures

AISC I3.4 TamTarfa enAeBlEdleKmineRbIcnÞl; EdkFñwmEtÉgdac;xatRtUvEtmanersIusþg; RKb;edIm,I Tb;Tl;nwgbnÞúkGnuvtþn_TaMgGs;munnwgebtugTTYl)an %75 énersIusþg;rbs;va. ersIusþg;Tb; karBt; (flexural strength) RtUv)anKNnaedayviFIFm μta edayQrelI Charpter F of the Specifica-

tion ¬CMBUk 5 enAkñúgesovePAenH¦. edayGaRs½yeTAelIkarKNnarbs;va Bum<sRmab;kRmalebtug Gacpþl; b¤minGacpþl; lateral support sRmab;EdkFñwm. RbsinebIvaminpþl;Ca lateral support sRmab; EdkFñwmeT eKRtUvyk unbraced length bL mkKit ehIy lateral-torsional buckling GaclubelI flexural strength. RbsinebIeKmineRbIcnÞl;beNþaHGasnñeT EdkFñwmk¾GacRtUv)aneRbIedIm,ITb;Tl;nwg bnÞúksagsg;bnÞab;bnSMEdr. edIm,IkarBarbnÞúkTaMgenH eKRtUvbEnßmbnÞúk 22 /1/20 mkNftlb =

(Hansell et al., 1978).



K μancnÞl;³ eRkayeBlebtugrwgmaM Unshored: After Concrete cures eRkayeBleKTTYl)an composite behavior RKb;bnÞúkEdlGnuvtþCabnþbnÞab;TaMgGs;RtUv)an

RTedayFñwmsmas. b:uEnþ enAeBldac; RKb;bnÞúkTaMgGs;RtUv)anRTeday couple xagkñúg EdlRtUvKñanwg karEbgEckkugRtaMgenAeBldac;. dUcenHmuxkat;smasRtUvEtmanersIusþg;RKb;RKan;edIm,IRTbnÞúkTaMgenH EdlrYmbBa©ÚlTaMgbnÞúkEdlGnuvtþeTAelIFñwmEdkmunnwgebtugrwgmaM. karsagsg;edayTl; Shored Construction

kñúgkarsagsg;edayeRbIcnÞl; eKBicarNaEtFñwmsmas edaysareKminRtUvkar[EdkFñwmRT GVIepSgBIbnÞúkpÞal;rbs;vaeT. ersIusþg;kmøaMgkat; Shear Strength

AISC I3.6 tRmUv[kmøaMgkat;TaMgs;RtUvTb;Tl;edayRTnugrbs;EdkFñwm Edlpþl;[enA kñúg

Chapter F of the Specification.

]TahrN_ 9>3³ Edk 5012×W eFVIkarrYmKñaCamYynwgkRmalxNÐebtugkRmas; .4in . TTwgkRmal xNÐRbsiT§PaBKW .72in . eKmineRbIcnÞl; m:Um:g;Bt;EdlGnuvtþmkelIvamandUcteTA³ )anmkBITm¶n;Fñwm

kipsftM beam −= 13 )anmkBITm¶n;kRmalxNÐ kipsftM slab −= 77 nigBIbnÞúkGefr kipsftM L −= 38 . ¬enAkñúg]TahrN_enH eKminKitbnÞúksagsg;bEnßmeT¦. EdkEdleRbIKW 36A

ehIy psif c 4000' = . kMNt;faetI flexural rbs;FñwmenHRKb;RKan;b¤Gt;. sn μt;favaCa full

composite action ehIyBum<pþl;Ca lateral suppoet dl;muxkat;EdkmuneBlebtugrwgmaM. dMeNaHRsay³ muneBlebtugrwgmaM vamanEtbnÞúkGefrb:ueNÑaH ¬minmanbnÞúksagsg;enAkñúg]TahrN_ enHeT¦. dUcenHbnSMbnÞúk A4-1 lub ehIym:Um:g;emKuNKW ( ) ( ) kipsftMM Du −=+== 12677134.14.1 BI beam design chart enAkñúg Part 4 of the Manual sRmab;Edk 36A kipsftkipsftM nb −>−= 126195φ (OK) eRkayeBlebtugrwgmaM FñwmsmasRtUvTb;Tl;nUvm:Um:g;emKuN ( ) ( ) kipsftMMM LDu −=++=+= 8.168386.177132.16.12.1 kmøaMgsgát; C CatémøtUcCageKén



( ) kipsFA ys 2.529367.14 == b¤ ( )( ) kipsAf cc 2.979724485.0'85.0 =×= PNA KWsßitenAkñúgebtug ehIy kipsC 2.529= . BIrUbTI 9>8 km<s;rbs;bøúgkugRtaMgsgát;KW ( )( ) .162.2

72485.02.529

'85.0in

bfCa

c===

édXñas;m:Um:g;KW .014.9

2162.24

219.12

22inatdy =−+=−+=

design moment KW ( )( ) kipsftkipsftkipsinCM ybnb −>−==== 8.168338.4055014.92.52985.0φφ (OK)

cemøIy³ FñwmmanersIusþg;Bt; (flexural strength) RKb;RKan; . Cak;Esþg karsagsg;edayeRBIcnÞl;manRbsiT§PaBCagkarsagsg;EdlmineRbIcnÞl; edaysar KmineRbImuxkat;EdkedIm,IRTGVIepSgeRkABIbnÞúkxøÜnva. kñúgsßanPaBxøH kareRbIR)as;cnÞl;Gac[eKRbI R)as;muxkat;FñwmEdktUcCag. b:uEnþ eRKOgbgÁúMsmasCaeRcInminmaneRbIcnÞl;eT edaysartémøbEnßm rbs;cnÞl; CaBiesséføBlkmμ cMNayGs;ticCagkarsnSMsMécelITm¶n;Edk. 9>3> TTwgsøabRbsiT§PaB (Effect Flange Width ) Epñkrbs;kRmalxNÐEdleFVIkarCaeRKOgbgÁúMsmasCamYynwgEdkFñwmCaGnuKmn_eTAnwgktþaCa eRcIn EdlrYmmanRbEvgElVg nigKMlatFñwm. AISC I3.1 tRmUv[TTwgRbsiT§PaBrbs;kRmalxNÐenAelI EpñknImYy²rbs;G½kSFñwmKWtémøEdltUcCageKkñúgcMeNam³ !> mYyPaKR)aMbIénRbEvgElVg. @> mYyPaKBIrénKMlatFñwmEdlKitBIG½kSeTAG½kS. #> cm¶ayBIG½kSFñwmeTARCUgEKRmbs;kRmal. lkçxNÐTIbIRtUv)anGnuvtþcMeBaHEtFñwmxagb:ueNaÑaH dUcenHsRmab;Fñwmxagkñúg TTwgRbsiT§PaBTaMgmUlRtUv mantémøtUcCageKénmYyPaKbYnénRbEvgElVg b¤KMlatrbs;FñwmEdlKitBIG½kSeTAG½kS ¬edaysn μt;fa FñwmmanKMlates μ I¦.



]TahrN_ 9>4³ RbB½n§kRmalEdlpSMeLIgedayEdkFñwm 4412×W EdlmanKMlatBIKña ft9 nigRT kRmalebtugGarem:kRmas; .5.4 in . RbEvgElVgKW ft30 . edaybEnßmBIelITm¶n;rbs;kRmal eKman bnÞúkCBa¢aMgxNÐ psf20 nigbnÞúkGefr psf125 . EdkCaRbePT 36A ehIyersIusþg;rbs;ebtugKW

psif c 4000' = . cUreFVIkarGegátFñwmxagkñúgedayeKarBtam AISC Specificastion RbsinebIeKmineRbI cnÞl;beNþaHGasnñ. sn μt; full lateral support kñúgGMLúgeBlsagsg; ehIybnÞúksagsg;bEnßmKW

psf20 . eKpþl;nUv shear connector RKb;RKan;sRmab; full composite action. dMeNaHRsay³ bnÞúkEdlGnuvtþmuneBlebtugrwgmaMrYmmanTm¶n;rbs;kRmalxNÐ ( )( ) psf25.5615012/5.4 = .¬eTaHbICa normal-weight concrete manTm¶n; psf145 / EtebtugGarem: RtUv)ansnμt;famanTm¶n; psf150 ¦. sRmab;FñwmEdlmanKMlat ft9 bnÞúkGefrKW

t925.56 × ftlb /506= + Tm¶n;Fñwm fttlb /44=

ftlb /550 bnÞúksagsg;KW ( ) ftlb /180920 = EdlRtUv)anKitCabnÞúkGefr. bnÞúk nigm:Um:g;emKuNKW ( ) ( ) ftlbwww LDu /9481806.15502.16.12.1 =+=+= ( )( ) kipsftMu −== 6.10630948.0

81 2

BI load Factor Design Selection Table kipsftkipsftMM pbnb −>−== 6.106258φφ (OK) eRkayeBlebtugrwgmaM bnÞúksagsg;minmaneFVIGMeBIeToteT EtbnÞúlCBa¢aMgxNÐeFVIGMeBIvijmþg ehIyva RtUv)anKitCabnÞúkefr ¬emIl)TahrN_ 5>13¦³ ( ) ftlbwpart /180920 == ftlbwD /73018044506 =++= bnÞúkGefrCa ( ) ftlbwL /11259125 == bnÞúkGefr nigm:Um:g;GefrKW ( ) ( ) ftlbwww LDu /267611256.17302.16.12.1 =+=+= ( )( ) kipsftMu −== 30130676.2

81 2



TTwgRbsiT§PaBCatémøEdltUcCageKkñúgcMeNam ( ) .90

41230

4inspan

== KMlatFñwm ( ) .108129 in== edaysareRKOgbgÁúMEdlRtUvKNnaCaFñwmxagkñúg lkçxNÐTIbIminGacGnuvtþ)an. yk .90inb = CaTTwg søabRbsiT§PaB. enaH tamkarbgðajenAkñúgrUbTI 9>9 kmøaMgsgát;RtUvEtCatémøEdltUcCageKkñúg cMeNam ( ) kipsFA ys 4683613 == b¤ ( )( )( ) kipsAf cc 1377905.4485.0'85.0 == yk kipsC 468= . BIrUbTI 9>9 ( )( ) .529.1

90485.0468

'85.0in

bfCa

c===

.07.142529.15.433.10

22inatdy =−+=−+=

( )( ) kipsftkipsftkipsinCyM bnb −>−=−=== 301466.559507.1446885.0φφ (OK) RtYtBinitükmøaMgkat; ( ) kipsLwV u

u 1.402

30676.22

=== BItaragbnÞúkBRgayesμ IemKuN (facored uniform load tables) kipskipsVnv 1.40141 >=φ cemøIy³ FñwmBitCaeKarBtam AISC Specification.



9>4> Shear Connectors dUcEdleyIg)aneXIjrYcmkehIy kmøaMgkat;tamTisedkEdlekIteLIgcenøaHebtug nigEdkes μ I nwgkmøaMgsgát;enAkñúgebtug C . eyIgsMKal;kmøaMgkat;tamTisedkenHeday hV . dUcenH hV Catémø EdltUcCageKkúñgcMeNam ys FA / cc Af '85.0 b¤ nQ∑ . RbsinebI ys FA b¤ cc Af '85.0 lub vanwg man full composite action ehIyeKRtUvkarcMnYn shear connectors cenøaHm:Um:g;sUnü nigm:Um:g;Gtibrma KW

n

hQVN =1 ¬(>@¦

Edl nQ Ca nominal shear strength rbs; connector mYy². Connectors cMnYn 1N KYrRtUv)andak; edaymanKMlatesμ I²KñaelIRbEvgEdlvatRmUv. AISC Specification [smIkarsRmab;ersIusþg;TaMg stud connector nig channel shear connector. dUcEdl)anbgðajBIdMbUg stud connector CaRbePT EdleKniymeRbICageK ehIyeyIgBicarNaEtRbePTenH. sRmab; stud shear connector mYy uscccscn FAEfAQ ≤= '5.0 (AISC Equation I5-1) Edl =scA RkLaépÞmuxkat;rbs; stud

=cf ' ersIusþg;rgkarsgát;enA 28 éf¶ =cE m:UDuleGLasÞicrbs;ebtug =uF ersIusþg;rgkarTajrbs; stud sRmab; stud EdleRbICa shear connector enAkñúgFñwmsmas ersIusþg;rgkarTaj uF KW ksi60 . témø Edl[eday AISC Equation I5-1 KWQrelIkarBiesaFn_ (Ollgaard, Stutter, and Fisher, 1971). eKmineRbIemKuNersIusþg;sRmab; nQ eT flexural resistance factor bφ )anKitsRmab;RKb;ersIusþg;Edl manPaBminRbRktI. smIkar (>@ [cMnYn shear connector EdlRtUvkarenAcenøaHcMNucm:Um:g;sUnü nigcMNucm:Um:g; Gtibrma. dUcenH sRmab;FñwmTRmsamBaØEdlRTbnÞb;BRgayesμI eKRtUvkar connector cMnYn 12N ehIy BYkvamanKMlates μ I²Kña. enAeBlmanbnÞúkcMcMNuc AISC I5-6 TamTar[dak; connector cMnYn

1N enA cenøaHbnÞúkcMcMNuc nigcMNucm:Um:g;sUnüEdlenAEk,redIm,IbegáItm:Um:g;EdlTamTarenARtg;bnÞúk. EpñkenH RtUv)aneKsMKal;eday 2N ehIytRmUvkarenHRtUv)anbgðajenAkñúgrUbTI 9>10. cMNaMfacMnYn shear connector srubminTTYl\T§iBlBItRmUvkarenHeT.



tRmUvkarepSg²sRmab; Headed Struds (AISC I5) Miscellaneous Requirements for Headed Studs (AISC I5)

Ggát;p©itGtibrma ×= 5.2 kRmas;rbs;EdkFñwm RbEvgGb,brma ×= 4 Ggát;p©it stud KMlattambeNþayGb,brma ¬BIG½kSeTAG½kS¦ ×= 6 Ggát;p©it stud KMlattambeNþayGtibrma ¬BIG½kSeTAG½kS¦ ×= 8 kRmas;kRmalxNÐ KMlattamTTwgGb,brma ¬BIG½kSeTAG½kS¦ ×= 4 Ggát;p©it stud lateral cover Gb,brma mmin 25.1 == ¬minmankarkMNt;sRmab; vertical cover

Gb,brma¦

AWS Structural Code (AWS 1996) rayCabBa¢InUvGgát;p©it stud sþg;darCa 2/1 / 8/5 /

4/3 / 8/7 / nig .1in . edaypÁÚrpÁgGgát;p©itenHCamYynwgRbEvgGb,brmaEdltRmUveday AISC eyIg TTYl)anTMhM stud FmμtaKW 22/1 × / 2

128/5 × / 34/3 × / 2138/7 × nig 41× ¬b:uEnþ eKk¾GaceRbI

stud EdlEvgCagenHEdr¦. ]TahrN_ 9>5³ KNna shear connectors sRmab;RbB½n§kRmalenAkñúg]TahrN_ 9>4. dMeNaHRsay³ segçbTinñn½yEdl)anTTYlBI]TahrN_ 9>4³ 4421×W / Edk 36A psif c 4000' =



kRmas;kRmalxNÐ .5.4 int = RbEvgElVg ft30= BI]TahrN_ 9>4 kmøaMgkat;tamTisedk hV EdlRtUvKñanwg full composite action KW kipsCVh 468== sakl,g stud 22/1 × . Ggát;GnuBaØatGtibrmaKW ( ) .5.0.125.1450.05.25.2 inint f >== (OK) RkLaépÞmuxkat;rbs; shear connector mYyKW ( ) 2

2.1963.0

45.0 inAsc ==

π RbsinebIeyIgsnμt;ebtugCaebtugTm¶n;Fm μta (normal-weight concrete) m:UDuleGLasÞicrbs;ebtugKW ( ) ksifwE ccc 34924145' 5.15.1 === BI AISC Equation I5-1 ersIusþg;rgkmøaMgkat;rbs; connector mYyKW uscccscn FAEfAQ ≤= '5.0

( ) ( ) kips60.11349241963.05.0 == ( ) kipskipsFA usc 60.1178.11601963.0 >== yk kipsQn 60.11= ehIy KMlattambeNþayGb,brmaKW ( ) .35.066 ind == KMlattamTTwgGb,brmaKW ( ) .25.044 ind == KMlattambeNþayGtibrmaKW ( ) .365.488 ind == cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalFñwmKW 3.40

60.11468

1 ===n

hQV

N

ykcMnYnGb,brma 41 sRmab;Bak;kNþalFñwm b¤cMnYnsrub 82 . RbsinebIenARtg;muxkat;nImYy²eKeRbI stud cMnYnmYy KMlatEdlcaM)ac;KW ( ) .4.4

821230 ins == yk .4ins =

sRmab;muxkat;mYyeRbI stud BIrRKab; ( ) .8.8

2/821230 ins == yk .5.8 ins =



kartMerob stud mYyNak¾manlkçN³RKb;RKan; ehIyKMlatmYyNak¾sßitenAcenøaHEdnkMNt;TabbMput nigEdnkMNt;x<s;bMput. kartMerob stud RtUv)anbgðajenAkñúgrUbTI 9>11. eTaHbICakartMerobenHRtUvkar shear connector eRcInCagtRmUvkark¾eday EteKgayRsYlkñúgkarTTYl)anKMlattamtRmUvkar. cemøIy³ eRbI stud cMnYn 86 edImEdlmanTMhM .2.2/1 inin × tMerobdUcbgðajkñúgrUbTI 9>11.

9>5> karKNnamuxkat; (Design) CMhandMbUgkñúgkarKNnamuxkat;rbs;RbB½n§kRmalxNÐKWCakareRCIserIskRmas;rbs;kRmal xNÐ eTaHbIvaCakRmaltan; b¤kRmalrnUt ¬Edl)anBI steel deck¦ k¾eday. kRmas;CaGnuKmn_eTAnwg KMlatFñwm nigbnSMCaeRcInénkRmas;kRmal nigKMlatFñwmEdlRtUvkarkarGegát dUcenHeKnwgGacrk)an nUvRbB½n§kRmal EdlmanlkçN³esdækic©bMput. karKNnakRmalxNÐminRtUv)anelIkykmkniyay enAkñúgesovePAenHeT b:uEnþeyIgsn μt;faeyIgsÁal;kRmas;kRmalxNÐ nigKMlatFñwm. edaykareFVIsn μt; EbbenH eyIgGacGnuvtþnUvCMhanxageRkamedIm,IbMeBjnUvkarKNnaRbB½n§kRmalxNÐ EdlK μancnÞl;. !> kMNt;m:Um:g;emKuNEdleFVIGMeBImun nigeRkayebtugrwgmaM @> eRCIserIsmuxkat;EdkFñwmsakl,g

#> KNna design strength rbs;EdkFñwm nwgeRbobeFobvaCamYynwgm:Um:g;emKuNEdleFVIGMeBI muneBlebtugrwgmaM. eKRtUvyk unbraced length mkKit RbsinebIBum<min)anpþl;Ca lateral

support RKb;RKan;. RbsinebImuxkat;EdkFñwmenHminRKb;RKan; eKRtUvsakl,gmuxkat; FMCagenH.

$> KNna design strength rbs;muxkat;smas nigeRbobeFobvaeTAnwgm:Um:g;emKuNsrub. Rb sinebImuxkat;smasminRKb;RKan; eRCIserIsmuxkat;EdkFñwmepSgeTotsRmab;sakl,g.



%> RtYtBinitüersIusþg;rgkmøaMgkat; (shear strength) rbs;EdkFñwm. ^> KNna shear connectors³

a. KNna hV / kmøaMgkat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk. b. EckkmøaMgenHeday nQ ¬ersIusþg;rgkmøaMgkat;rbs; connector eTal¦ edIm,I

TTYl)ancMnYn chear connector srubEdlRtUvkar. cMnYn connector enHnwgpþl;nUv full composite action. RbsinebIeKcg;)an partial composite behavior eKGac kat;bnßycMnYn connectors enH ¬manbkRsayenAkñúgEpñkTI 9>7¦

&> RtYtBinitüPaBdab ¬RtUv)anbkRsayenAkñúgEpñkTI 9>6¦ kargard¾sMxan;enAkñúgdMeNIrkar trial-and-orror Edl)anerobrab;xagelIenHKWkareRCIserIsmux kat;EdkFñwmsakl,g. rUbmnþEdlnwg[nUvRkLaépÞcaM)ac; ¬b¤Gacniyaymü:ageTotKWTm¶n;EdlRtUvkar elIRbEvgÉktþa¦ GacekIteLIg)an RbsinebIeKsn μt;km<s;Fñwm. edaysn μt;vaeFVIkarCaeRKOgbgÁúMsmas TaMgRsug (full composite action) ehIy PNA sßitenAkñúgkRmalxNÐ ¬Edlmann½yfa EdkFñwmlub ehIyvaCakrNIEdleKeRcInCYbRbTHCageK¦ eyIgGacsresr design strength ¬edayeyageTAelI rUbTI 9>12¦ Ca ( ) ( )yFATyM ysbbnb φφφ ==

edaydak;[ design strength esμ Inwgm:Um:g;emKuN ehIyedaHRsayrk sA eyIgTTYl)an uysb MyFA =φ nig

yFM

Ayb

us φ=

b¤ ( )2/2/ atdFM

Ayb

us −+=φ

¬(>#¦



eKk¾GacsresrsmIkar (># vaCaTm¶n;CagkarsresrCaRkLaépÞ. edaysarRbEvg ft1 manmaD 3144/ ftAs ehIyEdkeRKOgbgÁúMmanTm¶n;maD 3/490 ftlb

( ) ftlbAA

w ss /4.3490

144== ¬sRmab; sA KitCa 2.in ¦

BIsmIkar (># dUcenHTm¶n;Edl)a:n;sμankñúgmYy ft KW ( ) ftlb

atdFM

wyb

u /2/2/

4.3−+

=φ

¬(>$¦

Edl uM KitCa kipsin −. / yF KitCa ksi / ehIy d / t nig a KitCa .in . eKGaceRbIsmIkar (># b¤ (>$ edIm,IeRCiserIsmuxkat;sakl,g. smIkarTaMgBIrTamTarnUvkm<s;Edlsnμt; nigkar)a:n;s μan 2/a . dUcenH CaTUeTAbøúkkugRtaMgmankm<s;tUcNas; kRmitlMeGogkñúgkarKNna 2/a nwgman\T§iBltictYc elItémøEdl)anKNna sA . eKsnμt; 0.12/ =a . RbsinebIeKeRbIsmIkar (>$ ehIyeKsn μt; nominal depth d enaHeKGaceFVIkareRCIserIsrUbrag sakl,g)any:aggayRsYl. kareRbIsmIkarenHk¾pþl;nUvkarKNnaTm¶n;FñwmedaypÞal;. ]TahrN_ 9>6³ RbEvgElVgrbs;RbB½n§kRmalKW ft30 ehIyKMlatFñwmKW ft10 edayKitBIG½kSeTAG½kS. eRCIserIs rolled steel shape nig shear connector EdlcaM)ac;edIm,ITTYl)ankareFVIkarCaeRKOgsmas TaMgRsugCamYynwgkRmalxNÐebtugGarem:kRmas; .5.3 in . bnÞúkbEnßmEdlmanGMeBIelIkRmalxNÐrYm manbnÞúkCBa¢aMgxNÐ psf10 nigbnÞúkGefr psf55 . ersIusþg;ebtugKW psif c 4000' = nigEdkEdleRbI CaRbePT 36A . snμt;faFñwmman full lateral support kñúgGMLúgeBlsagsg; ehIymanbnÞúksagsg;

psf20 . dMeNaHRsay³ bnÞúkEdlRtUvRTmuneBlebtugrwgmaMKW kRmalxNÐ³ ( )( ) psf75.4315012/5.3 = Tm¶n;kñúg :1 ft ( ) ftlb /5.4371075.43 = bnÞúksagsg;³ ( ) ftlb /2001020 = ¬Tm¶n;FñwmnwgRtUvKitenAeBleRkay¦ bnÞúkEdlRtUvRTeRkayeBlebtugrwgmaMKW ( ) ftlbwpart /1001010 == ftlbwww partslabD /5.5371005.437 =+=+=



( ) ftlbwL /5501055 == ( ) ( ) ftkipswww LDu /525.1550.06.15375.02.16.12.1 =+=+= ( )( ) kipsftMu −== 6.17130525.1

81 2

sakl,gkm<s; .16ind = . BIsmIkar (>$ Tm¶n;FñwmEdl)anKNnaKW ( )

( )( )( ) ftlb

atdFM

wyb

u /8.2115.32/163685.0

126.1714.32/2/

4.3=

−+×

=−+

=φ

sakl,g 2616×W . RtYtBinitüFñwmEdkedayminmancnÞl;sRmab;bnÞúkEdlGnuvtþmuneBlebtugrwgmaM ¬Tm¶n;rbs;kRmalxNÐ Tm¶n;rbs;Fñwm nigbnÞúksagsg;¦ ( ) ( ) ftkipswu /8762.0200.06.1026.04375.02.1 =++=

( )( ) kipsftMu −== 6.98308762.081 2

BI Load Factor Design Selection Table kipsftkipsftMM pbnb −>−== 6.98119φφ (OK) eRkayeBlebtugrwgmaM nigeRkayeBlEdleKTTYl)an composite behavior ftkipswwww beampartslabD /5535.0016.0100.04375.0 =++=++= ( ) ( ) ftkipswww LDu /544.1550.06.15535.02.16.12.1 =+=+= ( )( ) kipsftMu −== 17430544.1

81 2

muneBlKNna design strength rbs;muxkat;smas dMbUgeyIgRtUvkMNt;TTwgsøabRbsiT§PaB. sRmab; Fñwmxagkñúg TTwgRbsiT§PaBCatémøtUcCageKkñúgcMeNam ( ) .90

41230

4span in== b¤ KMlatFñwm ( ) .1201210 in==

yk .90inb = . sRmab; full composite behavior kmøaMgsgát;enAkñúgebtugenA ultimate ¬es μ InwgkmøaMg kat;tamTisedkenARtg;épÞb:Hrvagebtug nigEdk¦ CatémøEdltUcCageKkñúgcMeNam ( ) kipsFA ys 5.2763668.7 == b¤ ( )( )( ) kipsAf cc 10715.390485.0'85.0 == yk kipsVC h 5.276== . km<s;bøúkkugRtaMgsgát;enAkñúgkRmalxNÐKw ( )( ) .9036.0

90485.05.276

'85.0in

bfCa

c===

ehIyédXñas;rbs; internal resisting couple KW



.89.102

9036.05.3269.15

22inatdy =−+=−+=

design flexural strength KW ( ) ( )( ) kipsftkipsftkipsinCyM bnb −>−==== 174213.255089.105.27685.0φφ (OK) RtYtBinitükmøaMgkat; ( ) kips

LwV u

u 2.232

3015442

=== BI factored uniform load tables kipskipsVnv 2.233.76 >=φ (OK) cemøIy³ eRbI 2616×W

eKRtUvkarm:UDuleGLasÞicrbs;ebtugedIm,IKNna shear connector. BI]TahrN_ 9>5/ ksiEc 3492= sRmab;ebtugFm μtaCamYynwg psif c 4000' = . sakl,g stud .22/1 in×

¬ 2.1963.0 inAsc = ¦ Ggát;p©itGtibrma ( ) .5.0.8625.0345.05.25.2 inint f >=== (OK)

BI AISC Equation I5-1/ ersIusþg;rgkmøaMgkat;rbs; connector mYyKW uscccscn FAEfAQ ≤= '5.0

( ) ( )349241963.05.0= kips60.11=

( ) kipskipsFA usc 60.1178.11601963.0 >== dUcenHyk kipsQn 60.11= cMnYn stud EdlRtUvkarenAcenøaHcugFñwm nigkNþalElVgKW

8.2360.11

5.2761 ===

n

hQVN eRbI 24 sRmab;Bak;kNþalFñwm b¤Casrub 48

nig KMlattambeNþayGb,brmaKW ( ) .35.066 ind == KMlattamTTwgGb,brmaKW ( ) .25.044 ind == KMlattambeNþayGtibrmaKW ( ) .285.388 int == RbsinebIeKeRbI stud mYysRmab;muxkat;nImYy² KMlatRbhak;RbEhlKW ( ) .5.7

481230 ins ==

KMlatenHsßitenAcenøaHEdnx<s;bMput nigEdnTabbMput dUcenHvabMeBjlkçxNÐ.



cemøIy³ ykkarKNnaEdlbgðajenAkñúgrUbTI 9>13.

9>6> PaBdab (Deflections) edaysarm:Um:g;niclPaBrbs;muxkat;bMElg (transformed section) FM dUcenHPaBdabrbs;Fñwm smasnwgtUcCagFñwmFmμta. b:uEnþ eKGacTTYl)anm:Um:g;niclPaBFMenHEteRkayeBlebtugrwgmaMEt b:ueNÑaH. PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaMRtUv)anKNnaCamYynwgm:Um:g; niclPaBrbs;FñwmEdk. PaBdabbEnßmnwgekIteLIgenAeBlEdlFñwmrgnUvbnÞúkefrdUcCa Tm¶n;rbs;CBa¢aMg xNÐ enAeRkayeBlebtugrwgmaM. tMbn;m:Um:g;viC¢man ebtugnwgrgkmøaMgsgát;Cab;rhUt ehIyrgnUv)atuPUt EdleKsÁal;faCa creep. Creep CakMhUcRTg;RTayEdlekIteLIgeRkamGMeBIrbs;bnÞúksgát;. eRkay eBlekItmankMhUcRTg;RTaydMbUg kMhUcRTg;RTaybEnßmnwgekItmaneLIgedayGRtayWtelIry³eBld¾ Evg. \T§iBlenAelIFñwmsmasKWkarekIneLIgnUvkMeNag EdlbNþal[PaBdabtambBaÄrekIneLIgEdr. eKGackMNt;EtPaBdabry³eBlyUr (long-term deflection) edayeRbIbec©keTsEdleKniymeRbI. bec©keTsenHKWeRbImuxkat;ebtugEdl)ankat;bnßyenAkñúgmuxkat;bMElg dUcenHeKnwgTTYl)anm:Um:g; niclPaBtUcCagmun ehIyeKnwgTTYl)anPaBdabFMCagmun. muxkat;Edl)ankat;bnßyRtUv)anKNna edayeRbI n2 b¤ n3 CMnYs[pleFobm:UDulCak;Esþg n . enAkñúgesovePAenH eyIgeRbI n2 . PaBdab EdlekIneLIgeday creep minRtUv)anENnaMeday AISC Specification eT. sRmab;karsagsg;edayK μancnÞl; eKmanm:Um:g;niclPaBbIxusKñasRmab;KNna long-term

deflection. !> eRbI sI / m:Um:g;niclPaBrbs; rolled steel shape

sRmab;PaBdabEdlekIteLIgedaysarbnÞúkGnuvtþn_muneBlebtugrwgmaM.



@> eRbI trI / m:Um:g;niclPaBrbs; transfored section EdlKNnaCamYynwg nb / sRmab;PaB dab EdlekIteLIgedaybnÞúkGefr nigsRmab;PaBdabdMbUg (initial deflection) EdlekIt edaybnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaM.

#> eRbI trI EdlKNnaCamYynwg nb 2/ sRmab; long-term deflection EdlekIteLIgedaysar bnÞúkGefrEdlGnuvtþeRkayeBlebtugrwgmaM.

]TaheN_ 9>7³ KNnaPaBdabPøam² (immediate deflection) nig long-term deflection sRmab;Fñwm enAkñúg]TahrN_ 9>4. dMeNaHRsay³ segçbTinñn½yBI]TahrN_ 9>4³ 4421×W / Edk 36A kRmas;kRmalxNÐ .5.4 int = ehIyTTwgRbsiT§PaBKW .90inb = psif c 4000' = bnÞúkGefrEdlGnuvtþmuneBlebtugrwgmaMKW ftlbwD /550= ¬kRmalxNÐbUknwgFñwm¦

bnÞúksagsg;KW ftlbwconst /180= bnÞúkGefrKW ( ) ftlbwL /11259125 == bnÞúkCBa¢aMgxNÐKW ( ) ftlbwpart /180920 ==

PaBdabPøam²³ sRmab;FñwmbUknwgkRmalxNÐ ftlbw /550=

( )( )( )( ) .41.0

84329000384123012/55.05

3845 44

1 inEI

wL

s=

×==Δ

sRmab;bnÞúksagsg; ftlbw /180= ( )( )

( )( ) .1342.084329000384

123012/18.053845 44

2 inEI

wL

s=

×==Δ

PaBdabPøam²srubKW .544.01342.041.021 in=+=Δ+Δ sRmab;PaBdabEdlenAsl; eKRtUvkarm:Um:g;niclPaBrbs;muxkat;bMElgBIrKW trI CamYynwg

TTwgkRmalxNÐbMElg nb / nig trI CamYynwgTTwgkRmalxNÐbMElg nb 2/ . sRmab;ebtugTm¶n; FmμtaEdlman psif c 4000' = / ksiEc 3492= nigpleFobm:UDulKW



3.8349229000

===c

sEEn yk 8=n

sRmab;PaBdabrbs;muxkat;smasEdlminTak;Tgnwg creep TTwgRbsiT§PaBKW .25.11

890 in

nb

== rUbTI 9>14 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnasRmab;TItaMgG½kSNWt nigm:Um:g;niclPaB RtUv)ansegçbenAkñúgtarag 9>4. PaBdabdMbUgEdlbNþalBITm¶n;CBa¢aMgxNÐKW

( )( )( )( ) .0441.0

256629000384123012/180.05

3845 44

3 inEI

Lw

tr

part =×

==Δ

PaBdabEdlbNþalBIbnÞúkGefrKW ( )( )

( )( ) .2755.0256629000384

123012/125.153845 44

4 inEILw

tr

L =×

==Δ

tarag 9>4

eRKOgbgÁúM A y Ay I d 2AdI + ebtug 50.62 2.25 113.9 85.43 2.571 420

4412×W 13.00 14.83 192.8 843 10.01 2146

63.62 306.7 2566in.4

821.462.637.306==

∑∑

=A

Ayy



PaBdabry³eBlyUrEdlbNþalBI creep. eRbITTwgkRmalxNÐbMElg ( ) .625.5

8290

2in

nb

==

muxkat;bMElgRtUv)anbgðajenAkñúgrUbTI 9>15. karKNnaTIRbCMuTm¶n;nwg m:Um:g;niclPaBRtUv)ansegçb enAkñúgtarag 9>5. edayehAm:Um:g;niclPaBenHCa trI ' eyIgGacKNnaPaBdabry³eBlyUrEdlekIt eLIgeday creep KW

( )( )( )( ) .0504.0

224529000384123012/180.05

'3845 44

5 inEI

Lw

tr

part =×

==Δ

tarag 9>5


4412×W 13.00 14.83 192.8 843 8.311 1741

38.31 249.8 2245in.4

519.631.388.249==

∑∑

=AAyy

cemøIy³ xageRkamenHCakarsegçbrbs;PaBdab PaBdabPøam²munTTYl)an composite behavior .544.01342.04100.021 in=+=Δ+Δ PaBdabry³eBlxøICamYynwgCBa¢aMgxNÐedayK μanbnÞúkGefr



.454.00441.04100.031 in=+=Δ+Δ PaBdabry³eBlxøIedaybEnßmbnÞúkGefr .730.02755.00441.04100.0431 in=++=Δ+Δ+Δ PaBdabry³eBlEvgedayK μanbnÞúkGefr .460.00504.04100.051 in=+=Δ+Δ PaBdabry³eBlEvgedaymanbnÞúkGefr .736.00504.02755.04100.0541 in=++=Δ+Δ+Δ edaysarbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMmantémøtUc PaBdabEdl)anBI creep mantémøtUcenAkñúg]TahrN_enH. 9>7> FñwmsmasCamYynwgkRmalBum<Edk (Composite Beams with Formed Steel Deck) kRmalxNÐenAkñúgsMNg;eRKagEdkRtUv)anpÁúMeLIgkñúgTRmg;kRmalEdkrnUt (ribbed steel

deck) EdlRtUv)anTukenAnwgkEnøgedIm,I[vakøayeTACaEpñkrbs;eRKOgbgÁúM. eTaHbICamankrNIelIk Elgk¾eday k¾rnUtrbs;bnÞHEdkRtUv)andak;[EkgnwgFñwmkRmal ehIyRsbeTAnwgrtEdlRTFñwmenaH. rUbTI 9>16 bgðajBIrnUtEdlmanTisEkgnwgFñwm. eKdMeLIg shear stud enAelIFñwmsmasEdlman kRmalrnUt tamviFIdUcKñanwgkardMeLIg shear srud enAelIFñwmsmasEdlKμankRmalrnUt. eKcat;Tukfa karP¢ab;Kñarvag deck eTAnwgFñwmEdkpþl;nUvTRmxag (lateral support)

sRmab;FñwmEdkmuneBlebtugrwgmaM. karKNna nigkarviPaKFñwmsmasCamYynwg formed steel deck mansar³sMxan;dUcKñanwgkrNIFñwm smasCamYynwgkRmalEdlmankRmales μ IEdr EtxageRkamCakrNIelIkElgmYycMnYn³

!> eKminKitebtugenAkñúgrnUt ¬EdlenABIeRkamEpñkxagelIrbs; deck¦ enAeBlrnUtTaMgenaH EkgnwgFñwm (AISC I3.5b). enAeBlrnUtRsbnwgFñwm ebtugenAkñúgrnUtenaHRtUv)anKitbBa©Úl eTAkñúgkarkMNt;lkçN³muxkat; ehIyRtUv)anbBa©ÚleTAkñúgkarKNna cA .

@> lT§PaBrbs; shear connector GacRtUv)ankat;bnßy #> CaTUeTA eKminGacTTYl)an full composite behavior eT. mUlehtuKWfa KMlatrbs; shear

connector RtUv)ankMNt;edayKMlatrbs;rnUt ehIyeKminGaceRbIRKb;cMnYn connector Edl



RtUvkar. eTaHbICaeKGaceRbI partial composite design edayK μan formed steel deck k¾ eday k¾vaRtUv)anelIkykmkniyayenATIenH BIeRBaHPaKeRcInvaRtUvkar formed steel deck. tamBitvaminEmnCaKuNvibtþieT EtvaCaCeRmIsxagEpñkesdækic©.

FñwmsmasPaKeRcInCamYynwg formed steel deck CakRmalFñwmEdlmanrnUtEkgnwgFñwm ehIy

eyIgnwgniyayEtkñúgkrNIenH. tRmUvkarcaM)ac;EdlGnuvtþenAeBlrnUtmanTisRsbeTAnwgFñwmRtUv)an bgðajenAkñúg AISC I3.5 c.

lT§PaBEdlkat;bnßyrbs; shear connectors Reduced Capacity of Shear connector

edayBwgEp¥kelIkarBiesaF AISC I3.5b tRmUv[KuN shear strength rbs; shear connector nQ eTAnwgemKuNkat;bnßyenAeBlEdlrnUtEkgeTAnwgFñwm³

0.10.185.0≤⎥

⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

r

s

r

r

r hH

hw

N (AISC Equation I3-1)

Edl =rN cMnYn stud kñúgmYyrnUtRtg;kEnøgEdlkat;KñaCamYynwgFñwm ¬EdlkMNt;RtwmbIenAkñúgkar KNna¦

=rw TTwgmFümrbs;rnUt =rh km<s;rbs;rnUt =sH RbEvgrbs; stud EdlkñúgkarKNnavaminRtUvFMCag ( )3+rh . TMhMTaMgenHRtUv)anbgðajenAkñúgrUbTI 9>17.



Partial Composite Action kareFVIkarCaeRKOgbgÁúMsmasedayEpñk (partial composite action) ekItmaneLIgenAeBlEdl vaminman shear connector RKb;RKan;edIm,IkarBarPaBrGilrvagebtug nigEdkFñwm. TaMgebtug nigEdk minGaceFVIkardl; strength rbs;vaeBjeljeT ehIykmøaMgsgát;RtUv)ankMNt;RtwmkmøaMgGtibrma ¬EdlCaersIusþg;rbs; shear connector nQ∑ ¦ EdlGacbBa¢ÚnkmøaMgkat;tamépÞb:HrvagEdk nigebtug. rMlwkfa C CatémøEdltUcCageKkñúgcMeNam ys FA / cc Af '85.0 nig nQ∑ . CamYynwg partial composite action CaTUeTAG½kSNWt)aøsÞic (PNA) sßitenAñúgmuxkat;Edk. TI taMgenHnwgeFVI[karviPaKersIusþg;mankarBi)akCagTItaMgrbs; PNA EdlsßitenAkñúgkRmalxNÐbnþic EteKalkarN_cMbgKWdUcKña. enAeBlEdleKeFVI elastic analysis k¾dUcCaenAeBlEdleKKNnaPaBdab eKRtUveFVIkar KNna m:Um:g;niclPaBrbs; partially composite section. eKGaceRbIExSekag parabolic transition BI sI ¬sRmab;EtEdkFñwm¦ eTA trI ¬sRmab; fully composite section¦ )an (Hansell et al., 1978). xageRkam CasmIkarEdlnwgpþl;nUvlT§plRbhak;RbEhlsRmab;m:Um:g;niclPaBRbsiT§PaBEdlbgðaj eday Commentary to the AISC Specification³ ( )strfnseff IICQII −∑+= / (AISC Equation C-I3-6) Edl fC CakmøaMgsgát;enAkñúgebtugsRmab; fully composite condition ¬témøEdltUcCageKkñúg cMeNam ys FA nig cc Af '85.0 ¦. edaysarEt nQ∑ CakmøaMgsgát;Cak;EsþgsRmab;krNI partially



composite enaHpleFob fn CQ /∑ CacMENkrbs; compositeness Edlman. RbsinebIpleFobenH tUcCag 25.0 enaHeKminKYreRbI AISC Equation C-I3-6 (Hansell et al., 1978). eKminGacTTYl)anersIusþg;EdkeBjenAkñúg partially composite beam eT dUcenHvaTamTar nUvmuxkat;EdkFñwmFMCag muxkat;EdkFñwmsRmab; fully composite behavior. b:uEnþ vaRtUvkar shear connector ticCag ehIytémørbs;EdkFñwm nig shear connectors ¬EdlrYbbBa©ÚlTaMgtémødMeLIg¦ RtUv)anKitcUleTAkñúgkarviPaKEpñkesdækic©. enARKb;eBlEdl fully composite beam manlT§PaB Tb;Tl;FM ¬EdleKEtgEtCYbRbTHkrNIEbbenH¦ eKGaceFVIkarkat;bnßycMnYn shear connector Edl eFVI[FñwmkøayCa partially composite beam. tRmUvkarepSg² Miscellaneous Requirements xageRkamCatRmUvkarEdl)anBI AISC Section I3.5 a nig b. GVIEdlnwgerobrab;xageRkamCa tRmUvkarbEnßmBIelIGVIEdl)anerobrab;BIcxagedIm³

- km<s;rnUtGtibrma mminhr 75.3 == - TTwgmFümGb,brmarbs;rnUt mminwr 50.2 == b:uEnþtémørbs; rw EdleRbIenAkñúgkar

KNnaminKYrFMCag clear width rbs;EpñkxagelIbMputrbs; deck eT. - kRmas;kRmalGb,brmaenABIelIEpñkx<s;bMputrbs; deck mmin 50.2 == . - Ggát;p©it stud Gtibrma .4/3 in= . karTamTarsRmab; formed steel deck enHCakarbEnßmBI

elIGgát;p©itGtibrma ft5.2 . - km<s;Gb,brmarbs; stud BIelIEpñkx<s;bMputKW .1 2

1 in - KMlattambeNþayGtibrmarbs; shear stud mmin 915.36 == - eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlatmin[FMCag mmin 46018 = eday stud b¤ eday

spot weld. kareFVIEbbenHedIm,IkarBar uplift.

Tm¶n; deck nigTm¶n;kRmal Slab and Deck Weight edIm,IsRmYldl;karKNnaTm¶n;kRmal eyIgeRbIkRmas;rbs;kRmalTaMgmUledayvas;BI)at rbs; deck eTAépÞxagelIrbs;kRmalxNÐ. eTaHbICaviFIenH)a:n;sμanmaDebtugelIsk¾eday Etvaman



suvtßiPaB. sRmab;Tm¶n;maDebtugGarem: eyIgeRbITm¶n;ebtugmaDsuT§bUkbEnßm 3/805 mkgpcf = . CaTUeTA edaysarkRmalxNÐenAelI formed steel deck CaebtugEdlBRgwgedayEdktic ¬eBlxøHeRbI welded wire mesh CMnYs[kareRbI reinforcing bar¦ karbEnßm 3/805 mkgpcf = sRmab;EdkBRgwg GacmantémøFM b:uEnþ deck manTm¶n;cenøaHBI 2/6.92 mkgpsf = eTA 2/5.143 mkgpsf = . eKGaceRbIvFImü:ageTot edayKitplbUkrvagkRmas;kRmalEdlenABIelI deck Edlx<s;CageK CamYynwgBak;kNþalkm<s;rbs;rnUtCakRmas;ebtugkñúgkarKNnaTm¶n;rbs;kRmal. CaTUeTA kñúgkar Gnuvtþ eKGacrkplbUkrvagTm¶n;kRmal nig deck enAkñúgtaragEdlpþl;[edayeragcRkplit deck. ]TahrN_ 9>8³ kRmalxNÐRTedayFñwmEdleRbI formed steel deck EdlbgðajenAkñúgrUbTI 9>18 Ca mYynwgkRmalebtugGarem:EdlkRmas;srubKW .75.4 in . rnUt deck EkgnwgFñwm. RbEvgElVgKW ft30 ehIyFñwmmanKMlatBIKña ft10 edayKitBIG½kSeTAG½kS. EdkeRKOgbgÁúMCaRbePTEdk 36A ehIyersIusþg; rbs;ebtugKW psif c 3000' = . Tm¶n;rbs;kRmal nig deck KW psf50 . Tm¶n;GefrKW psf40 nigTm¶n; CBa¢aMgKW psf10 . kñúgkarsagsg;enH eKminmaneRbIcnÞl;beNþaHGasnñeT ehIyTm¶n;sagsg;KW psf20 . !> eRCIserIs W shape @> KNna shear connector #> RtYtBinitüPaBdab. PaBdabry³eBlyUrsrubGnuBaØatGtibrmaKW 240/1 énRbEvgElVg.

dMeNaHRsay³ !> KNnaFñwm eRCIserIsrUbragsakl,gedayQrelI full composite behavior kRmalxNÐ³ ( ) ftlb /5001050 = CBa¢aMgxNÐ³ ( ) ftlb /1001010 = bnÞúkGefr³ ( ) ftlb /4001040 =



( ) ( ) ftkipswww LDu /360.14.06.11.05.02.16.12.1 =++=+= ( )( ) kipsftMu −== 1533036.1

81 2

edaysnμt;fa .16ind = / .12/ ina = nigsn μt;Tm¶n;rbs;FñwmBIsmIkar (>$³ ( )

( )( )( ) ftlb

atdFM

wyb

u /4.17175.42/163685.0

121534.32/2/

4.3=

−+×

=−+

=φ

sakl,g 2616×W . RtYtBinitüersIusþg;rgkarBt;muneBlebtugrwgmaM bnÞúksagsg;³ ( ) ftlb /2001020 = ( ) ( ) ftkipswww LDu /9512.04.06.1026.05.02.16.12.1 =++=+=

( )( ) kipsftMu −== 107309512.081 2

2616×W Ca compact section sRmab; 36A nigedaysar steel deck nwgpþl; lateral support RKb;RKan; dUcenH nominal strength nM esμ InwgersIusþg;m:Um:g;)aøsÞic pM . BI Load Factor Design Selection Table kipsftkipsftM pb −>−= 107119φ (OK) eRkayeBlebtugrwgmaM bnÞúkemKuNsrubEdlRtUvRTedayFñwmsmas EdlRtUv)anEksRmYledaysar Tm¶n;rbs;EdkFñwmKW ( ) ( ) ftkipswu /391.14.06.11.0026.05.02.1 =+++= ehIym:Um:g;emKuNKW ( )( ) kipsftMu −== 15630391.1

81 2

TTwgkRmalxNÐRbsiT§PaBrbs;muxkat;smasRtUvEtmantémøtUcCageKkñúgcMeNam ( ) .90

41230

4span in== b¤ KMlatFñwm ( ) .1201210 in==

yk .90inb = . sRmab; fully composite action kmøaMgsgát; C enAkñúgebtugKWCatémøtUcCageKkñúg cMeNam ( ) kipsFA ys 5.2763668.7 == b¤ ( ) ( )[ ] kipsAf cc 9.7455.175.490385.0'85.0 =−=



EdleKKitEtebtugenAelIEpñkx<s;bMputrbs; deck ¬dUcbgðajenAkñúgrUbTI 9>19¦ b:ueNÑaHsRmab;smIkar TIBIrxagelI. CamYynwg kipsC 5.276= km<s;rbs;karBRgaykugRtaMgsgát;enAkñúgebtugKW ( )( ) .205.1

90385.05.276

'85.0in

bfCa

c===

édXñas;m:Um:g;rbs; internal resisting couple KW .99.11

2209.175.4

269.15

22inatdy =−+=−+=

ehIy design strength KW ( )( ) kipsftkipsftM nb −>−== 156235

1299.115.27685.0φ (OK)

RtYtBinitükmøaMgkat; ( ) kipsLwV u

u 9.202

30391.12

=== BI factored uniform load tables kipskipsVnv 9.203.76 >=φ (OK) cemøIy³ !> eRbI 2616×W @> Shear connectors edaysarFñwmenHmanersIusþg;m:Um:g;FMKYrsm eKGac[vaeFVIkarCa patial composite behavior. dMbUg eyIgRtUvrkcMnYn shear connector caM)ac;sRmab; full composite behavior nwgbnÞab;mkkat;bnßycMnYn conntector. sRmab; fully composite beam/ kipsVC h 5.276== . sakl,g stud .34

3 in× ¬ 24418.0 inAsc = ¦mYyenARtg;muxkat;mYy³ Ggát;p©itGtibrma ( ) .8625.0345.05.25.2 int f === b¤ .

43 in lub



Ggát;p©itCak;Esþg .43 in= (OK)

KNnaemKuNkat;bnßyersIusþg;rbs; stud 1=rN

km<s;rbs; stud BIelIEpñkx<s;bMputrbs; deck .5.15.13 in=−= = témøGnuBaØat (OK) BI AISC Equation I3-1, emKuNkat;bnßy 0.10.185.0

≤⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

r

s

r

r

r hH

hw

N

0.1275.10.15.1

35.125.2

0.185.0

>=⎟⎠⎞

⎜⎝⎛ −⎟⎠⎞

⎜⎝⎛=

eKminRtUvkarkat;bnßyersIusþg; stud eT. sRmab; psif c 3000' = m:UDuleGLasÞicrbs;ebtugKW ksifwE ccc 30243145' 5.15.1 === BI AISC Equation I5-1, ersIusþg;rgkmøaMgkat;rbs; connector mYyKW uscccscn FAEfAQ ≤= '5.0

( ) ( ) kips04.21302434418.05.0 == ( ) kipskipsFA usc 04.2151.26604418.0 >== dUcenHyk kipsQn 04.21= cMnYnrbs; stud EdlRtUvkarenAcenøaHcugrbs;Fñwm nigkNþalElVgKW 1.13

04.215.276

1 ===n

hQVN

yk 14 sRmab;Bak;kNþalFñwm dUcenHsrub 28 . CamYy stud mYysRmab;rnUtmYy KMlatKW .6in ehIycMnYnGtibrmaENnaMKW ( ) 2860

61230

>= EdlTamTar ebIeKeRbI stud mYysRmab;ral;BIrrnUt dUcenHeKRtUvkarva 30 edIm EdlenAEtCacMnYneRcIn. Rbsin ebIeKeRbI stud mYysRmab;ral;bIrnUt enaHKMlatnwgkøayCa ( ) .1863 in= ehIycMnYnrbs; stud nwg ( ) 2018/1230 = EdlvatUcCagtRmUvkarsRmab; full composite action. b:uEnþ vaman flexural

strength FM dUcenH partial composite action GacnwgRKb;RKan;. sakl,g stud 20 edIm sRmab;FñwmmYy dUcenH 1N Edlpþl;[ 102/20 == ( )04.2110=∑ nQ



kipskips 5.2764.210 <= dUcenH kipsVC h 4.210== edaysar C tUcCag ys FA dUcenHEpñkxøHrbs;muxkat;EdkFñwmRtUvrgkmøaMgsgát; ehIyG½kSNWt)aøsÞic KWsßitenAkñúgmuxkat;Edk. edIm,IviPaKkrNIenH dMbUgeyIgRtUvkMNt;faetI PNA sßitenAelIsøabxagelI b¤sßitenAelIRTnug. RbsinebI PNA sßitenA)atrbs;søabxagelI enaHtYsøabTaMgmUlnwgrgkmøaMgsgát; ehIykmøaMgsgát;pÁÜb EdlbgðajenAkñúgrUbTI 9>20 KW ( )( ) kipsFtbP yffyf 31.6836345.05.5 ===

kmøaMgsuT§EdlRtUvepÞrenARtg;épÞb:HrvagEdk nigebtugKW ( ) ( ) kipsPPFAPTCT yfyfysyfs 9.13931.6825.276 =−=−−=−=− EdlvatUcCagkmøaMgTajsuT§Cak;Esþg kips4.210 dUcenHsøabxagelIminRtUvkarrgkmøaMgsgát;eBj kRmas;søabrbs;vaeT. enHmann½yfa PNA sßitenAkñúgsøab. BIrUbTI 9>21 kmøaMgkat;tamTisedkEdl RtUvepÞrKW

( ) hyfyfyss VFtbFtbFACT =−−=− '' ( )[ ] 4.21036'5.525.276 =− t

edayKNnarkkm<s;énkmøaMgsgát;enAkñúgsøab eyIgTTYl)an .1669.0' int =



kmøaMgTajpÁÜbnwgeFVIGMeBIenAelITIRbCMuTm¶n;rbs;RkLaépÞBIeRkam PNA. muneBleyIgKNna moment strength eKRtUvkMNt;TItaMgTIRbCMuTm¶n;sin. karKNnacm¶ayBITItaMgx<s;bMputrbs;EdkFñwm y RtUv)an segçbenAkñúgtarag 9>6. tarag 9>6

eRKOgbgÁúM A y Ay 3616×W 7.68 78452/69.15 = 25.60

søab ( )50.51669.0− = 918.0− 0834.02/1669.0 = 08.0−

srub 6.762 60.17 .898.8

762.617.60 in

AAyy ==

∑∑

= km<s;rbs;bøúkkugRtaMgsgát;enAkñúgebtugKW ( )( ) .9168.0

90385.04.210

'85.0in

bfCa

c===

édXñas;sRmab;kmøaMgsgát;rbs;ebtugKW .11.13

29168.075.4819.8

2inaty =−+=−+

édXñas;m:Um:g;sRmab;kmøaMgsgát;enAkñúgEdkKW .736.8

21669.0819.8

2' inty =−=−

Kitm:Um:g;eFobkmøaMgTaj nigedayeyagtamrUbTI 9>20 eyIgTTYl)an nominal strength³



( ) ( )736.811.13 sn CCM += ( ) ( )( )( ) kipsftkipsin −=−=+= 9.253.3047736.83650.51669.011.134.210

Design strength KW ( ) kipsftkipsftM nb −>−== 1562169.25385.0φ (OK) eKRtUvP¢ab; deck eTAnwgsøabFñwmedayKMlat .18in dUcenHeKminRtUvkar spot weld edIm,IkarBar uplift eT. cemøIy³ @> eRbI shear connector dUcbgðajenAkñúgrUbTI 922.

#> PaBdab muneBlebtugrwgmaM ftkipswww beamslabD /526.0026.0500.0 =+=+= ( )( )

( )( ) .098.130129000384

123012/526.053845 44

1 inEILw

s

D =×

==Δ

PaBdabEdlbNþalmkBIbnÞúksagsg;KW ( )( )

( )( ) .418.030129000384

123012/200.05384

5 442 in

EILw

s

const =×

==Δ

PaBdabsrubmuneBlebtugrwgmaMKW .52.1418.0098.121 in=+=Δ+Δ sRmab;PaBdabEdlekItmaneRkayeBlebtugrwgmaM eKRtUvkarm:Um:g;niclPaBrbs;muxkat; bMElgBIrKW trI CamYynwgTTwgkRmalbMElg nb / nig trI CamYynwgTTwgkRmalbMElg nb 2/ . pleFobm:UDulKW 6.9

302429000

===c

sEEn yk 10=n



sRmab;PaBdabrbs;muxkat;smasEdlBak;B½n§nwg creep TTwgRbsiT§PaBKW .9

1090 in

nb

== rUbTI 9>23 bgðajBImuxkat;bMElgEdlRtUvKña. karKNnaTItaMgG½kSNWt nigm:Um:g;niclPaB RtUv)anbgðajenAkñúgtarag 9>7. tarag 9>7


2616×W 7.68 12.60 96.77 301 8.693 881

srub 36.93 144.30 1059in.4

.907.393.363.144 in

AAyy ==

∑∑

=

edaysareKeRbI partial composite action dUcenHeKRtUvkareRbIm:Um:g;niclPaBbMElgEdlkat; bnßy. BI AISC Equation C-I3-6 m:Um:g;niclPaBRbsiT§PaBKW ( )strfnseff IICQII −∑+= /

( ) 4.2.96230110595.276/4.210301 in=−+= PaBdabEdlekIteLIgedaysarbnÞúkGefrKW ( )( )

( )( ) .2613.02.96229000384

123012/400.053845 44

3 inEI

Lw

eff

L =×

==Δ

PaBdabEdlbNþalmkBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKYrQrelIm:Um:g;niclPaBbM ElgEdlTTYlCamYynwg n2 RbesIrCagCamYynwg n . dUcenH eRbITTwgkRmalbMElg ( ) .5.4

10290

2in

nb

==

BIrUbTI 9>24 nig tarag 9>8 m:Um:g;niclPaBbMElgKW 4.4.920' inI tr =



tarag 9>8

eRKOgbgÁúM A y Ay I d 2AdI + ebtug 14.62 1.625 23.76 12.87 3.780 221.8

2616×W 7.68 12.60 96.77 301 7.195 698.6

srub 22.30 120.53 920.4in.4

.405.530.225.120 in

AAyy ==

∑∑

=

m:Um:g;niclPaBRbsiT§PaBEdleyIgnwgehAfa effI ' KW ( )strfnstr IICQII −∑+= '/'

( ) 4.3.8413014.9205.276/4.210301 in=−+= PaBdabry³eBlyUrEdlbNþalBIbnÞúkefrEdlGnuvtþeRkayeBlebtugrwgmaMKW ( )( )

( )( ) .0747.03.84129000384

123012/100.05 44 in=

×=Δ

PaBdabsrubKW .43.10747.02613.0098.1431 in=++=Δ+Δ+Δ nig ( ) .43.1.50.1

2401230

240ininL

>== (OK) cemøIy³ #> PaBdabGacTTYlyk)an.



9>8> taragsRmab;karviPaK nigkarKNnaFñwmsmas Tables for Composite Beam Analysis and Design

enAeBlG½kSNWt)aøsÞicsßitenAkñúgmuxkat;Edk karKNna flexural strength Gacnwgmankar lM)ak. eK)anbegáItrUbmnþedIm,IsRmYldl;karKNnaenH (Hansell et al., 1978) b:uEnþtaragEdlbgðaj enAkñúg Part 5 of the manual manPaBgayRsYlCag. eKmantaragBIrKW³ design strengths rbs;bnSM énrUbragepSg²CamYynwgkRmalsRmab; MPaksiFy 25036 ≈= nigsRmab; MPaksiFy 35050 ≈= nig taragénm:Um:g;niclPaB “lower bound” sRmab;bnSMdUcKña. Design strength table EdlmaneQ μaHfa “Composite Beam Selection Table,” GaceRbI)an sRmab;EtrUbragEdlman compact web nigersIusþg; shear connector srub ysn FAQ 25.0≥∑ ¬Edn kMNt;EdlENnaMTabCageKsRmab; partially composite beams¦ eK[ersIusþg;KNna (design strength) nMφ sRmab;TItaMgrbs; PNA 7 EnøgdUcbgðajenA kñúgrUbTI 9>25³ Epñkx<s;bMputrbs;søabxagelI/ EpñkTabbMputrbs;søabxagelI/ bITItaMgEdlmanKMlat es μ I²KñaEdlsßitenAkñúgsøabxagelI/ nigBIrTItaMgenAkñúgRTnug*. TItaMg PNA TabCageK ¬nIv:U &¦ RtUvnwg EdkkMNt;EdlENnaMTabCageK ysn FAQ 25.0=∑ . PNA TItaMg ^ RtUvnwg nQ∑ EdlsßitenAcenøaH TItaMg & nigTItaMg %.

edIm,IeRbItaragsRmab;viPaKFñwmsmas dMbUgrkEpñkrbs;taragEdlRtUvnwgrUbragEdk

ehIyGnuvtþ dUcxageRkam³ * nimitþsBaØa nMφ RtUv)aneKeRbIenAkñúgtaragsRmab; design strength of composite shapes, nig pbMφ RtUv)aneRbIsRmab; design

strength of steel shape alone. emKuNRtUv)ansMKal;edayviFIBIrepSgKñaBIeRBaHvamantémøBIrepSgKña.



!> eRCIserIs nQ∑ . enHCakarkMNt;rbs; Manual sRmab;kmøaMgsgát; C EdlCatémøtUcCag eKén ys FA / cc Af '85.0 nigersIusþg;rbs; shear connector srub ¬EdleyIgehAfa

nQ∑ ¦. @> eRCIserIs 2Y cm¶ayBITItaMgx<s;bMputrbs;EdkFñwmeTAkmøaMgsgát;pÁÜbenAkñúgebtugEdl

KNnaCa

22 atY −=

TMhMenHRtUv)anbgðajenAkñúgrUbTI 9>26. #> Gan nMφ RbsinebIcaM)ac;eKRtUveFVI interpolation

sRmab;karKNna eKGacbBa©Úl nMφ EdlTamTareTAkñúgtarag ehIyeKGacGaceRCIserIsEdk Fñwm nig nQ∑ . eKGacRtUvkartémø 2Y dUcenHeKRtUvsn μt;km<s;rbs;karBRgaykugRtaMgsgát;rbs; ebtug ehIyeKGaceFVIkarKNnaeLIgvijeRkayeBlEktRmUv. Manual [nUvsmIkarsRmab;)a:n;sμan Tm¶n;Fñwm EtRbsinebIeKeRbItarag eKminRtUvkarsmIkarenaHeT.

taragk¾[pgEdrnUvtémø pbMφ EdlGacRtUvkarsRmab;RtYtBinitüFñwmEdlK μancnÞl;kñúg GMLúg eBlebtugrwgmaM ehIy 1Y Cacm¶ayBITItaMgx<s;bMputrbs;EdkFñwmeTA PNA. ]TahrN_ 9>9³ KNna design strength rbs;FñwmsmasenAkñúg]TahrN_ 9>1 nig 9>2 edayeRbI taragenAkñúg Part 5 of the Manual. dMeNaHRsay³ BI]TahrN_ 9>1 FñwmsmaspSMeLIgedayEdk 3616×W CamYynwgkRmalxNÐEdlman kRmas; .5int = nigTTwgRbsiT§PaB .87inb = . ersIusþg;sgát;enA @* éf¶rbs;ebtugKW psif c 4000' = . kmøaMgsgát;enAkñúgebtugCatémøtUcCageKén



( ) kipsFA ys 6.381366.10 == b¤ ( )( ) kipsAf cc 1487875485.0'85.0 =×= yk kipsC 6.381= . km<s;rbs;bøúkkugRtaMgsgát; ( )( ) .290.1

87485.06.381

'85.0in

bfCa

c===

cm¶ayBITItaMgx<s;bMputrbs;EdkeTAkmøaMgsgát; C KW .36.4

2290.15

22 inatY =−=−=

bBa©ÚleTAkñúgtaragCamYynwg kipsQn 382=∑ nig 36.42 =Y . edayeFVI interpolation eyIg TTYl)an kipsftM n −= 332φ edayepÞógpÞat;CamYynwglT§plenAkñúg]TahrN_ 9>2 eyIgeXIjfavamantémødUcKña. karKNnatam rUbmnþ nigedayeRbItaragTTYl)anlT§plRsedogKña enAeBlEdl PNA sßitenAkñúgmuxkat;EdkFñwm. cemøIy³ Design strength kipsft −= 332 taragsRmab;m:Um:g;niclPaB lower bound EdlsMKal;eday LBI pþl;nUvkar)a:n;sμanm:Um:g; nicl PaBrbs;muxkat;bMElgmanlkçN³suvtßiPaBsRmab;FñwmdUcKñaEdlmanenAkñúg design strength

table. karsnμt;d¾cMbgkñúgkareFVItaragenHKWfamanEtRkLaépÞebtugEdlTb;Tl;nwgm:Um:g;eTEdlman RbsiT§PaBkñúgkarKNnam:Um:g;niclPaB. kmøaMgenAkñúgebtugKW nQC ∑= nig RkLaépÞénmuxkat; bMElgEdlRtUvKñaKW

y

nnc F

QQA ∑=

∑=

area rmedin transfo stress

edIm,ICakarsRmYlteTAeTotkñúgkarKNna eKecalm:Um:g;niclPaBrbs;ebtugeFobnwgG½kSTIRbCMuTm¶n;. edIm,IbgðajBIviFIsaRsþenH eKnwgyktémømYyenAkñúgtaragmkbMEbkenAkñúg]TahrN_ 9>10. ]TahrN_ 9>10³ karKNnapþl;nUvlT§plCa 3116×W CamYynwg kipsQn 241=∑ ¬TItaMg PNA 3¦ .42 inY = nig ksiFy 36= . KNnam:Um:g;niclPaB lower bound. dMeNaHRsay³ RkLaépÞebtugEdlRtUv)aneRbIKW



2.694.636241 in

FQAy

nc ==

∑=

muxkat;bMElgEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>27 ehIykarKNnaRtUv)ansegçbenAkñúgtarag 9>9. kMNt;TItaMgTIRbCMuTm¶n; Kitm:Um:g;eFobG½kSenA)atrbs;muxkat;Edk.

tarag 9>9

eRKOgbgÁúM A y Ay I d 2AdI + ebtug 6.694 19.88 133.1 - 6.88 316.9

3116×W 9.12 7.94 72.4 375 5.06 608.5

srub 15.81 205.5 925.4in.4

.00.1381.15

5.205 inAAyy ==

∑∑

=

m:Um:g;niclPaBBItaragm:Um:g;niclPaB lower bound KW 4.925inI LB = edayepÞógpÞat;CmYynwg lT§plEdl)anKNna. cemøIy³ 4.925inI LB =

]TahrN_ 9>11³ eFVIkarKNna]TahrN_ 9>8 eLIgvijCamYynwgCMnYyrbs;taragenAkñúg Part 5 of the

Manual. dMeNaHRsay³ !> KNnaFñwm

BI]TahrN_ 9>8 kipsftM u −=153 ¬edayminKitbBa©ÚlTm¶n;Fñwm¦. edaysnμt;fa .2ina = eyIgTTYl)an



.75.32275.4

22 inatY =−=−=

BI Composite Beam Selection Table, ral;karbnSMénEdkFñwm/ nQ∑ nig 2Y Edlpþl;nUv design strength FMCag kipsft −153 KWCaFñwmsakl,gEdlGacTTYlyk)an. lT§PaBBIrnwgRtUv)an segçbenAkñúgtarag 9>10. tarag 9>10

rUbrag TItaMg PNA nQ∑ (kips) nMφ (ft-kips)

¬edayeFVI interpolation¦

2616×W 7 69.1 160

2214×W 3 159 159

Edk 2214×W CarUbragEdlRsalCag b:uEnþedaysar nQ∑ FMCag vanwgRtUvkar shear

connector eRcInCag ¬GaceRcInCagBIrdg¦. sRmab;mUlehtuenH sakl,g 2616×W . KNna 2Y eLIgvij³ ( )( ) .3011.0

90385.01.69

'85.0'85.0in

bfQ

bfCa

c

n

c==

∑==

.60.42

3011.075.42

2 inatY =−=−= ¬Edl .90inb = KW)anmkBI]TarhN_ 9>8¦ kipsftM n −= 4.164φ BI]TahrN_ 9>8/ kipsftM u −=156 CamYynwgkarKitbBa©ÚlTm¶n;Fñwm . vanwgtUcCag design

strength kipsft −4.164 dUcenHkareRCIserIsenHGacTTYlyk)an. dUcKñaBI]TahrN_ 9>8 TaMg flexural strength kñúgeBlsagsg; nig shear strength KWRKb;RKan;sRmab; 2616×W . cemøIy³ !> eRbI 2616×W . @> Shear connector dMbUg sakl,g stud .34/3 in× . cMnYnrbs; strud EdlRtUvkarKW 3.3

04.211.69

1 ==∑

=n

nQQN yk 4 sRmab;Bak;kNþalFñwm dUcenHsrubKW 8 edIm



Stud 8 edImRtUvnwgKMlat ( ) .45

81230 in=

KMlatenHFMCagKMlatGnuBaØatGtibrma .36in dUcenHeKRtUveRbI stud eRcInCagenH. RbsinebI eKdak; stud ral; 6 rnUtmþg KMlatnwgesμ Inwg 36 ehIycMnYn stud srubKW ( ) ,10

361230

= 51 =N kmøaMgkat;EdlRtUvKñaEdlRtUvepÞrKW ( ) kipsQn 2.10504.215 ==∑ edIm,IgayRsYlkñúgkareRbItarag eyIgnwgyktémø kipsQn 104=∑ enaH ( )( ) .4532.0

90385.0104 ina ==

.523.42

4532.075.42 inY =−= BI Composit Beam Selection Table, design strength KW kipsftkipsftM n −>−= 156182φ (OK)

cemøIy³ @> eRbI stud .34/3 in× cMnYn 10 edIm edayKMlates μ I²Kña. edIm,IkarBar uplift eFVI spot weld ral;KMlat .18in ¬sßitenAcenøaH stud¦. #> PaBdab BI]TahrN_ 9>8 PaBdabrbs;EdkFñwmmuneBlTTYl)an composite behavior KW .098.11 in=Δ ¬edayminKitbnÞúksagsg;¦ sRmab;PaBdabEdlekIteLIgeRkayeBlebtugrwgmaM eKGaceRbIm:Um:g;niclPaB lower bound Edl)anBItarag. eRbI 2616×W CamYynwg kipsQn 104=∑ ¬PNA TItaMg ^¦ nig .523.42 inY = 4.623inI LB = vaminmankarEbgEckm:Um:g;niclPaBsRmab;karKNnaPaBdabbEnßmEdlekIteLIgedaysar creep. b:uEnþ m:Um:g;niclPaB lower bound mantémøtUcCagm:Um:g;niclPaBmuxkat;bMElgCak;Esþg ehIy\T§iBlTaMgmUlKWnwgpþl;nUvPaBdabFMCagkar)a:n;s μan. RbsinebIbnÞúkefrry³eBlyUrtUc eKGaceRbIm:Um:g;niclPaB lower bound. ftkipswww LD /500.0400.0100.0 =+=+=



ehIyPaBdabEdlRtUvKñaKW ( )( )

( )( ) .5044.062329000384

123012/500.05384

5 44

2 inEI

wL

LB=

×==Δ

PaBdabsrubKW .602.15044.0098.121 in=+=Δ+Δ PaBdabGnuBaØatGtibrmaKW ( ) .602.1.500.1

2401230

240ininL

<== (N.G.) kñúgkarKNna Rtg;cMNucenH eyIgmanCeRmIsBIr³ ¬!¦ KNnaPaBdabEdlmanPaBsuRkitCageday eRbImuxkat;bMElg b¤¬@¦ eRCIserIskarbnSMrvagEdkFñwm nig shear connector CamYynwgm:Um:g;niclPaB lower bound. edaysareKalbMNgrbs;]TahrN_enHcg; bgðajBIkareRbItarag eyIgnwgeRCIserIsCeRmIsTI @. KNnam:Um:g;niclPaB lower bound EdlRtUvkar. PaNdabEdlekItBIkRmalxNÐ nigTm¶n;Fñwm nwgminpøas;bþÚr dUcenHPaBdabGnuBaØatGtibrmaEdlekIteLIgedaysarbnÞúkEdlGnuvtþeRkayeBlebtug rwgmaMKW 2Δ Gtibrma .4020.0098.150.150.1 1 in=−=Δ−= BI

LBEIwL

3845 4

2 =Δ

LBI EdlRtUvkarKW ( )( )

( )( )4

4

2

4.782

4020.029000384123012/500.05

3845 in

EwLI LB =

×=

Δ≥

sRmab; 2616×W CamYynwg PNA # nig .5.42 inY = / m:Um:g;niclPaB lower bound KW 4.804inI LB = . BI Composite Design Selection Table, sRmab; PNA # kmøaMgkat;tamTisedkKW

kipsQn 208=∑ edIm,ITTYltémøRtwmRtUv 2Y nig LBI dMbUgKNnaTItaMgrbs;kmøaMgsgát;enAkñúgebtug ( )( ) .9063.0

90385.0208

'85.0in

AfQa

cc

n ==∑

=

.30.42

9063.075.42

2 inatY =−=−= BItaragm:Um:g;niclPaB lower bound edayeFVI interpolation



44 .782.788 ininI LB >= (OK) cMnYnrbs; shear connector EdlRtUvkarKW 9.9

04.21208

1 ==∑

=n

nQQN yk 10 sRmab;Bak;kNþalFñwm b¤srub 20 edIm

edaysarKMlatrbs;rnUt deck, stud mYysRmab;ral;rnUt 3 sRmab;KMlat .18in nwgpþl;nUv stud 20 edIm. cemøIy³ #> edIm,IbMeBjtRmUvkarPaBdab begáIncMnYn stud BI 10 eTA 20 dak;mYyenAkñúgral;rnUt 3. ]TahrN_ 9>11 bgðajplRbeyaCn_rbs;tarag. CaBiess composite Beam Selection

Table sRmYlkarKNna partially composite beam Edl PNA sßitenAkñúgmuxkat;EdkFñwm. 9>9> FñwmCab; (Continuous Beams)

sRmab;FñwmTRmsmBaØ cMNucénm:Um:g;sUnüenARtg;TRm. cMnYn connector EdlRtUvkarenAcenøaH TRm nigcMNucEdlmanm:Um:g;GtibrmaKWcMnYnBak;kNþaléncMnYnsrubRtUvkar. sRmab;FñwmCab; cMNucrbt; k¾CacMNucénm:Um:g;sUnüEdr nigCaTUeTAeKRtUvkar connector 12N sRmab;ElVgnImYy². rUbTI 9>28 a

bgðajBIRbePTFñwmCab; nigtMbn;EdlRtUvkar shear connector. enAtMbn;m:Um:g;GviC¢man kRmalebtug nwgrgkmøaMgTaj dUcenHvanwgKμanRbsiT§PaB. enAkñúgtMbn;enH vanwgminman composite behavior Edl eyIgRtUvBicarNaenaHeT. RbePT composite behavior EtmYyKt;EdlGacmanKWenAcenøaHFñwmEdk nig EdkBRgwgtambeNþayenAkñúgkRmal. muxkat;FñwmsmasEdlRtUvKñaRtUv)anbgðajenAkñúgrUbTI 9>28 b. RbsinebIeK eRbIKMnitenH eKRtUvpþl;nUvcMnYn shear connector RKb;RKan;edIm,ITTYlnUvdWeRkénPaBCab; rvagEdkFñwm nigEdkBRgwg.

AISC Specification in Section I3.2 pþl;nUvCeRmIsBIrsRmab;m:Um:g;GviC¢man. !> edayQrEtelIersIusþg;rbs;EdkFñwmb:ueNÑaH. @> edayrYmbBa©ÚlTaMgEdkBRgwgenAkñúgmuxkat;smasRtUvRbQmnwglkçxNÐxageRkam³

a. EdkFñwmRtUvEt compact nigman latereal support RKb;RKan; b. eKRtUvEtdak; shear connector enAtMbn;m:Um:g;GviC¢man ¬cenøaHcMNucm:Um:g;sUnü

nigcMNucm:Um:g;GviC¢manGtibrma¦



c. EdkBRgwgenAkñúgTTwgRbsiT§PaBRtUvEtmanRbEvgbgáb;RKb;RKan; ¬TMBk;¦ ersIusþg;rbs;muxkat;smasKYrEtQrelIkarBRgaykugRtaMg)aøsÞicCamYynwg 85.0=bφ .

RbsinebIeKKit composite behavior AISC I5.2 tRmUv[ykkmøaMgkat;tamTisedkEdl RtUv)anepÞrrvagcMNucénm:Um:g;GviC¢manGtibrma nigcMNucm:Um:g;sUnümantémøtUcCageKkñúgcMeNam

yrr FA nig nQ∑ Edl =rA RkLaépÞrbs;EdkBRgwgenAkñúgTTwgRbsiT§PaBrbs;kRmal =yrF yield stress rbs;EdkBRgwg ersIusþg;bEnßmEdlTTYlBIkarbBa©ÚlEdkBRgwgmantémøNas; b:uEnþeBlxøHeKeRbI cover plate enAkñúg tMbn;m:Um:g;GviC¢man.



9>10> ssrsmas (Composite Columns)

ssrsmasRtUv)anEbgEckCaBIrTRmg;KW EdkbMBgTIbmUl b¤RCugEdlbMeBjedayebtug b¤ rolled steel shape dak;enAkñúgebtugCamYynwgEdkBRgwgbBaÄr nigEdkkgTTwgdUcenAkñúgssrebtug BRgwgedayEdk. rUbTI 9>29 bgðajBITRmg;TaMgBIrenH.

karviPaKssrsmasRtUv)aneFVIeLIgkñúgviFIdUcKñasRmab;Ggát;rgkarsgát;eRKOgbgÁúMEdkFm μtaEdr edayeRbIsmIkardUcKñaBI AISC Charpter E b:uEnþCamYynwgtémø yF / E nig r EdlRtUv)anEkERbedIm,I TTYllT§plEdlTTYl)anBIkarBesaF nigkarKNnaRtUvKña. munBicarNasmIkar AISC sRmab;témø TaMgenH eyIgRtUvRtYtBinitüBIeKalkarN_rbs;smIkarsin. RbsinebIeKFananUvsßanPaBlMnwg eKKitfa ersIusþg;rbs;Ggát;smasrgkarsgát;CaplbUkénersIusþg;tamG½kSrbs;EdkFñwm/ EdkBRgwg nigebtug. vaRtUv)aneKehAfa squash load ehIyRtUv)an[eday ccyrrysn AfFAFAP '85.0++= ¬(>%¦ Edl =sA RkLaépÞmuxkat; rolled steel shape =rA RkLaépÞmuxkat;srubrbs;EdkBRgwgbBaÄr =yrF yield stress rbs;EdkBRgwg =cA RkLaépÞmuxkat;rbs;ebtug srésEdkBRgwgCaeBlbc©úb,nñCaRbePT deformed EdlépÞrbs;vamansac;lanecjEdlCYy begáItPaBs¥itrvaEdk nigebtug)anl¥. RkLaépÞmuxkat; rA EdlRtUv)aneRbIkñúgkarKNnaCa nominal

area EdlKitfaRkLaépÞrbs;EdkrelagEdlmanTm¶n;kñúgmYyÉktþaRbEvgdUcKñanwg deformed bar. tarag 9>11 bgðajBI nomial diameter nigRkLaépÞsRmab;TMhMEdksþg;darEdlkMNt;eday ASTM

(1996) nig ACI (1995). edIm,ITTYl)ankugRtaMgsrub EckbnÞúkEdlTTYl)anBIsmIkar 9>5 edayRkLaépÞrbs;EdkFñwm³



s

cc

s

yrrymy

s

nAAf

AF

AFFAP '85.0++== ¬(>^¦

témørbs; myF EdlTTYlBIsmIkar (>^ ¬enAeBlEdleRbICMnYs[témø yF enAkñúgsmIkarGgát;rgkar sgát;¦ [lT§pll¥sRmab;EdkbMBg;TIbmUl b¤RCugEdlbMeBjedayebtugEdlebtugsßitenAkñúg steel

shape. ¬EdkBRgwgbBaÄrminRtUv)aneRbICamYynwgEdkbMBg;TIbmUl b¤RCug (concrete-filled pipe or

tube) eT dUcenH rA GacniwgmantémøsUnüsRmab;ssrsmasRbePTenH¦.

sRmab;eRKOgbgÁúMEdkEdkbgáb;kñúgebtug vaminmanEdkhMuB½T§vaeT ehIy structural stability Reseach Council (SSRC, 1979) ENnaMfaemKuNkat;bnßyersIusþg; ACI code (ACI, 1995) Edl mantémø 7.0 RtUv)anGnuvtþeTAelItYénEdkBRgwg nigebtugénsmIkar (>^ dUcxageRkam³ ( )

s

cc

s

yrrymy A

AfAF

AFF '85.07.07.0 ++= ¬(>&¦

s

cc

s

yrry A

AfAF

AF '595.07.0 ++=

edIm,IkarBar\T§iBl slenderness eKRtUvEktRmUvPaBrwgRkajkñúgkarBt;rbs;Ggát;Edl smamaRt eTAnwgbrimaN LEI / . karEktRmUvenHRtUv)aneFVIeLIgedayEkERbtémørbs; E dUcxageRkam³

s

ccm A

AEEE ×+= constant ¬(>*¦

Edl =E m:UDuleGLasÞicrbs;EdkeRKOgbgÁúM

tarag 9>11 Ggát;Edk RkLaépÞmuxkat; elxEdk

in. mm in.2 mm2 3 0.375 9.50 0.11 71.00 4 0.500 12.70 0.20 129.00 5 0.625 15.87 0.31 200.00 6 0.750 19.05 0.44 283.87 7 0.875 22.23 0.60 387.10 8 1.000 25.40 0.79 509.70 9 1.128 28.65 1.00 645.16 10 1.270 32.26 1.27 819.35 11 1.410 35.81 1.56 1006.45 14 1.693 43.00 2.25 1451.61 18 2.257 57.33 4.00 2580.64



=cE m:UDuleGLasÞicrbs;ebtug eTaHbICaPaBrwgRkaj (stiffeness) smamaRteTAnwgm:Um:g;niclPaB pleFobRkLaépÞsRmab;ssr smaspþl;lT§pll¥CagpleFobm:Um:g;niclPaB (SSRC, 1979). témøefrenAkñúgsmIkar 9>8 KWes μInwg

4.0 sRmab;EdkTIbmUl b¤RCugEdlbMeBjedayebtugEdlbgðajBIPaBGnuBaØaténPaBrwgRkajrbs; ebtug %40 nig 2.0 sRmab;EdkeRKOgbgÁúMEdlbgáb;kñúgebtug (encased shape). kaMniclPaBrbs;muxkat;smasKWFMCagkaMniclPaBrbs;muxkat;EdkeRKagbgÁúM nigrbs;ebtug. viFIEdlsuvtßiPaBKWRtUveRbIkaMniclPaBEdlmantémøFMénkaMniclPaBrbs;muxkat;EdkeRKOgbgÁúM b¤kaM niclPaBénmuxkat;ebtug EdleKGacykesμ Inwg 3.0 dgénvimaRtNamYyrbs;muxkat;enAkñúgbøg; buckling. edaykMNt;kaMniclPaBrbs;muxkat;smasCa mr enaHeKTTYl)an brrm 3.0≥= Edl =r kaMniclPaBrbs;muxkat;EdkeRKOgbgÁúMenAkñúgbøg; buckling =b vimaRtrbs;muxkat;ebtuenAkñúgbøg; buckling

tRmUvkarrbs; Specification AISC provisions sRmab;ssrsmasmansar³sMxan;dUcKñaeTAnwgGVIEdlerobrab;xagelI. eK eRbI Equation E2-1 nig E2-3 BI Chapter E of the specification edIm,IkMNt; design strength b:uEnþ témørbs; yF / E nig r RtUv)anEksRmYl. eKRtUvBwgEp¥kelIsmIkar (>^ nig (>& edIm,IeFVIkarEk sRmYltémøTaMgenH. BI AISC Section I2.2, témøEksRmYlrbs; yF KW ( ) ( )sccsryrymy AAfcAAFcFF /'/ 21 ++= (AISC Equation I2-1)

Edltémøefr 1c nig 2c RtUv)anKitsRmab;PaBxusKñarvag encased sectoon nig concrete-filled pipes and tubes: 0.11 =c nig 85.02 =c sRmab; pipes and tubes

7.01 =c nig 6.02 =c sRmab; encased shapes

témøEdlEksRmYl AISC E KWdUcKñaeTAnwgGVIEdl[edaysmIkar (>* b¤ ( )sccm AAEcEE /3+= (AISC Equation I2-2) Edl 4.03 =c sRmab; pipes and tubes 2.04 =c sRmab; encased shapes



AISC I2.2 kMNt;témø mr [esμ IeTAnwgGVIEdl[edaysmIkar (>( brrm 3.0≥= edIm,I[ssrsmasmanlkçN³RKb;RKan; eKRtUvBinitüemIlnUvkarkMNt;xageRkamEdl[eday AISC

I2.1³ !> EdkeRKOgbgÁúMRtUvEtmany:agtic %4 énRkLaépÞmuxkat;srub b¤Ggát;rgkarsgát;eFVIkardUc

ssrebtugGarem:CaCageFVIkardUcssrsmas. @> Encased sections RtUvEteKarBtamlkçxNÐlMGitxageRkam³

a. eKRtUvEteRbITaMgEdlbBaÄr nigEdkkg. KMlatrbs;EdkkgminRtUvFMCagBIrPaKbI én vimaRttUcCageKrbs;ebtug. RkLaépÞmuxkat;rbs;Edkem nigEdkkgminRtUvtUcCag

./.007.0 2 inin b¤ mmmm /18.0 2 énKMlatEdk. b. vaRtUvEtmankRmas;ebtugkarBarEdky:agtic mmin 38.5.1 ≈ sRmab;Edkkg

nigEdkbBaÄr.

c. EdkbBaÄrEdlRTbnÞúk (load-carrying longitudinal reinforcement) RtUvEtCab;enA framed level. EdkbBaÄrsRmab;Tb;ebtugGacpþac;enARtg; framed level.

#> ersIusþg;rbs;ebtug cf ' RtUvEtsßitenAcenøaH MPaksi 213 ≈ nig MPaksi 558 ≈ sRmab;eb tugTm¶n;Fm μta ¬minmanlT§plBiesaFn_sRmab; cf ' FMCag MPa55 eT¦ nigy:agticbMput

MPaksi 284 ≈ sRmab;ebtugTm¶n;Rsal. $> kñúgkarKNna Yield stress rbs;EdkeRKOgbgÁúM nigEdkBRgwgbBaÄrminRtUvFMCag ksi55

MPa380≈ eT. karkMNt;RtUv)anTTYlBIkarBicarNa local stability. enAeBlEdlEdk eRKOgbgÁúMhMuB½T§edayebtug vanwgminman local stability eT. ebtugnwgGachMuB½T§Edk)an RKb;RKan;ebIvaminmankarpÞúHépÞebtug (spall). RbsinebIeKsn μt;[ebtugman spall enAeBl ebtugman strain 0018.0 enaHkugRtaMgEdkRtUvKñaenAkñúgEdkKW

( ) ksiEF 2.52290000018.0maxmax === ε EdlRtUv)anKitCatémøkMNt;Rtwm ksi55 . %> edIm,IkarBar local buckling enAkñúg pipes b¤ tubes EdlbMeBjedayebtug kRmas;rbs;

pipes b¤ tubes minRtUvtUcCag



EFbt y 3/= sRmab;muxkat;ctuekaNEdlmanTTwgxageRkA b b¤ EFDt y 8/= sRmab;muxkat;rgVg;EdlmanGgát;p©itxageRkA D

]TahrN_ 9>12³ Ggát;rgkarsgát;smasEdlman 13612×W RtUv)andak;enAkñúgssrebtugEdlman TMhM .2220 in× dUcbgðajenAkñúgrUbTI 9>30. eKeRbIEdk 10# bYnedImCaEdkbBaÄr nigEdk 3# CaEdk kgEdlmanKMlat .13in edayKitBIG½kSeTAG½kS. Edkman yield stress MPaFy 50= ehIyeKeRbI EdkBRgwgRbePT Grade 60. ersIusþg;rbs;ebtugKW ksif c 5' = . KNna design strength sRmab;RbEvg RbsiT§PaB ft16 sRmab;G½kSTaMgBIr.

cemøIy³ eKkMNt;témøEksRmYl myF nig mE Edl)anBI AISC Equation I2-1 nig I2-2. témøEdl RtUvkarsRmab;smIkarTaMgenHKW³ ksiFyr 55= témøEdlkMNt;eday AISC I2.1

( ) 2.08.527.14 inAr == =cA net area rbs;ebtug ( ) 08.59.394402220 −−=−−= rs AA

2.0.395 in= sRmab; ksif c 5' =

( ) ksifwE ccc 39045145' 5.15.1 === BI AISC Equation I2-1, yield stress EdlEksRmYlKW ⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

s

cc

s

ryrymy A

AfcAAFcFF '21

( ) ( ) ksi60.849.39

39556.09.39

08.5557.050 =⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+=



BI AISC Equation I2-2, m:UDuleGLasÞicEdlEksRmYlKW ( ) ksi

AAEcEE

s

ccm 36730

9.3939539042.0290003 =⎟

⎠⎞

⎜⎝⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

kaMniclPaBEdlRtUv)aneRbIenAkñúgsmIkarGgát;rgkarsgát;én AISC Cahpter E GacCa r sRmab;Edk eRKOgbgÁúM b¤ b3.0 edayykmYyNaEdlmantémøFMCag. enAkñúg]TahrN_enH buckling nwgekIteLIg eFobnwgG½kS y rbs;Ggát; dUcenH r sRmab;muxkat;KW inry 16.3= . enAkñúgbøg; buckling ( ) .6203.03.0 inb == ¬lub¦ dUcenH .6inrm = . eKGacKNna design strength dUcKñasRmab;Ggát;rgkarsgát;FmμtaedayeRbI témøEksRmYl myF / mE nig mr CMnYs[ yF / E nig r ( ) 5.14888.0

3673060.84

61216

<===ππ

λm

my

mc E

FrKL

( ) ( )( ) ( ) ksiFF myc

cr 55.7660.84658.0658.024888.02

=== λ nominal strength KW ( ) kipsFAP crsn 305455.769.39 === ehIy design strength KW ( ) kipsPnc 2600305485.0 ==φ cemøIy³ design compressive strength KW kips2600 taragsRmab;viPaK nigKNna Tables for Analysis and Design Part 5 of the Manual mantaragEdlsRmYly:agxøaMgdl;karviPaK nigkarKNnassrsmas. taragTaMgenHmanlkçN³RsedogKñanwg column strength table enAkñúg Part 3 of the Manual. eK [ axial compressive design strength CaGnuKmn_eTAnwgRbEvgRbsiT§PaBsRmab; concrete-filled

pipes and tubes nigsRmab; encased W-shapes. sRmab; encased column Edkem nigEdkkgEdlbM eBjtRmUvkar AISC RtUv)anrab;bBa©Úl. eK[témø mymx rr / sRmab;krNITaMgenaHEdl LKLK yx ≠ .



]TahrN_ 9>13³ Ggát;rgkarsgát;EdlmanRbEvg ft18 RtUvRTnUvbnÞúkeFVIkar (service load) srub kips1000 EdlpSMeLIgedaycMENkes μ IKñaénbnÞúkefr nigbnÞúkGefr. Ggát;enHmanTRm pinned enAcug

TaMgsgçag CamYynwgTRmbEnßmenAkm<s;Bak;kNþaltamG½kSexSay. eRbItaragenAkñúg Part 5 of the

Manual edIm,IeRCIserIsEdk W EdlmanrUbragkaerEdlbgáb;kñúgebtug (square encased W-shape)

CamYynwgRkLaépÞebtugEdltUcCageKEdlGaceFVIeTA)an. eRbIEdk 36A Edksrés grade 60 nig ksif c 5.3' = .

dMeNaHRsay³ bnÞúktamG½kSemKuNKW ( ) ( ) kipsPu 14005006.15002.1 =+= tamkarGegátelItaragbgðajfa sRmab; ksif c 5.3' = nigtémøén mymx rr / ERbRbYlBI 0.1 eTA 22.1 EdltémøPaKeRcInes μ Inwg 0.1 . edaysar 22.12 >=

LKLK

y

x

LK x nwglub. snμt;fa 0.1/ =mymx rr rYcbBa©ÚleTAkñúgtaragCamYynwg ft

rrLKKLmymx

x 180.1

18/

===

taragxageRkambgðajBICeRmIsEdlGaceFVI)an TMhMmuxkat;ebtug EdkeRKOgbgÁúM mymx rr / nc Pφ

18×18 W10×112 1.0 1450kips

20×20 W12×87 1.0 14250kips

eTaHbICassr 20×20 RtUvkarEdkeRKOgbgÁúMtUcCagk¾eday EtlkçxNÐtRmUv[ykTMhMebtugGb,brma dUcenHeyIgeRCIserIs 18×18. cemøIy³ eRbIssrmuxkat; 18×18 CamYynwg W10×12 Edksrés #8 bYnedIm Edkkg #3 edayKMlat

12in.. KitBIG½kSeTAG½kS.


T.Chhay 428 Plate Girders

X. rtEdkbnÞH Plate Girder

10>1> esckþIepþIm (Introduction) CaTUeTA plate girder RtUv)aneKKitCa flexural member Edlmuxkat;rbs;vaRtUv)anpÁúMeLIg eday plate elements. AISC cat;TukFñwmxusBI plate girder edayQrelI web slenderness. Plate

girder CaFñwmFMTaMgElVg nigmuxkat; Edlmuxkat;FMenHCavi)akmkBIElVgEvg. RbsinebIeKminman hot-

rolled steel shape FMRKb;RKan;sRmab;ElVg nigkardak;bnÞúkEdl[ CaTUeTACeRmIsTImYyKWeKeRbI rolled

shape CamYynwg cover plate bEnßmenAelIsøabmYy b¤enAelIsøabTaMgBIr. RbsinebICeRmIsenHminGac pþl;ersIusþg;m:Um:g;RKb;RKan; muxkat;EdlmanlkçN³RtUvkarBitR)akdGacRtUv)anplitBI plate elements. b:uEnþRbsinebIElVgmanRbEvgEvg enaHkm<s; nigTm¶n;rbs; built-up girder GacnwgFM eBlenaHeKGac eRbICeRmIsepSgeTot dUcCa truss.


rtEdkbnÞH 429 T.Chhay

muxkat;rbs; plate girder GacmaneRcInTRmg;. rUbTI 10>1 bgðajBIlT§PaBrbs;muxkat; plate

girder xøH. TRmg;Fmμtarbs; plate girder KWRTnugeTalCamYYynwgsøabBIresμ IKña EdlRKb;EpñkTaMgGs; P¢ab;KñaedaykarpSar. muxkat;RbGb;EdlmanRTnugBIr nigsøabBIrCa torsionally superior shape nig GacRtUv)aneRbIenAeBlEdleKRtUvkar unbraced length FM. Hubrid girder CaRbePTrtEdlEdksøab manersIusþg;FMCagEdkRTnug ehIyeBlxøHk¾RtUv)aneKeRbIR)as;. muneBlEdlkarpSarRtUv)aneRbITUlMTUlay kartP¢ab;eRKOgpÁúMrbs;muxkat;KWCakarBicarNacMbg kñúgkarKNna plate girder. RKb;tMNTaMgGs;RtUv)aneFVIeLIgedayeRbIrIev dUcenHeKminmanviFIedIm,IP¢ab; søabeTARTnugedaypÞal;eT. eKRtUvbBa©Úlmuxkat;bEnßmedIm,IepÞrbnÞúkBIeRKOgbgÁúMmYyeTAeRKOgbgÁúMmYy eTot. bec©keTsFm μtakñúgkartP¢ab;KWkareRbIEdkEkgmYyKUedaydak;xñgTl;xñgedIm,IP¢ab;søabeTART nugdUcbgðajenAkñúgrUbTI 10>1 b. RbsinebIeKRtUvkar web stiffener EdkEkgmYyKUk¾RtUv)aneRbI sRmab;eKalbMNgenH. edIm,IeCosvagkarRbqaMgKñarvag stiffener angle nig flang angle eKRtUvbEnßm filler plate eTAelIRTnug dUcenH stiffener GacXøatBI lange angle dUcbgðajenAkñúgrUbTI 10>1 c. Rb sinebIeKRtUvkarmuxkat;ERbRbYl eKGaceRbI cover plate EdlmanRbEvgepSgKñamYy b¤eRcInP¢ab;eTAnwg søabedarIev. eTaHbICaeKGaceRbI cover plate CamYynwg welded plate girder k¾eday k¾viFId¾samBaØ CageKKWkareRbInUv flange plate EdlmankRmas;epSgKña EdlpSar end-to-end enATItaMgepSgKñatam beNþayrbs; girder. eKGacemIleXIjy:agc,as;fa welded plate girder KWl¥Cag riveted pr bolted

girder edayKitelIPaBgayRsYl nigRbsiT§PaB. eyIgBicarNaEt I-shaped welded plate girder enAkñúgCMBUkenH. munnwgBicarNaBItRmUvkarCak;lak;rbs; AISC Specification sRmab; plate girder eyIgcaM)ac; RtYtBinitükñúgviFITUeTAbMputBIPaBxusKñarbs; plate girder nig rolled beam Fmμta. eTaHbICaeyIg)an sikSaBI flexural member enAkñúgCMBUk 5, “Beams” k¾eday k¾ plate girder mantRmUvkar flexural

strength nig shear strength BiessepSg. 10>2> karBicarNaTUeTA (General Considerations) bBaðad¾FMkñúgkarKNnaeRKOgbgÁúMEdkKWkarpþl;nUv local stability b¤lMnwgsRmab;eRKOgbgÁúMTaMg mUl. edaysar standard hot-rolled structural shapes manlkçN³smamaRtdUcenHbBaða local



stability RtUv)ankat;bnßy b¤RtUv)ankat;bnßydl;kMritGb,brma. b:uEnþenAeBlEdleKeRbI plate girder,

designer RtUvEtKitBIktþaCaeRcInEdlPaKeRcIn rolled shape minmanbBaðak¾eday. RTnugesþIg nig x<s;begáItnUvbBaðaCaeRcInenAeBlEdlcapÁúMCamYynwg plate girder edayrYmbBa©ÚlTaMg local instability. karyl;dwgBIeKalkarN_rbs; AISC provions sRmab; plate girder TamTarnUvcMeNHdwgBI stability

theory CaBiess plate stability. b:uEnþenAkñúgesovePAenHbgðajEteKalkarN_tRmUvkarrbs; Specifi-

cation nigkarGnuvtþrbs;vaEtb:ueNÑaH. RbsinebImankarcab;Garm μN_ nigcg;EsVgyl;bEnßm Guide to

stability Criteria for Metal Structures (Johnston, 1976) CacMNucsRmab;cab;epþImd¾l¥ ehIy Buckling Strength of Metal Structures (Bleich, 1952) nig Theory of Elastic stability

(Timoshenko and Gere, 1961) nwgpþl;nUvmUldæanRKwHén stability theory. Plate girder QrelIersIusþg;EdlmaneRkayeBlRTnug buckle dUcenH flexural strength PaK eRcInnwgekItBIsøab. sßanPaBkMNt;EdlRtUvBicarNaKWsøabrgkarTaj yield nigsøabrgkarsgát; buckle. søabrgkarsgát;Edlrg buckle GacmanTRmg; vertical buckling enAkñúgRTnug b¤ flange

local buckling (FLB) b¤vaGacekIteLIgedaysar lateral-torsional buckling (LTB). enAkñúgRTnug girder TItaMgEdlmankmøaMgkat;FMeRcInEtsßitenAEk,rTRm nigenARtg; b¤enAEk,r G½kSNWt. bøg;emnwgeRTteFobeTAnwgG½kSbeNþayrbs;Ggát; ehIykugRtaMgemCakmøaMgTaj Ggát;RTUg b¤kmøaMgsgát;Ggát;RTUg. kmøaMgTajGgát;RTUgminbegáItbBaðaeT EtkmøaMgsgát;Ggát;RTUg bNþal[RTnug buckle. bBaðaenHGaceCosvag)antambIrebob³ (1) eKGaceFVI[pleFobkm<s;elIkRmas; (depth-to-

thickness ratio) rbs;RTnugmantémøtUcl μmEdlGaclubbM)at;bBaðaenH)an (2) eKGaceRbI web

stiffeners edIm,IbegáItCa panel edIm,IbegáIn shear strength b¤ (3) eKGaceRbI web stiffeners edIm,I begáItCa panel EdlTb;Tl;nwgkmøaMgsgát;Ggát;RTUgtamry³ tension field action. rUbTI 10>2 bgðaj BIKMnitén tension field action. enAcMNucEdlCitekItman buckling RTnug)at;bg;lT§PaBrbs;vakñúg karTb;Tl;kmøaMgsgát;Ggát;RTUg ehIykugRtaMgenH)anpøas;bþÚreTA stiffeners xag nigsøab. Stiffener Tb; Tl;nwgbgÁúMkmøaMgsgát;Ggát;RTUgbBaÄr ehIysøabTb;Tl;nwgbgÁúMkmøaMgedk. eKRtUvkar[RTnug Tb;Tl;nwgkmøaMgTajGgát;RTUg dUcenHeTIbmanBakü tension-field action. kareFVIkarenHmanlkçN³ dUcKñanwg pratt truss EdlGgát;RTnugbBaÄrRTkmøaMgsgát; Ggát;RTnugGgát;RTUgRTkmøaMgTaj dUcbgðaj kñúgrUbTI 10>2 b. edaysarCak;Esþg tension field ekItman)anluHRtaEtRTnugcab;epþIm buckling



dUcenH vaGaccUlrYmenAkñúgersIusþg;kmøaMgkat;rbs;RTnug)anluHRtaEtRTnug buckling sin. ersIusþg; srubnwg pSMeLIgedayersIusþg;muneBl buckling nigersIusþg;eRkayeBl buckling EdlTTYlBI tension

field action.

RbsinebI unstiffened web minmanlT§PaBGacTb;Tl;nwgkmøaMgkat;Gnuvtþn_ enaHeKRtUveRbI stiffener EdlmanKMlates μ I²KñaedIm,IbegáIn tension field action. muxkat;EdlRtUvkar stiffener

RtUv)aneKehAfa intermidate stiffener manTMhMtUcBIeRBaHeKalbMNgdMbUgrbs;vaKWpþl;nUv stiffener RbesIrCagkarTb;Tl;kmøaMgGnuvtþn_edaypÞal;. eKGacRtUvkar stiffener bEnßmenARtg;cMNucbnÞúkcMcMNucsRmab;eKalbMNgkarBarRTnugBIbnÞúk sgát;edaypÞal;. stiffener enHRtUv)aneK[eQ μaHfa bearing stiffener ehIyvaRtUvEtsmamaRtedIm,I Tb;Tl;bnÞúkGnuvtþn_. vak¾GaceFVIkarCa intermidate stiffener kñúgeBlCamYyKñapgEdr. rUbTI 10>3 bgðajBI bearing stiffener EdlpSMeLIgedaybnÞHctuekaNEkgBIrenAsgxagRTnug girder. bnÞHEdk bEnßmRtUv)ankat;biutenARCugxagkñúgTaMgelI nigeRkamedIm,IeCosvagTwkbnSar flange-to-web. Rbsin



ebIeKsnμt; stiffener [Tb;Tl;bnÞúkGnuvtþn_srub P edaysuvtßiPaB ¬karsnμt;ecalnUvkarcUlrYmrbs; RTnug¦ enaHeKGacsresr bearing stress Rtg;épÞb:HCa

pbp A

Pf =

Edl =pbA projected bearing area at2= ¬emIlrUbTI 10>3¦ b¤eKGacsresr bearing load CMnYs[kareRbI bearing stress Ca pbp AfP = ¬!0>!¦

elIsBIenH stiffener mYyKUCamYynwgRTnugEdlmanRbEvgxøIRtUv)anKitCassrEdlmanRbEvg

RbsiT§PaBtUcCagkm<s;rbs;RTnug ehIyRtUv)anGegátedayeRbI Specification provision dUcGgát;rg karsgát;déTeTotEdr. muxkat;enHRtUv)anbgðajenAkñúgrUbTI 10>4. CaTUeTA ersIusþg;sgát;KYrQrelIkaM niclPaBeFobG½kSkñúgbøg;rbs;RTnug EdlPaBK μanlMnwgeFobnwgG½kSemd¾éTRtUv)ankarBaredayRTnug xøÜnÉg.

sßanPaBkMNt;EdlTTYl)anBIkarGnutþrbs;bnÞúkcMcMNuceTAelIsøabxagelIrbs;RTnug yielding, RTnug crippling (buckling) ehIy sidesway buckling. Sidesway web buckling ekItmanenAeBl kmøaMgsgát;enAkñúgRTnugbgá[søabrgkarTaj buckle tamTTwg. )atuPUtenHGacekItmanenAeB Edl søabminmanlT§PaBRKb;RKan;RbqaMgnwgclnaeTAvijeTAmkrbs; stiffener b¤ lateral bracing.



TwkbnSarsRmab;kartP¢ab;eRKOgbgÁúMrbs; plate girder RtUv)anKNnadUcKñanwgkarKNnatMN pSardéTeTotEdr. TwkbnSar flang-to-web RtUvEtTb;Tl;nwgkmøaMgkat;tamTisedkenARtg;épÞb:Hrvag eRKOgbgÁúMBIr. kmøaMgkat;Gnuvtþn_enH RtUv)aneKehAfa shear flow EdlCaTUeTARtUv)anKitCakMlMagkñúg mYyÉktþaRbEvgrbs; girder edIm,IGacTb;Tl;edayTwkbnSar. BICMBUk 5 shear flow EdlQrelI elastic behavior RtUv)an[eday

xIVQf =

Edl Q Cam:Um:g;TImYyénRkLaépÞrvagbøg;kmøaMgkat;tamTisedk nigépÞénmuxkat;xageRkAeFobnwgG½kS NWt. smIkarxagenHCasmIkar %>^ sRmab;kugRtaMgkmøaMgkat;EdlKuNedayTTwgrbs;bøg;kmøaMgkat;. edaysarEtCaTUeTAkmøaMgkat;Gnuvtþn_ERbRbYl dUcenHRbsinebIeKeRbIkarpSaredayEdlminCab; enaH KMlatrbs;vanwgERbRbYleTAtamenaHEdr. 10>3> tRmUvkarrbs; AISC (AISC Requirments) tRmUvkarsRmab; plate girder RtUv)anbriyayenAkñúg Chapter 6 of the AISC Speciffication ehIy Appendix G manniyayBIeKalbMNgkñúgkarGnuvtþrbs; plate girder. eTaHCa flexural member RtUv)ancat;cMNat;fñak;Ca beam b¤ plate girder k¾eday k¾vaenAEtCa GnuKmn_eTAnwg web slendernedd wth / Edl h Cakm<s;rbs;RTnugcenøaHépÞxagkñúgrbs;søab nig wt CakRmas;rbs;RTnug. RbsinebI yfw fth /2550/ < ¬xñat IS ¦ yfw fth /970/ < ¬xñat US¦



Ggát;RtUv)ancat;cMNat;fñak;Ca beam ehIyeKRtUvGnuvtþkarpþl;[rbs; AISC Chapter F edaymin KitfaGgát;enHCa bult-up BI plate b¤Ca hot-rolled shape. RbsinebI yfw fth /2550/ > ¬xñat IS¦ Ggát;RtUv)ancat;cMNat;fñak;Ca plate girder ehIyeKRtUvGnuvtþkarpþl;[rbs; AISC Chapter G. dUc enH flexural member Edlman slender web Edl slenderness RtUv)ankMNt;enAkñúg AISC Chapter

B RtUv)anKitCa plate girder. cMNaMfa enAeBlEdleKeRbI hybrid girder témøkMNt;rbs; wth / KW QrelI yfF yield stress rbs;søab. mUlehtuKWfa lMnwgrbs;RTnugRbqaMgnwg flexural buckling KWGa Rs½ynwg strain enAkñúgsøab (Zahn, 1987). edIm,Ibgáa vertical buckling rbs;søabeTAkñúgRTnug AISC Appendix G2 )an[nUvEdnkMNt; x<s;bMputsRmab;pleFobTTwgelIkRmas; (width-thickness ratio) wht . témøEdlkMNt;enHCa GnuKmn_eTAnwg aspect ratio ha / rbs; girder plate EdlCapleFobKMlatrbs; intermediate

stiffener elIkm<s;RTnug ¬emIlrUbTI 10>5¦³ sRmab; 5.1/ ≤ha /

yfw Fth 2000≤ ¬xñat US¦

yfw Fth 5250≤ ¬xñat IS¦ (AISC Equation A-G1-1)

sRmab; 5.1/ >ha /

)5.16(14000

+≤

yfyfw FFth ¬xñat US¦

( )11496530

+≤

yfyfw FFth ¬xñat IS¦ (AISC Equation A-G1-2)

Edl a Ca clear distance rvag stiffeners.



10>4> ersIusþg;rgkarBt; (Flexural Strength) Design flexural strength rbs; plate girders KW nbMφ / Edl 90.0=bφ . Norminal

flexural strength nM KWQrenAelIsøabrgkarTaj yielding b¤k¾søabrgkarsgát; buckling. eKGac kMNt; Bucling strength rbs;søabrgkarsgát;eday flang local buckling (FLB) b¤k¾ lateral-

torsional buckling (LTB). Vertical buckling rbs;søabrgkarsgát;eTAkñúgRTnugRtUv)andkecjBI karBicarNaedaysarkarkMNt;Edl[eday AISC Equation A-G1-2 nig A-G1-2 (Cooper,

Galambos, and Ravindra, 1978). Tension Flange Yielding BICMBUk 5/ kugRtaMgBt;GtibrmaenAkñúg flexural member EdlekageFobeTAnwgG½kSxøaMgrbs;va KW

xb S

Mf =

Edl xS Cam:UDulmuxkat;eGLasÞic (elastic section modulus) eFobG½kSxøaMg. sresrsmIkarm:Um:g; Bt;CaGnuKmn_eTAnwgm:UDulmuxkat; nigkugRtaMg eKTTYl)an bx fSM = ¬!0>@¦ AISC Appendix G2 [ nominal flexural strength EdlQrelIsøabrgkarTajEdl yield Ca ytextn FRSM = (AISC Equation A-G2-1) Edl =xtS elastic section modulus EdlsMedAelIxagEdlrgkarTaj =eR emKuN hybrid girder =ytF yield stress rbs;søabrgkarTaj emKuN hybrid girder eR es μ Inwg 0.1 sRmab; nonhybrid girder. sRmab; hybrid girder

( )( )( ) 0.1

/2123/12 3

≤+

−+=

fw

fwe AA

mmAAR

Edl =wA RkLaépÞrbs;RTnug fA10≤ =fA RkLaépÞrbs;søabrgkarsgát;

yfyw FFm /= ¬karkMNt;enHKWsRmab;sßanPaBkMNt;rbs;søabrgkarTaj yield. sRmab;søabrgkarsgát; eKk¾eRbIemKuN hybrid girder Edr Et m RtUv)ankMNt;epSg¦.



Compression Flange Buckling Nominal flexural strength EdlRtUvnwgsøabrgkarsgát; buckling k¾QrelIsmIkar !0>@ Edr. BI AISC Appendix G2, ersIusþg;enHRtUv)ansresrCa crePGxcn FRRSM = (AISC Equation A-G2-2) Edl =xcS m:UDulmuxkat;eGLasÞicsMedAelIxagEdlrgkarsgát; =PGR emKuNkat;bnßyersIusþg;edIm,IkarBar elastic web buckling =crF kugRtaMgeRKaHfñak;enAkñúgsøabrgkarsgát;EdlQrelI LTB b¤ FLB

=eR emKuN hybrid girder ¬EdlKitedaysmIkardUcKñasRmab;søabrgkarTaj yield b:uEnþ cryw FFm /= ¦.

emKuNkat;bnßyersIusþg;rbs; plate girder PGR RtUv)aneday

0.19703001200

1 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

crwr

rPG Ft

ha

aR ¬xñat US¦ (AISC Equation A-G2-3)

0.125503001200

1 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

crwr

rPG Ft

ha

aR ¬xñat IS¦ (AISC Equation A-G2-3)

Edl 10/ ≤= fw AAa =ch cm¶ayBIrdgBITIRbCMuTm¶n;eTAépÞxagkñúgrbs;søabrgkarsgát; ¬ hhc = sRmab; girder

Edl mansøabesμ IKña¦ kugRtaMgeRKaHfñak; crF KWQrelI lateral-torsional buckling b¤ flange local buckling.

AISC Specification eRbInimitþsBaØa λ / pλ nig rλ edIm,IedaHRsayCamYynwg slanderness para-

meter sRmab;sßanPaBkMNt;TaMgBIr ehIyeKeRbInUvsMnMuénsmIkarxageRkamsRmab;edaHRsay crF . smIkarRtUv)anbgðajenATIenHkñúgTRmg;BnøatbnþicbnþÜckñúgbMNgbBa¢ak;BIkarpþl;[. sRmab; lateral

torsional buckling eKeRbI slenderness énEpñkrbs;tMbn;sgát;rbs; girder dUcenH

T

brL

=λ (AISC Equation A-G2-7)

yfp F

300=λ ¬xñat US¦

yfp F

792=λ ¬xñat IS¦ (AISC Equation A-G2-8)

yf

r F756

=λ ¬xñat US¦ yf

r F1985

=λ ¬xñat IS¦ (AISC Equation A-G2-9)



Edl bL Ca unbraced length nig Tr CakaMniclPaBeFobG½kSexSaysRmab;Epñkénmuxkat;Edlman søabrgkarsgát; nigmYyPaKbIénRTnugEpñkrgkarsgát;. sRmab; girder sIuemRTIDub TMhMenHes μ ImYyPaK R)aMmYyénkm<s;RTnug. ¬emIlrUbTI 10>6¦ enaH³ RbsinebI pλλ ≤ / kar)ak;KWekIteLIgedaysar yielding yfcr FF = (AISC Equation A-G2-4) RbsinebI rp λλλ ≤< / kar)ak;KWekIteLIgedaysar inelastic LTB nig

yfpr

pyfbcr FFCF ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

λλλλ

211 (AISC Equation A-G2-5)

Edl bC RtUv)an[eday AISC Equation F1-3. RbsinebI rλλ > / kar)ak;nwgekIteLIgedaysar elastic LTB nig 2λ

PGcr

CF = (AISC Equation A-G2-6)

Edl bPG CC 286000= (AISC Equation A-G2-10)

sRmab;søabrgkarsgát; buckling EdlQrelI flange local buckling pleFobTTwgelI kRmas; (width-thickness ratio) nigEdnkMNt;rbs;vaKW³

f

f

tb2

=λ (AISC Equation A-G2-11)

yf

p F65

=λ ¬xñat US¦ yf

p F170




cyf

r kF /230

=λ ¬xñat US¦ cyf

p kF /605


Edl wc thk //4= / 763.035.0 ≤≤ ck enaH³ RbsinebI pλλ ≤ / kar)ak;nwgekIteLIgedaysar yielding nig yfcr FF = (AISC Equation A-G2-4) RbsinebI rp λλλ ≤< / kar)ak;nwgekIteLIgedaysar inelastic FLB nig

yfpr

pyfbcr FFCF ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

λλλλ

211 (AISC Equation A-G2-5)

Edl 0.1=bC RbsinebI rλλ > / kar)ak;ekIteLIgedaysar elastic FLB nig 2λ

PGcr

CF = (AISC Equation A-G2-6)

Edl cPG kC 26200= (AISC Equation A-G2-14) karKNna flexural strength RtUv)anbgðajenAkñúg]TahrN_ 10>1/ cMNuc (a). 10>5> ersIusþg;kmøaMgkat; (Shear Strength) Design shear strength rbs; plate girder KW nvVφ Edl 9.0=vφ . Shear strength Ca Gnu-Kmn_eTAnwgpleFobkm<s;elIkRmas; (depth-to-thickness ratio) rbs;RTnug nigKMlatrbs; interme-

diate stiffener. Shear capacity manbgÁúMersIusþg;BIr³ ersIusþg;muneBl buckling nigersIusþg;eRkay eBl buckling. ersIusþg;eRkayeBl)ak;sMGageTAelI tension field action EdlGacmanlT§PaB begáItedaysarvtþmanrbs; intermediate stiffener. RbsinebIminmanvtþman stiffener b¤k¾manKMlat q¶ayBIKñaeBk vak¾minGacman tension field action ehIy shear capacityGacmanEtersIusþg;muneBl buckling. Nominal shear strength Edl[eday AISC Appendix G3 mandUcxageRkam³ sRmab;

yf

v

w Fk

th 187≤ ¬xñat US¦

yf

v

w Fk

th 491≤ ¬xñat IS¦

ywwn FAV 6.0= (AISC Equation A-G3-1) sRmab;

yf

v

w Fk

th 187> ¬xñat US¦

yf

v

w Fk

th 491> ¬xñat IS¦



( ) ⎟⎟

⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+

−+=

2/115.1

16.0ha

CCFAV vvywwn (AISC Equation A-G3-2)

Edl ( )2/

55ha

kv +=

5= RbsinebI 3>ha (AISC Equation A-G3-4)

5= RbsinebI ( )

2

/260

⎥⎦

⎤⎢⎣

⎡>

wthha

AISc Equation A-G3-1 [nUv shear strength enAeBlEdlKμanvtþman tension-field action ehIy kar)ak;rbs;RTnugKWedaysar yielding. AISC A-G3-2 rab;bBa©Úl tension-field action. eKk¾Gac sresr AISC Equation A-G3-2 Ca

( )2/115.1

16.06.0ha

CFCFAV vywvywwn

+

−+=

GgÁTImYyenAkñúgsmIkarxagelIenHCa web shear buckling strength ehIyGgÁTIBIrCa post-buckling

strength. emKuN vC CapleFob critical web buckling stress elI web shear yield stress

ehIyRtUv)ankMNt;dUcxageRkam³ sRmab;

yf

v

wyf

vFk

th

Fk 234187 ≤≤ (US)

yf

v

wyf

vFk

th

Fk 614491 ≤≤ (IS)

w

yfvv th

FkC

/

/187= (US)

w

yfvv th

FkC

/

/491= (IS) (AISC Equation A-G3-5)

sRmab; yf

v

w Fk

th 234> (US)

yf

v

w Fk

th 614> (IS)

( ) yww

vv

FthkC 2/

44000= (US)

( ) yww

vv

FthkC 2/

303380= (IS) (AISC Equation A-G3-6)

dMeNaHRsayrbs; AISC Equation A-G3-1 nig A-G3-2 RtUv)ansRmYledaytaragEdl[ enAkñúg Numerical Values section of the Specification. Tables 9-36 nig 10-36 Tak;Tgnwg)a:ra: Em:RténsmIkarTaMgBIrenHsRmab;Edk 36A ehIy Tables 9-50 nig 10-50 sRmab;EdkEdlman yield

stress MPaksi 34550 ≈ . eyIgnwgniyaylMGitBIkareRbIR)as;tarag TaMgenHenAkñúg]TahrN_xagmux. Tension field minGacekItmaneBjenAkñúg panel xagcugeT. eKGacdwgy:agc,as;edaycat;

TukbgÁúM tension field tamTisedkEdlbgðajenAkñúgrUbTI 10>7. bgÁúMtamTisbBaÄrRtUv)anTb;eday



stiffener. Tension field enAkñúg panel CD RtUv)anrkSalMnwgeday tension field enAkñúg panel BC . dUcenH panel xagkñúgRtUv)anf<k;Cab;eday panel EdlenAEk,r. b:uEnþ panel AB minmankarf<k;enAxag eqVgeT. eTaHbICakarf<k;Gacpþl;[eday stiffener xagcugEdlKNnaedIm,ITb;Tl;karBt;EdlekItBI tension field k¾eday k¾vamineFVIkarCakarf<k;Edr. edaysar tension field minekItmanenAeBjkm<s; RTnug dUcenH internal stiffener k¾RbQmnwgkarBt;xøHEdlekItBI tension field EdllyecjenAkñúg panel EdlenAEk,r b:uEnþm:Um:g;Bt;enHminsMxan;eT. dUcenHkarf<k;Cab;sRmab; panel BC RtUv)anpþl; [enAxageqVgeday beam-shear panel RbesIrCag tension field panel Edl)anbgðaj. dUcenH nominal shear strength KWdUcKñanwg flexural member EdlKμan tension-fiels panel

vywwn CFAV 6.0= (AISC Equation A-G3-3)

cMNaMfasmIkarxagelIenHCaGgÁTImYyrbs; AISC Equation A-G3-2. Tension-field action

minRtUv)anGnuBaØatsRmab; hybrid girder b¤enAeBl 3/ >ha b¤enAeBl ( )[ ]2//260/ wthha > ¬Edl krNIxageRkayTaMgBIrenHRtUvKñanwg 5=vk ¦. dUcenH AISC Equation A-G3-3 GnuvtþenAkñúgsßanPaB TaMgenH. AISC G4 erobrab;faeKminRtUvkar intermediate stiffener enAeBl yww Fth /418/ ≤ ¬xñat US¦ b¤ yww Fth /1097/ ≤ EdlTaMgenHGacbgðajdUcxageRkam. enAeBlEdlK μan interme-

diate stiffener 3/ >ha nig 5=vk [

w

yw

w

ywv th

F

th

FC

/

/418

/

/5187== (US)

w

yw

w

ywv th

F

th

FC

/

/1097

/

/13187== (IS)

ehIy nominal shear strength



[ ]w

ywywwn th

FFAV

/

/4186.0= (US) [ ]

w

ywywwv th

FFAV

/

/10976.0= (IS)

dUcenHenAeBlEdl yww Fht /418/ ≤ (US) yww Fth /1097/ ≤ (IS)

ywwv FAV 6.0≥

b:uEnþsmIkarenHRtUvnwgEdnkMNt;x<s;bMput (shear yielding) dUcenHsBaØaFMCagRtUv)andkecj eK)an ywwv FAV 6.0= (AISC Equation A-G3-1)

EdlCa nominal strength enAeBlEdl ywvw Fkth /187/ ≤ (US) ywvw Fkth //491/ ≤ (IS) RbsinebIeKminKit tension-filed action eTenaH eKTTYl)an shear strength BI AISC

Appendix F2 dUcxageRkam³ sRmab;

yw

v

w Fk

th 187≤ (US)

yw

v

w Fk

th 491≤ (IS)

wywv AFV 6.0= (AISC Equation A-F2-1)

sRmab; yw

v

wyw

vFk

th

Fk 234187 ≤< (US)

yf

v

wyf

vFk

th

Fk 614491 ≤≤ (IS)

w

ywvwywv th

FkAFV

/

/1876.0= (US) (AISC Equation A-F2-2)

w

ywvwywv th

FkAFV

/

/4916.0= (IS)

sRmab; yf

v

w Fk

th 234> (US)

yf

v

w Fk

th 614> (IS)

( )2/26400

w

vwv

thkAV = (US) (AISC Equation A-G3-6)

( )2/182

w

vwv

thkAV = (IS)

segçbmk nominal shear strength RtUv)ankMNt;dUcxageRkam !> kMNt; aspect ratio ha / @> kMNt; vk nig vC

#> sRmab;RKb; panel rbs; hybrid girder nigsRmab; panel xagcugrbs; nonhybrid girders:

RbsinebI yw

v

w Fk

th 187≤ (US)

yw

v

w Fk

th 491≤ (IS)

wywv AFV 6.0=



RbsinebI yw

v

w Fk

th 187> (US)

yw

v

w Fk

th 491> (IS)

vwywv CAFV 6.0= sRmab; panel d¾éTeTotrbs; nonhybrid girder Edlman tention-field action:

RbsinebI yw

v

w Fk

th 187≤ (US)

yw

v

w Fk

th 491≤ (IS)

wywv AFV 6.0= RbsinebI

yw

v

w Fk

th 187> (US)

yw

v

w Fk

th 491> (IS)

( ) ⎟⎟

⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+

−+=

2/115.1

16.0ha

CCAFV vvwywv

RbsinebIeKmineRbI tension-field action eKnwgGnuvtþ provisions of Appendix F2:

RbsinebI yw

v

w Fk

th 187≤ (US)

yw

v

w Fk

th 491≤ (IS)

wywv AFV 6.0=

RbsinebI yw

v

wyw

vFk

th

Fk 234187 ≤< (US)

yf

v

wyf

vFk

th

Fk 614491 ≤≤ (IS)

w

ywvwywv th

FkAFV

/

/1876.0= (US)

w

ywvwywv th

FkAFV

/

/4916.0= (IS)

RbsinebI yf

v

w Fk

th 234> (US)

yf

v

w Fk

th 614> (IS)

( )2/26400

w

vwv

thk

AV = (US)

( )2/182

w

vwv

thkAV = (IS)

karkMNt; shear strength RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc (b). Intermediate Stiffeners



RbsinebIeKRtUvkar intermediate stiffener edIm,ITTYl shear strength RKb;RKan;enAeBlEdl eKeRbI tension-field action RkLaépÞmuxkat;Gb,brmarbs; stiffener eTal b¤KURtUv)an[eday AISC

Appendix G4 KW ( ) 018115.0 2 ≥⎥

⎦

⎤⎢⎣

⎡−−= w

nv

uvw

yst

ywst t

VVCDht

FF

Aφ

(AISC Equation A-G4-1)

Edl =stA RkLaépÞmuxkat;srubrbs; stiffener EdlRtUvkarenAeBlEdleKeRbI tension-field action

=ystF yield stress rbs; stiffener =D GnuKmn_énTRmg;rbs; stiffener 0.1= sRmab; stiffener KU ¬EdkEkg b¤EdkbnÞH¦ 8.1= sRmab; stiffener EdkEkgeTal 4.2= sRmab; stiffener EdkbnÞHeTal eKRtUvkarRkLaépÞEdlkMNt;eday AISC Equation A-G4-1 edIm,ITb;Tl;nwgbgÁúMkmøaMgbBaÄrrbs; kmøaMgsgát;Ggát;RTUgenAkñúg panel. Table 10-36 nig 10-50 enAkñúg Numerical Values section of the Specification Edl[nUv shear strength EdlQrelI tension-field action ehIyk¾[pg EdrnUvRkLaépÞ stiffener EdlcaM)ac;edaysMEdgCaPaKryénRkLaépÞRTnugsRmab;témøepSg²rbs;

ha / nig wth / . m:Um:g;niclPaBGb,brmarbs; stiffener EdlKiteFobnwgG½kSenAkñúgbøg;rbs;RTnug ¬b¤sRmab; stiffener eTaleFobnwgépÞrbs; stiffener Edlb:HnwgRTnug¦ RtUv)an[enAkñúg AISC Appendix F2.3

KW jatI wst

3= Edl

( )5.02

/5.2

2 ≥−=ha

j (AISC Equation A-F2-4)

eTaHbICa intermediate stiffener minRtUv)anKNnaCaGgát;rgkarsgát;k¾eday k¾karkMNt;pleFobTTwg elIkRmas;sRmab;eCosvag local buckling GacRtUv)aneRbIkñúgkarkMNt;smamaRtrbs;muxkat; stiffener. Table B5.1 nig AISC B5 minmankarENnaMsRmab; plate girder stiffener eT. EdnkMNt; pleFob TTwgelIkRmas;sRmab; outstanding legs rbs;EdkEkgKUEdlCab;RtUv)aneRbIenATIenH



yFtb 95= (US)

yFtb 250= (IS)

Tal;EtvaeFVIkarCa bearing stiffener ebImindUecñaHeT intermediate stiffener minRtUv)anTamTar [RTsøabrgkarTajeT dUcenHRbEvgrbs;vaGaceBlxøHmanRbEvgxøICagkm<s;RTnug h ehIyeKGac eCosvagnUvbBaðaplitEdlbNþalmkBIkardak;[RtUvKña. eyagtam Appendix F2.3 of the speci-

fication RbEvgrbs; stiffener KYrEtsßitenAkñúgEdnkMNt;Edlcm¶ayrvagTwkbnSarEdltP¢ab; stiffener eTARTnug nigTwkbnSarEdltP¢ab;RTnugeTAsøabrgkarTaj. cm¶ayenHRtUv)ansMKal;eday c enAkñúgrUb TI 10>8 KYrEtsßitenAcenøaHbYneTAR)aMmYydgénkRmas;RTnug.

karkMNt;smamaRtmuxkat;rbs; intermediate stiffener edayk,Ünrbs; AISC minTamTarkar KNnakmøaMgNamYyeT b:uEnþkmøaMgRtUvEtepÞrBI stiffener eTARTnug ehIykartP¢ab;KYrEtRtUv)anKNna sRmab;kmøaMgenH. Basler (1961) ENnaM[eRbI shear flow

EF

hf y3

045.0= ¬!0>#¦ Intemittent fillet weld Gb,brmaTMngCaRKb;RKan; (Salmon and John, 1996). manEtkar

ENnaMBI AISC enAkñúg Appendix F2.3 eTEdlTamTar clear distance cenøaH fillet wled EdlminCab; min[FMCag wt16 b¤ cmin 25.10 ≈ .

10>6> GnþrGMeBIénkarBt; nigkmøaMgkat; (Interaction of Flexural and Shear) CaTUeTA kugRtaMgRtg;cMNucmYykñúgRTnugrbs; plate girder KWCabnSMénkmøaMgkat; nigm:Um:g;Bt;Ca mYynwgkugRtaMgG½kSemFMCagbgÁúMkugRtaMgdéTeTot. CaTUeTA kugRtaMgEdlbnSMenaHminmanbBaðaeT Rb sinebIminman tension-field action eRBaHGnþrGMeBIénkmøaMgkat; nigm:Um:g;Bt;RtUv)anecalkñúgkrNIenH. RbsinebIman tension field, kugRtaMgTajGgát;RTUgnwgeTAdl;kMritx<s;bMput ehIykarbnSMkugRtaMg



RtUv)anBicarNa. AISC TamTarfaGnþrGMeBIRtUvKitenAeBlman tension field CamYynwgkmøaMgkat; nig m:Um:g;Bt; nun VVV φφ ≤≤6.0 nig nun MMM φφ ≤≤75.0 Edl 90.0=φ . vaRtUvEtbMeBjsmIkarGnþrGMeBIxageRkam 375.1625.0 ≤+

n

u

n

uV

VMM

φφ (AISC Equation A-G5-1)

karRtYtBinitüsRmab;GnþrGMeBIrbs;m:Um:g;Bt; nigkmøaMgkat;RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc

(C). 10>7> Bearing Stiffeners eKRtUvkar bearing stiffener enAeBlRTnugminmanersIusþg;RKb;RKan;sRmab;sßanPaBkMNt;Na mYyén web yielding, web crippling, b¤ sidesway web buckling. sßanPaBkMNt;TaMgenHRtUv)an bgðajenAkñúg Charpter K of the Specification (“Concentrated Forces, Ponding, and Fatigue”). sRmab; web yielding, design strength rbs;RTnugKW nRφ Edl 0.1=φ nigenAeBlEdlbnÞúksßitenA cm¶ayesμ Inwgkm<s; girder BIxagcug ( ) wywn tFNkR += 5 (AISC Equation K1-2)

enAeBlEdlbnÞúksßitenAcm¶aytUcCagkm<s; girder BIxagcug ( ) wywn tFNkR += 5.2 (AISC Equation K1-3) Edl =k cm¶ayBIépÞxageRkArbs;søabeTAeCIgrbs; fillet enAelIRTnug ¬sRmab; rolled beam¦

b¤eTA eCIgrbs;TwkbnSar ¬sRmab; welded girger¦ =N RbEvgrbs; bearing rbs;bnÞúkcMcMNucEdlvas;tamTisrbs;G½kSbeNþayrbs; girder

¬mintUcCag k sRmab;Rbtikm μcug¦ ¬eyIg)anerobrab;BIsßanPaBkMNt;enHenAkñúgCMBUk 5 rYcehIy¦.

sRmab; web crippling emKuNrsIusþg; 75.0=φ nigenAeBlbnÞúksßitenAy:agticcm¶ayBak; kNþalkm<s; girder BIcug

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+=

5.12 31135 sRmab; 0≤

dN (AISC Equation K1-4)



enAeBlbnÞúksßitenAcm¶aytUcCagkm<s;rbs; girder BIcugrbs; girder

w

fyw

f

wwn t

tFtt

dNtR

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+=

5.12 2.04168 sRmab; 0>

dN (AISC Equation K1-5b)

Edl =d srubrbs; girder =ft kRmas;rbs;søab girder ¬eyIgk¾)anerobrab;BIsßanPaBkMNt;enHenAkñúgCMBUk 5¦ eKRtUvkar bearing stiffeness edIm,IbgáarEt sidesway web buckling eRkamsßanPaBkMNt; mYycMnYnEtb:ueNÑaH. eKRtUvRtYtBinitü sidesway web buckling enAeBlEdlsøabrgkarsgát;minTb; RbqaMgnwgclnaeTAsøabrgkarTaj. Design strength KW nRφ / Edl 85.0=φ . RbsinebIsøabRtUv)anTb;min[vil

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

3

2

3

//4.01

f

wfwrn bl

thh

ttCR (AISC Equation K1-6)

[smIkarxagelIenHminRtUvkarRtYtBinitüeTRbsinebI ( ) ( ) 3.2/// >fw blth ] RbsinebIsøabRtUv)anGnuBaØat[vil

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

2

3

//4.0

f

wfwrn bl

thh

ttCR (AISC Equation K1-7)

[smIkarxagelIenHminRtUvkarRtYtBinitüeTRbsinebI ( ) ( ) 7.1/// >fw blth ] Edl 960000=rC enAeBlEdl yu MM < Rtg;TItaMgrbs;kmøaMg

480000= RbsinebImindUecñaHeT =l unbraced rbs;søabEdlFMCageK eTaHbICaeKeFVIsmamaRtRTnugedIm,ITb;Tl;edaypÞal;nUvbnÞúkcMcMNuck¾eday k¾CaTUeTAeKenAEt dak; bearing stiffener. RbsinebIeKmineRbI stiffener Rtg;kEnøgbnÞúkcMcMNucmanGMeBInImYy²enaH eKmin caM)ac;RtYtBinitüsßanPaBkMNt; web yielding, web crippling nig sidesway web buckling eT.

Bearing strength rbs; stiffener RtUv)an[enAkñúg AISC J8 Ca nRφ Edl 75.0=φ nig pbyn AFR 8.1= (AISC Equation J8-1)

smIkarenHKWdUcKñanwgsmIkar !0>! Edlman bearing strength yp Ff 8.1= .



AISC K1.9 TamTar[eRbI full-depth bearing stiffener CaKU ehIyviPaKvaCassrrgbnÞúk tamG½kSdUckarENnaMxageRkam³ !> muxkat;rbs;Ggát;rgbnÞúktamG½kSpSMeLIgeday stiffener plate nigRtUv)andak;sIuemRTItam

beNþayrbs;RTnug ¬emIlrUbTI 10>4¦. RbEvgenHminGacFMCag 12 dgénkRmas;RTnugeT sRmab; stiffener xagcug b¤ 25 dgénkRmas;RTnugeT sRmab; stiffener xagkñúg.

@> RbEvgRbsiT§PaBKYrykes μ Inwg 75.0 dgénRbEvgCak;Esþg Edl hKL 75.0= . Gnuvtþkarpþl;[EdlmanenAkñúg AISC Chapter E. AISC K1.9 [pgEdrnUvlkçxNÐbEnßmxageRkamsRmab; bearing stiffeners.

pleFobTTwgelIkRmas;RtUvbMeBjtRmUvkarxageRkam³

yFtb 95≥ (US)

yFtb 250≥ (IS)

TwkbnSarEdltP¢ab; stiffener eTARTnugKYrmanlT§PaBedIm,IepÞrkmøaMgkat;TTwgEdlmintémø esμ IKña. Cavi)ak eKGacKNnaTwkbnSar[RTbnÞúkcMcMNucTaMgmUl.

karviPaK bearing stiffener RtUv)anbgðajenAkñúg]TahrN_ 10>1 cMNuc (d). ]TahrN_ 10>1³ Plate girder Edl)anbgðajenAkñúgrUbTI 10>9 RtUv)anGegátedayeKarBtam AISC

Speciffication. bnÞúkCabnÞúkeFVIkarEdlmanpleFobbnÞúkGefrelIbnÞúkefresμ Inwg 3 . bnÞúkBRgayKW ftkips /4 edayrYmbBa©ÚlTaMgTm¶n;rbs; girder. søabrgkarsgát;man lateral support enARtg;cug nig

Rtg;cMNucEdlbnÞúkmanGMeBI. søabrgkarsgát;RtUv)anTb;nwgkarvilenARtg;cMNucxagelI. eK)andak; bearing stiffener dUcbgðajRtg;cug nigRtg;bnÞúkcMcMNucmanGMeBI. eKRcibEKmrbs; stiffener .1in Rtg; EKmxagkñúgTaMgelI nigeRkam edIm,IeCosTwkbnSar flange-to-web. vaminman intermediate stiffener eT ehIyEdkEdleRbITaMgGs;CaRbePTEdk 36A . edaysnμt;faTwkbnSarKWRKb;RKan; cUrRtYtBinitü

a. flexural strength b. shear strength c. flexural-shear interaction d. bearing stiffener



dMeNaHRsay³ rUbTI 10>10 bgðajdüaRkambnÞúk/ düaRkamkmøaMgkat;TTwg nigdüaRkamm:Um:g;Bt;edayQr elIbnÞúkemKuN. epÞógpÞat;témøEdl)anbgðajRtUv)anTuk[GñkGanCaGñkKit. CMhandMbUgenAkñúgkarviPaKKWkMNt;faetIGgát;enHRtUvnwgkarkMNt;rbs; AISC Ca palte girder b¤Gt; 168

8/363

==wth

7.16136

970970==

yfF

edaysar yfw Fth /970/ > dUcenH flexural member enHCa plate girder ehIyeKGacGnuvtþkar pþl;[rbs; AISC Appendix G.

RTnugRtUvEtbMeBj slenderness limitation rbs; AISC G1. témøkMNt;én wth / GaRs½yeTA nwg aspect ratio ha / . sRmab; plate girder enH bearing stiffener mannaTICa intermediate

stiffener ehIy ( ) 286.2

631212

=≈ha

pleFobenHCatémøRbhak;RbEhlBIeRBaH a minR)akdCa ft12 eT. enAkñúg panel xagkñúg ft12 CaKMlat stiffener EdlKitBIG½kSeTG½kSRbesIrCag clear spacing. sRmab; panel xagcug a KWtUcCag

ft12 edaysarEt double stiffener enARtg;TRm.



edaysar ha / FMCag 5.1 AISC A-Equation A-G1-2 lub³

( ) ( )168322

5.16363614000

5.1614000

=>=+

=+ wyfyf t

hFF

(OK) a. Flexural strength

Flexural strength nwgRtUv)ankMNt;eday strength rbs;søabrgkarTaj b¤rbs;søabkarsgát;. kñúgkrNImYyNak¾eday eKRtUvkarm:Dulmuxkat;eGLasÞic (elastic section modulus). eday sarPaBsIuemRTI xxcxt SSS == karKNnasRmab; xI m:Um:g;niclPaBeFobG½kSxøaMgRtUv)ansegçbenAkñúgtaragTI 10>1. eKmin Kitm:Um:g;niclPaBrbs;søabnImYy²eFobnwgG½kSTIRbCMuTm¶n;rbs;vaeT BIeRBaHvamantémøtUceFob nwgGgÁdéT. m:UDulmuxkat;eGLasÞicKW 3.1248

5.3240570 in

cIS x

x ===



tarag 10>1 eRKOgbgÁúM A I d 2AdI +

RTnug - 7814 - 7814

søab 16 - 32 16380

søab 16 - 32 16380

40574

eKnwgRtUvkar hybrid girder factor eR sRmab; tension flange strength nig compression

flange strength. edaysar girder enHCa nonhybrid dUcenH 0.1=eR BI AISC Equation A-G2-1, tension flange strength EdlQrelI yielding KW ( )( ) kipsftkipsinFRSM ytextn −=−=== 3744.44930360.11248 Compression flange buckling strength Edl[eday AISC Equation A-G2-2: crePGxcn FRRSM = Edl critical buckling stress crF KWQrelI lateral-torsional buckling b¤ flange local buckling. edIm,IRtYtBinitü lateral-torsional buckling, eyIgRtUvkarkaMniclPaB Tr . BIrUbTI 10>11

( )( ) ( )( ) 433 .4.3418/35.10121161

121 inI y =+=

( ) ( ) 2.94.198/35.100.116 inA =+= .138.4

94.194.341 in

AI

r yT ===

Unbraced length rbs;søabrgkarsgát;KW ft12 ehIy slenderness parameter sRmab; lateral-torsional buckling KW ( ) 80.34

138.41212

===T

brL

λ

5036

300300===

yfp F

λ



edaysar pλλ < / ksiFF yfcr 36==

Critical buckling stress crF RtUv)anKNnarYcehIysRmab; flange local buckling. Slenderness parameter EdlTak;TgKW ( ) 8

0.1216

2===

f

f

tb

λ

83.1036

6565===

yfp F

λ

mþgeTot/ edaysar pλλ < dUcenH ksiFF yfcr 36== edIm,IKNnaemKuNkat;bnßyersIusþg;rbs; palte girder PGR eKRtUvkartémørbs; ra

( )( ) 10477.1

1662.23

0.1168/363

<====f

wr A

Aa

BI AISC Equation A-G2-3

0.19703001200

1 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

crw

c

r

rPG Ft

ha

aR

( ) 9943.036

970168477.13001200

477.11 =⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

témøenHesÞIrEtesμ Inwg 0.1 edaysar flexural member enHesÞIrEtminGaccat;cMNat;fñak;Ca plate girder ehIyvaxiteTArkcMNat;fñak;Ca beam. BI AISC Equation A-G2-2, nominal

flexural strength sRmab;søabrgkarsgát;KW ( )( )( )360.19943.01248== crePGxcn FRRSM



kipsftkipsin −=−= 3723.44670 lT§plenHtUcCag nominal strength sRmab;søabrgkarTajbnþicbnþÜc dUcenHvalub. Design

strength KW ( ) kipsftM nb −== 3350372390.0φ ` BIrUbTI 10>10 m:Um:g;emKuNGtibrmaKW kipsftkipsftM u −<−= 33503168 (OK)

cemøIy³ a. Flexural strength KWRKb;RKan;. b. Shear strength

Shear strength CaGnuKmn_eTAnwg web slenderness ratio wth / nig aspect ratio ha / . dMbUgeyIgRtUvkMNt;faetIeKGaceRbI tension-field action enAkñúgtMbn;epSgBIenA end panel b¤ Gt;. eKGaceRbIva)anenAeBlEdl ha / tUcCag 0.3 nigtUcCag

( ) 395.2168260

/260 22

=⎥⎦⎤

⎢⎣⎡=⎥

⎦

⎤⎢⎣

⎡

wth

témøRbhak;RbEhlrbs; ha / KW 286.2 dUcenHeKGaceRbI tension-field action )an. kMNt; vk nig vC . BI AISC Equation A-G3-4

( ) ( )

957.5286.255

/55 22 =+=+=ha

kv

KNna vC 07.76

36957.5187187 ==

yw

vFk

19.9536957.5234234 ==

yw

vFk

edaysar ywvw Fkth /234168/ >= / enaHeKGackMNt; vC BI AISC Equation A-G3-6

( )( )

( ) ( )2580.0

36168957.544000

/44000

22 ===yww

vv

FthkC

edaysar ywvw Fkth /187/ > / eKnwgeRbI AISC A-G3-2 EdlKit tension-field action

edIm,IKNna nominal strength ¬elIkElg panel xagcug¦

( ) ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

+

−+=

2/115.1

16.0ha

CCFAV vvywwn



( )( )( )

kips6.263286.2115.1

2580.012580.03662.236.02

=⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+

−+=

Design shear strength KW ( ) kipsVnv 2376.26390.0 ==φ BIrUbTI 10>10 kmøaMgkat;emKuNGtibrmaenAkñúgRtg;cm¶aymYyPaKbYnBITRmrbs; girder KW

kips102 dUcenH shear strength KWRKb;RKan;Rtg;kEnøgEdleKGnuBaØat[eRbI tension –field

action. sRmab; panel xagcug tension-field action minRtUv)anGnuBaØat ehIyeKRtUvkMNt;

shear strength BI AISC Equation A-G3-3: ( )( )( ) kipsCFAV vywwn 6.1312580.03662.236.06.0 === Design strength KW ( ) kipsVnv 1186.13190.0 ==φ

kmøaMgkat;emKuNGtibrmaenAkñúg panel xagcug KW kipskipsVu 118234 >= (N.G.)

eKmanCeRmIsBIrsRmab;begáIn shear strength KWedaykat;bnßy web slenderness¬edaybegáIn kRmas;rbs;va¦ b¤kat;bnßy aspect ratio rbs; panel xagcugnImYy²edaybEnßm intermediate

stiffener. Stiffener RtUv)anbEnßmenAkñúg]TahrN_enH. karkat;bnßy web slenderness edIm,ITTYl)an shear strength RKb;RKan;GaceFVI[ flexural member enHcUleTAkñúgcMNat;fñak; Ca beam EdleFVI[karviPaKpøas;bþÚrTaMgRsug.

eKkMNt;TItaMgrbs; intermediate stiffener TImYytamviFIdUcteTA³ dMbUg[ shear

strength BI AISC Equation A-G3-3 es μ Inwg shear strength EdlRtUvkar ehIyedaHRsayrk témø vC EdlRtUvkar. bnÞab;mkkMNt vk BI Equation A-G3-6 nigbnÞab;mkeTotkMNt; ha / BI Equation A-G3-4. edayeFVIdUckarerobrab;xagelIeyIgTTYl)an

( )vywwvnv CFAV 6.0φφ = (AISC Equation A-G3-3) ( ) ( )( )( ) 5096.0

3662.236.09.0234

6.0===

ywwv

nvv FA

VCφ

φ

( ) yww

vv

FthkC 2/

44000=



( ) ( ) ( ) 77.1144000

361685096.044000/ 22

=== ywwvv

FthCk

( )2/

55ha

kv += (AISC Equation A-G3-4)

8594.0577.11

55

5=

−=

−=

vkha

KMlat stiffener EdlRtUvkarKW ( ) .1.54638594.08594.0 inha === eTaHbICa a RtUv)ankMNt;Ca clear spacing k¾eday eyIgnwgKitvaedaysuvtßiPaBCaKMlatBIG½kS eTAG½kS ehIydak; intermediate stiffener TImYyenAcm¶ay .54in BIcugrbs; girder. kardak; enHnwgpþl;[nUv design strength mantémøRbhak;RbEhl kmøaMgkat;emKuNGtibrma kips234 . eKminRtUvkar stiffener bEnßmeT edaysarkmøaMgkat;emKuNenAxageRkA panel xag cugtUcCag design strength kips237 . eKGacsRmYlkarkMNt;KMlat stiffener edayeRbItaragenAkñúg Numerical Value

section of the Specification. eyIgnwgbgðajbec©keTsenHenAkñúg]TahrN_ 10>2. cemøIy³ b. Shear strength KWRKb;RKan;. bEnßm intermediate stiffener mYycm¶ay .54in BIcugrbs;

girder nImYYy² c. Flexural shear interaction

eKRtUvRtYtBinitü flexural-shear interaction enAeBlEdlman tension field ¬EdleRkABI panel xagcug¦ nigenAeBlEdlbMeBllkçxNÐTaMgBIrxageRkam. !> kmøaMgkat;TTwgsßitenAcenøaH nun VVV φφ ≤≤6.0 sRmab; girder enH kmøaMgkat;TTwgeRkABI panel xagcugKW ( ) 2372376.0 ≤≤ uV

237142 ≤≤ uV @> m:Um:g;Bt;emKuNsßitenAcenøaH nun MMM φφ ≤≤75.0 sRmab; girder enH ( ) 3350335075.0 ≤≤ uM



33502510 ≤≤ uM tamkarGegátelIrUbbgðajfavaminmanbnSMénkmøaMgkat; nigm:Um:g;Bt;EdlbMeBjlkç-

xNÐTaMgenHeT. cemøIy³ c. eKminRtUvkarRtYtBinitü flexural-shear interaction eT.

d. Bearing stiffener

eKpþl;nUv bearing stiffener enARtg;bnÞúkcMcMNucmanGMeBInImYy² dUcenHeKminRtUvkarRtYtBinitü karpþl;[rbs; AISC Chapter K sRmab; web yielding, web crippling b¤ sidesway web

buckling eT. sRmab; bearing stiffener enAxagkñúg nigenAelITRm 0.10

75.05.7==

tb

0.108.1536

9595>==

yF (OK)

sRmab; bearing stiffener xagkñúg dMbUgKNna bearing strength. BIrUbTI 10>12 ( )( ) 2.750.975.015.722 inatApb =−==

BI AISC Equation J8-1, ( )( ) kipsAFR Pbyn 8.631750.9368.18.1 === ( ) kipskipsRn 604748.63175.0 >==φ (OK)



RtYtBinitüersIusþg;rbs; stiffener CaGgát;rgkarsgát;. eyagtamrUbTI 10>12 eyIgGaceRbIRb EvgRTnug .375.9 in Edl[RkLaépÞmuxkat;sRmab;ssr ( )( ) ( )( ) 2.77.1475.98/35.775.02 inA =+= m:Um:g;niclPaBrbs;RkLaépÞenHeFobnwgG½kSenAelIRTnugKW ( )2AdII +∑=

( ) ( ) ( ) 4233

.2.22728/3

25.775.05.7

125.775.02

128/3375.9 in=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +++=

ehIykaMniclPaBKW .922.3

77.142.227 in

AIr ===

Slenderness ratio KW ( ) 05.12

922.36375.0

===r

Khr

KL BI AISC Table 3-36 enAkñúg Numerical Values section of the Specification, ksiFcrc 37.30=φ nig ( ) kipskipsAFP crcnc 6044977.1437.30 >=== φφ (OK) BIrUbTI 10>13/ sRmab; bearing stiffener enARtg;TRm design bearing strength KW ( ) ( )( ) ( )( )[ ] kipskipsAFR pbyn 23494875.05.64368.175.08.1 >===φφ (OK)

RtYtBinitü stiffener-web assembly CaGgát;rgkarsgát;. eyagtamrUbTI 10>13 m:Um:g;nicl PaBeFobG½kSenAkñúgbøg;rbs;RTnugKW

( )2AdII +∑= ( ) ( ) ( ) 4

233.3.454

28/3

25.775.05.7

125.775.04

128/35.4 in=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +++=

ehIyRkLaépÞ nigkaMniclPaBKW ( ) ( )( ) 219.245.775.048/35.4 inA =+= nig .334.4

19.243.454 in

AIr ===



Slenderness ration KW ( ) 90.10

334.46375.0

==r

Kh BI AISC Table 3-36, kipsFcrc 41.30=φ . Design strength KW ( ) kipskipsAFP crcnc 23473619.2441.30 >=== φφ (OK) cemøIy³ d. Bearing stiffener KWRKb;RKan;. 10>8> kaKNnamuxkat; (Design) kic©kardMbUgkñúgkarKNna plate girder KWkarkMNt;TMhMrbs;RTnug nigsøab. RbsinebIeKRtUvkar GBaØtiCam:Um:g;niclPaB eKRtUveRCIserIsykviFIbMErbMrYlTMhMsøabedayeRbI cover plate b¤kRmas;rbs; søabmanTMhMxusKñaenATItaMgepSgKñatambeNþayrbs; girder. karsMercedayeRbI intermediate

stiffener BIeRBaHvaCH\T§iBldl;kRmas;RTnug. RbsinebIeKRtUvkar bearing stiffener dac;xateKRtUvEt KNnava. cugeRkay bgÁúMepSg²RtUv)antP¢ab;edaykarKNnaTWkbnSary:agRtwmRtUv. xageRkamCa CMhankñúgkarKNna³ !> eRCIserIskm<s;srub



Girder EdlmansmamaRtl¥RtUvmankm<s;esμ Inwg 10/1 eTA 12/1 énRbEvgElVg. karkMNt; rbs; building code elI depth-to span ration b¤PaBdabGacman\T§iBlelIkkareRCIserIs.

@> eRCIserIsTMhMRTnugsakl,g eKGacKNnakm<s;RTnugedaydkkRmas;søabTaMgBIrBIkm<s;srubEdl)aneRCIserIs. Cak; Esþg dMNak;kalénkarKNnaenH eKRtUvEt)a:n;sμankRmas;søab. eKGacrkkRmas;RTnug

wt edayeRbIkarkMNt;xageRkam³

yfw Fth 2000= (US)

yfw Fth 5250= (IS) (AISC Equation A-G1-1)

sRmab; 5.1/ >ha ( )5.16

14000+

=yfyfw FFt

h (US) (AISC Equation A-G1-2)

( )11496530

+=

yfyfw FFth (IS)

#> )a:n;s μanTMhMsøab eKGac)a:n;s μanRkLaépÞsøabEdlRtUvkarBIrUbmnþFmμtaEdlbMEbkdUcxageRkam. yk

flangeswebx III += ( )2323 2/2

1212

121 hAhtyAht fwfw +≈+≈

Edl =fA muxkat;RkLaépÞrbs;søabmYy =y cm¶ayBIG½kSNWteGLasÞiceTATIRbCMuTm¶n;rbs;søab karcUlrYmrbs;m:Um:g;niclPaBénsøabnImYy²eFobnwgG½kSTIRbCMuTm¶n;rbs;vaRtUv)anecalenA kñúgsmIkar !0$>. eKGac)a:n;s μanm:UDulmuxkat;

( )hAht

hhA

hht

cIS f

wfwxx +=+≈=

62/2/2

2/12/ 223

RbsinebIeyIgsnμt;karKNnayktam compression flange buckling eyIgk¾Gacrkm:UDul muxkat;BI AISC Equation A-G2-2:

crePGxcn FRRSM =

crePG

bu

crePG

nxc FRR

MFRR

MS φ/==



Edl uM Cam:Um:g;Bt;emKuNGtibrma. eday[m:UDulmuxkat;EdlRtUvkaresμ InwgtémøRb hak;RbEhl eyIg)an hAht

FRR fw

crePG

bu +=Μ

6/ 2φ

nig 6ht

FRhRMA w

crePGb

uf −=

φ

RbsinebIeyIgsnμt;fa 0.1=PGR / 0.1=eR nig ycr FF = muxkat;EdlRtUvkarrbs;søab mYyKW

69.0w

y

uf

AhF

MA −=

Edl wA CaRkLaépÞRTnug. enAeBlEdleKkMNt;RkLaépÞsøamEdlRtUvkarrYcehIy eRCIs erIsTTwg nigkRmas;. RbsinebIeKeRbIkRmas;kñúgkar)a:n;s μankm<s;RTnug dUcenHeKmincaM)ac; eFVIkarEktRmUvkm<s;RTnugeT. Rtg;cMNucenH eKGacKNnaTm¶n;)a:n;sμanrbs; girder, ehIy eKRtUvkMNt; uM nig fA eLIgvij.

$> RtYtBinitü bending strength rbs;muxkat;sakl,g. %> RtYtBinitükmøaMgkat;

RbsinebIeKBicarNa end panel b¤RbsinebIeKmineRbI intermediate stiffener eTenaH eK Gacrk shear strength BI AISC Equation A-G3-3 Edl[ersIusþg;edayK μanvtþman rbs; tension field. eKk¾GaceRbI Table 9-36 b¤ 9-50 enAkñúg Numerical Values section of

the Specification sRmab;karKNnaenHEdr. RbsinebIeKmineRbItarag eKGackMNt;KMlat Intermediate dUcxageRkam³ a. [ shear strength EdlRtUvkares μ Inwg shear strength Edl[eday AISC Equation

A-G3-3 ehIyedaHRsayrktémø vC EdlRtUvkar. b. edaHRsayrk vk BI AISC Equation A-G3-5 b¤ A-G3-6 c. edaHRsayrktémø ha / BI AISC Equation A-G3-4. RbsinebIeKeRbI tension-fieal

action eKGaceRbI trial-and-error approach b¤ AISC Table 10-36 b¤ 10-50 edIm,I TTYl ha / EdlRtUvkar. RkLaépÞmuxkat;EdlRtUvkarrbs; stiffener EdlsMEdgCaPaK ryénRkLaépÞRTnugk¾RtUv)an[enAkñúgtaragsRmab;témøxøHén wth / nig ha / .



eRCIserIsTMhM stiffener sakl,gEdlbMeBjRkLaépÞtRmUvkar ehIyRtYtBinitüm:Um:g;ni- clPaBtRmUvkarrbs; AISC Appendix F.3.

^> RtYtBinitüGnþrGMeBIénkmøaMgkat; nigm:Um:g;Bt; &> RtYtBinitü web resistance sRmab;bnÞúkcMcMNuc (web yielding, web crippling nig web

sidesway buckling) RbsinebIeKRtUvkar bearing stiffener eKRtUvGnuvtþviFIsaRsþKNnaxageRkam³ a. sakl,gTTwgEdlRCugEKmrbs; stiffener enAEk,rEKmrbs;søab nigkRmas;EdlbMeBj

tRmUvkar width-thickness ratio

yFtb 95≤ (US)

yFtb 250≤ (IS)

b. KNnaRkLaépÞmuxkat;EdlRtUvkarsRmab; bearing strength. eRbobeFobRkLaépÞenH CamYynwgRkLaépÞsakl,g nigeFVIkarKNnaeLIgvijRbsinebIcaM)ac;.

c. RtYtBinitü stiffener-web assembly CaGgát;rgkarsgát;. *> KNnaTwkbnSar flange-to-web, TwkbnSar stiffener-to-web nigkartP©ab;epSgeTot

¬flange segment, web splices>>>¦ ]TahrN_ 10>2³ KNna plate girder TRmsamBaØEdlmanRbEvg ft60 nigRTbnÞúkeFVIkardUcEdl)an bgðajenAkñúgrUbTI 10>14 a. km<s;rbs; plate girder GnuBaØatGtibrmaKW .65in . eRbIEdk 36A nig

electrode XXE70 ehIysn μt;fa girder enHman lateral support Cab;. cug girder manTRmRbePT bearing ehIyminRtUv)an frame. dMeNaHRsay³ bnÞúkemKuNedayminKitTm¶n; girder RtUv)anbgðajenAkñúgrUbTI 10>14b. kMNt;km<s;srub ( ) .72

101260

10lengthSpan in==

( ) .6012

126012lengthSpan in==

eRbIkm<s;GnuBaØatGtibrma .65in sakl,gkRmas;søab .5.1 int f = nigkm<s;RTnug ( ) .625.1260 inh =−=



edIm,IkMNt;kRmas;RTnug dMbUgRtYtBinitütémøkMNt;rbs; wth / . sRmab; flexural member

EdlmanlkçN³Ca plate girder 7.161

36970970

==≥yfw Ft

h

.383.07.161

627.161

inhtw ==≤ BI AISC Equation A-G1-1 nig A-G1-2: sRmab; 5.1./ ≤ha 3.333

3620002000

==≤yfw Ft

h

.186.03.333

62 intw =≥ sRmab; 5.1/ >ha ( ) ( )

0.3225.163636

140005.16

14000=

+=

+≤

yfyfw FFth

.192.00.322

62 intw =≥



sakl,g web plate 6241 × . kMNt;TMhMsøabEdlRtUvkar. BIrUbTI 10>14 b m:Um:g;

Bt;emKuNGtibrmaKW ( ) ( ) kipsftM u −=+= 4614

86004.4

4604.186 2

BIsmIkar !0>% RkLaépÞsøabEdlRtUvkarKW

690.0w

y

uf

AhF

MA −= ( )

( )( )( ) 2.98.246

4/162366290.0

124614 in=−=

KNnaTm¶n; girder

RkLaépÞRTnug³ ( ) =4/162 2.5.15 in RkLaépÞsøab³ ( ) =98.242 2.96.49 in srub 2.46.65 in

Tm¶n;³ ( ) ftlb /7.222490144

46.65= yk ftlb /250

m:Um:g;Bt;EktRmUvKW ( )( ) kipsftM u −=

×+= 4749

860250.02.14614

2

ehIyRkLaépÞsøabEdlRtUvkarKW ( )

( )( )( ) 2.79.256

4/162366290.0

124749 inAf =−=

RbsinebIenArkSaTukkRmas;søabsnμt; enaHTTwgRtUvkarrbs;vaKW .2.17

5.179.25 in

tA

bf

ff ===

sakl,g flange plate 181 21 × . rUbTI 10>15 bgðajBImuxkat;sakl,g ehIyrUbTI 10>16

bgðajBIdüaRkamkmøaMgkat; nigdüaRkamm:Um:g;Bt;sRmab;bnÞúkemKuN EdlrYmbBa©ÚlTaMgTm¶n; girder Rb hak;RbEhl ftlb /250 .



RtYtBinitü flexural strength rbs;muxkat;sakl,g. BIrUbTI 10>15 m:Um:g;niclPaBeFobG½kS rbs;karBt;KW



( )( ) ( )( )( ) 423

.5940075.31185.1212

624/1 inI x =+= ehIym:UDulmuxkat;eGLasÞicKW 3.1828

5.3259400 in

cIS x

x === karRtYtBinitüén AISC Equation A-G2-1 nig A-G2-2 bgðajfasRmab; nonhybrid girder

Edlmanmuxkat;sIuemRTI enaH flexural strength nwgmingaylubeday tension flange

yielding dUcenH eKRtUvEtGegátEt compression flange buckling b:ueNÑaH. elIsBIenH edaysarEt girder enHman lateral support Cab; eKk¾mincaM)ac;BicarNaBI lateral-torsional

buckling Edr. sRmab;sßanPaBkMNt; én flange local buckling ( ) 6

5.1218

2===

f

f

tb

λ

83.1036

6565===

yfp F

λ

edaysarEt pλλ < / ksiFF yfcr 36== eKRtUvkartémøxageRkamsRmab;kMNt;emKuNkat;bnßyersIusþg; PGR ³ 2.5.15

4160 inAw =⎟⎠⎞

⎜⎝⎛=

( ) 2.275.118 inAf == 105741.0

275.15

<===f

wr A

Aa

2484/1

62==

wth

BI AISC Eqution A-G2-3/

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

crwr

rPG Ft

ha

aR 9703001200

1

( ) 9639.036

9702485741.03001200

5741.01 =⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

BI AISC Equation A-G2-2/ nominal flexural strength KW crePGxcn FRRSM =



( )( )( ) kipsftkipsin −=−== 5386.63430360.19639.01828 ehIy design sstrength KW ( ) kipsftkipsftM nb −>−== 4749475752869.0φ (OK) RtYtBinitü shear strength. kmøaMgkat;GtibrmamantémøGtibrmaenARtg;TRm

b:uEnþeKminGaceRbI vaenA end panel. eyIgnwgeRbI Table 9-36 enAkñúg Numerical Values

section of the Spec-sification edIm,ITTYl)anTMhM end panel EdlRtUvkar. eKRtUvbBa©ÚleTAkñúgtaragCamYynwg .248/ inth w = nig

ksiAV

w

nv 41.145.154.223==

φ

témøenHTamTar 5.0/ <ha ehIyvasßitenAeRkAtémørbs;taragEdlbBa¢ak;faeKminRtUvkar kRmas;RTnugeT. sakl,gRTnug 6216

5 × 4.198

16/562

==wth

2.38.1916562 inAw =⎟⎠⎞

⎜⎝⎛=

ksiAV

w

nv 5.1138.19

4.223==

φ

BI AISC Table 9-36/ sRmab; 198/ =wth nig 6.0/ =ha témørbs; wnv AV /φ Edl)aneFVI interpolation rYcKW ksi5.11 . dUcenH yk 6.0/ =ha nig ( ) .2.37626.06.0 inha === eTaHbICacm¶ay a EdlRtUvkarCa clear spacing k¾eday k¾kareRbIcm¶ayBIG½kSeTAG½kSman lkçN³samBaØCag nigsuvtßiPaBCagbnþicbnþÜc. ykcm¶ay .36in BIG½kSrbs; bearing

stiffener xagcugeTAG½kSrbs; intermediate stiffener. munnwgeFVIkarviPaK shear strength/ kMNt;\T§iBlénkarpøas;bþÚrkRmas;RTnug. dMbUg kMNt;Tm¶n; girder

RkLaépÞRTnug³ ( ) =16/562 2.38.19 in RkLaépÞsøab³ ( )( ) =185.12 2.00.54 in srub 2.38.73 in

Tm¶n;³ ( ) ftlb /250490144

38.73= ¬dUcKñanwgkarsnμt;BImun¦



bnÞab;mk ( )( ) ( )( )( ) 423

.6064075.31185.1212

6216/5 inI x =+=

3.18665.32

60640 incIS x

x ===

107178.027

38.19<===

f

wr A

Aa

BI AISC Equation A-G2-3/

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

crw

c

r

rPG Ft

ha

aR 9703001200

1

( ) 9814.036

9704.1987178.03001200

7178.01 =⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

Nominal flexural strength KW crePGxcn FRRSM =

( )( )( )( ) kipsftkipsin −=−== 5494.65930360.19814.01866 Design strength KW ( ) kipsftM nb −== 4944549490.0φ eTaHbICaersIusþg;enHFMCagtRmUvkarbnþicbnþÜck¾eday vanwgTUTat;CamYynwgTm¶n;rbs; stiffener

nig eRKOgbgÁúMdéTeTotEdleyIgmin)anKit. cemøIy³ eRbIRTnug 6216

5 × nigsøab 181 21 × dUcbgðajenAkñúgrUbTI 10>17.

kMNt;KMlat intermediate stiffener EdlRtUvkarsRmab; shear strength BIeRkA end panel. enA cm¶ay .36in BIcugxageqVg kmøaMgkat;KW kipsVu 4.210

123634.44.223 =⎟

⎠⎞

⎜⎝⎛−=

ksiAV

w

nv 86.1038.19

4.210==

φ

eKk¾GaceRbI tension-field action BIeRkA end panel dUcenHeKeRbI AISC Table 10-36. sRmab; 200/ =wth nig 6.1/ =ha ksiksi

AV

w

nv 86.102.11 >=φ (OK)

eRbI 6.1/ =ha enaH ( ) .2.99626.16.1 inha ===



cMNaMfaminmantémøNaRtUv)an[enAkñúgtaragenAeBlEdl 200/ =wth nig 6.1/ =ha eT. mUlehtuKWfa tension-field action minRtUv)anGnuBaØatenAeBlEdl

( ) 69.1200260

/260 22

=⎟⎠⎞

⎜⎝⎛=⎥

⎦

⎤⎢⎣

⎡>

wthha

sRmab;mUlehtuenH KMlat stiffener Gtibrma in2.99 nigGnuvtþsRmab;EpñkenAsl;rbs; girder b:uEnþedIm,ITTYl)anKMlatesμ IcenøaH end panel eKRtUveRbIKMlatBIG½kSeTAG½kS .81in dUcbgðajkñúgrUbTI 10>18. CamYynwgKMlatEdlkat;bnßyenH 306.1

6281

==ha

edIm,IKNna shear strength EdlRtUvKña eKbBa©Últémø 3.1/ =ha nig 200/ =wth eTAkñúg Table 10-36. edayeFVI interpolation eKTTYl)an 6.12=

w

nvAVφ

nig ( ) kipsAV wnv 2.24438.196.126.12 ===φ



muxkat;rbs; intermediate stiffener KWQrelIlkçxNÐbI³ (1) RkLaépÞGb,brma/ (2) m:Um:g;niclPaBGb,brma nig (3) pleFobTTwgelIkRmas;Gb,brma.

RkLaépÞEdlRtUvkarsRmab; stiffener KUKWCaGnuKmn_én wth / nig ha / ehIyeKGac rkva)anBI AISC Table 10-36 edayeFVI interpolatrion.

sRmab; 3.1/ =ha nig 200/ =wth / %3.2=stA énRkLaépÞrbs;RTnug

( ) 2.556.038.19023.0 in== BI AISC Equation A-F2-4/

( )5.02

/5.2

2 ≥−=ha

j

( )534.02

306.15.2

2 −=−=

edaytémørbs; 5.0<j dUcenHeRbI 5.0=j m:Um:g;niclPaBEdlRtUvkarKW ( ) ( ) 433 .24.15.016/581 injatI wst === eRbItémøGtibrmarbs; tb / 8.15

369595

==yF

sakl,g plate 441 × cMnYnBIr

8.15164/1

4≈==

tb (OK)

stA Edl[KW ( ) 22 .446.0.0.24142 inin >=⎟⎠⎞

⎜⎝⎛ (OK)



BIrUbTI 10>19 nigRTwsþIbTG½kSRsb eyIg)an ( )2AdII st ×∑=

( ) ( )( ) 4423

.24.1.97.11232/52425.012

425.0 inin >=×⎥⎥⎦

⎤

⎢⎢⎣

⎡++= (OK)

edIm,IkMNt;RbEvgrbs; stiffener dMbUgkMNt;cm¶ayrvag stiffener-to-web weld nig web-to-

flange weld ¬emIlrUbTI 10>8¦ cm¶ayGb,brma .25.1

16544 intw =⎟⎠⎞

⎜⎝⎛==

cm¶ayGtibrma .875.116566 intw =⎟⎠⎞

⎜⎝⎛==

RbsinebIeyIgsnμt;TMhM flange-to-web weld .165 in nigcm¶ayrvagTwkbnSar .25.1 in RbEvg

Rbhak;RbEhlrbs; stiffener KW −h TMhMTwkbnSar .44.6025.13125.06225.1 in=−−=− yk .60in cemøIy³ eRbI plate ftinin 5.4.4

1 ×× sRmab; intermesiate stiffener. RtYtBinitüGnþrGMeBIrbs;m:Um:g;Bt; nigkmøaMgkat; EdlRtUvkarsRmab;EtkEnøgNaEdlRtUvkar

tension field. témørbs;kmøaMgkat;EdlRtUveFVIkarGegátKW nun VVV φφ ≤≤6.0 b¤ ( ) 2.2442.2446.0 ≤≤ nV

2.2445.146 ≤≤ nV témørbs;m:Um:g;Bt;EdlRtUvRtYtBinitüKW



nun MMM φφ ≤≤75.0 b¤ ( ) 4944494475.0 ≤≤ uM 49443708 ≤≤ uM

BIrUbTI 10>16/ kipsVu 5.146= enAeBlEdl kipsx 5.1463.44.223 =− Edl =x cm¶ayBIcugxageqVgrbs; girder ft72.17= enARtg;TItaMgdUcKña m:Um:g;Bt;KW ( ) ( ) kipsftM u −=−= 3277

272.1734.472.174.223

2

enAkñúgtMbn;EdlkmøaMgkat;FMCag kips5.146 m:Um:gBt;tUcCag kipsft −3708 dUcenHeKmin caM)ac;BicarNaGnþrGMeBIénm:Um:g;Bt; nigkmøaMgkat;eT.

eKnwgdak; bearing stiffener Rtg;TRm nigRtg;kNþalElVg. edaysarvaman stiffener

enARtg;kEnøgbnÞúkcMcMNucmanGMeBInImYy² dUcenHeKminRtUvkarGegátPaBFn;rbs;RTnugeTAnwg bnÞúkTaMgenHeT. RbsinebImindak; stiffener eTenaH eKRtUvkarBarRTnugBI yielding nig crippling. edIm,IeFVIdUcenH eKRtUvkarRbEvg bearing N RKb;RKan;EdlTamTareday AISC

Equation K1-2 rhUtdl; K1-5. Sidesway web buckling minmanCasßanPaBkMNt;Edl GacekItmaneT BIeRBaH girder enHman lateral support Cab; ¬EdleFVI[ unbraced length

0=l nig ( )( ) 3.2// >fw blth ¦. sakl,gTTwg stiffener .8inb = . TTwgsrubnwgesμ I ( ) .31.1616/582 in=+ EdltUc

CagTTwgsøab .18in bnþic. BI AISC K1.9

yFt

b 95≤ b¤ .505.0

95368

95in

Fbt y

==≥

sakl,g stiffener 843 × BIr. snμt; web-to-flange weld .16

5 in nig cutout enAkñúg stiffener .2

1 in . RtYtBinitü stiffener enARtg;TRm. Bearing strength KW ( )pbyn AFR 8.175.0=φ

( )( )( )( ) kipskips 4.22354725.0875.0368.175.0 >=×−= RtYtBinitü stiffener Cassr. RbEvgrbs;RTnugEdleFVIkarCamYynwg stiffener plate edIm,IbegáIt

CaGgát;rgkarsgát;KWesμ Inwg 12 dgénkRmas;RTnugsRmab; end stiffener (AISC K1.9). dUc



Edl)aneXIjenAkñúgrUbTI 10>20 RbEvgenHKW ( ) .75.316/512 in= . edaysar stiffener RtUv manTItaMgenARtg;kNþalénRbEvgenH/ cMNucTRm ¬TItaMgrbs;Rbtikmμrbs; girder¦ RtUvEtman témøRbhak;RbEhlnwg .875.12/75.3 in= BIcugrbs; girder. dUcEdlbgðajenAkñúgrUbTI 10>21 b:uEnþQrelIkarKNnaenAelIRbEvgsrubrbs;RTnug in75.3 eKnwgTTYl)an

( ) ( ) 2.17.1375.3

165

4382 inA =⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

( ) ( ) 4233

.3.2713254

438

12875.02

1216/575.3 inI =

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛++=

.539.417.13

3.271 inAIr ===

( ) 24.10539.4

6275.0===

rKh

rKL

BI AISC Table 3-36/ ksiFcrc 43.30=φ . Design strength KW ( ) kipskipsAFP crcnc 4.22340117.1343.30 >=== φφ (OK) edaysarbnÞúkenAkNþalElVgtUcCagRbtikmμ eRbI stiffener dUcKñaenAkNþalElVg cemøIy³ eRbI plate 84

3 × BIrsRmab; bearing stiffener.



Rtg;cMNucenH RKb;eRKOgpÁúMrbs; girder TaMgGs;RtUv)ankMNt;TMhM. \LÚveyIgRtUveFVIkarsikSaBI kartP¢ab;. eKeRbI electroce XXE70 Edlman design strength ksiFw 5.31=φ . sRmab;karpSarsøabeTAnwgRTnug (flange-to-web weld) KNnakmøaMgkat;TTwgenARtg; kEnøgCYbKñarvagsøab nigRTnug³ témøGtibrmarbs; kipsVu 4.223= =Q RkLaépÞsøab 75.31× ¬emIlrUbTI 10>17¦

( )( ) 3.2.85775.31185.1 in== 4.60640inI x = témøGtibrmarbs; ( ) ./158.3

606402.8574.223 inkips

IQV

x

u ==

TMhMTwkbnSarGb,brma w sRmab;kRmas;bnÞHEdkEdlRtUvpSarKW .165 in .

RbsineKpSarminCab; RbEvgTwkbnSarGb,brmarbs;vaKW³ .5.14min inwL ≥×=

.25.11654 in=⎟⎠⎞

⎜⎝⎛= dUcenHyk in5.1

sakl,g fillet weld .1. 21

165 inin ×

lT§PaBkñúg 2707.0.1 ×××= WFwin φ ( )( )( ) ./92.1325.3116/5707.0 inkips==

lT§PaBTb;kmøaMgkat;rbs; base metal



( ) ( )[ ] ( ) ( )( )3654.016554.060.090.0 ⎟⎠⎞

⎜⎝⎛=== yyBM FtFtFt φ

./92.13./075.6 inkipsinkips <= eRbIersIusþg;TwkbnSarsrub ./075.6 inkips . ersIusþg;TwkbnSarmYyKURbEvg .5.1 in kips112.95.1075.6 =× edIm,IkMNt;KMlat/ yk

x

uI

QVs

=112.9

Edl s CaKMlatEdlKitBIG½kSeTAG½kSrbs;TwkbnSarKitCa .in ehIy .89.2

158.3112.9

/112.9 in

IQVs

xu===

edayeRbIKMlatBIG½kSeTAG½kS .75.2 in eyIgnwgTTYl)an clear spacing .25.15.175.2 in=− . AISC Specification [nUvKMlatminCab;GnuBaØatGtibrmarbs; fillet weld sRmab;karGnuvtþ enAkñúg Section B10, “Proportions of Beams and Girders”. karpþl;[sRmab; built-up

compression members (AISC E4) nig built-up tension members (AISC D2) RtUv)aneK eRbIsRmab;kartP¢ab;søabrgkarsgát; nigsøabrgkarTaj. sRmab;karsgát;

yFtd 127

≤ b:uEnþminRtUvFMCag .12in

sRmab;karTaj td 24≤ b:uEnþminRtUvFMCag .12in Edl =d clear spacing KitCa .in =t kRmas;rbs;bnÞHEdlRtUvpSarEdlesþIgCageKenAkñúg built-up shape edayGnuvtþkarkMNt;TaMgenH eyIg)an ( ) .12.8.31

365.1127127 inin

Ft

y>==

( ) .12.365.12424 inint >== dUcenH Clear spacing GnuBaØatGtibrmaKW .12in ehIy clear spacing EdlRtUvkar .25.1 in KW

RKb;RKan;.



eTaHbICaeKeRbIKMlatBIG½kSeTAG½kS .75.2 in sRmab;RbEvgTaMgmUlrbs; girder k¾eday k¾eKGacbegáInKMlatenHRtg;kEnøgNaEdlkmøaMgkat;tUcCagtémøGtibrma kips4.223 . eyIg nwg GegátKMlatbIepSgKña

!> KMlattRmUvkarEdlCitCageK .75.2 in @> KMlatBIG½kSeTAG½kSGnuBaØatGtibrma .5.135.112 in=+ #> Intermediate spacing .5in enAeBleyIgeRbIKMlat .5in

sIQV

x

u 112.9= b¤ ( ) ( ) kipsI

QsV xu 9.12860640

52.857112.9112.9

===

eyagtamrUbTI 10>16 nig[ x Cacm¶ayBITRmxageqVg eKTTYl)an kipsxVu 9.12834.44.223 =−= ftx 77.21= enAeBleKeRbIKMlat .5.13 in ( )

( ) kipsQs

IV xu 75.47

5.132.85760640112.9112.9

===

rUbTI 10>16 bgðajfaminmankmøaMgkat;EdlmantémøtUcEbbenHeT dUcenHeKminGaceRbIKMlat Gtibrma)aneT.

cemøIy³ eRbI fillert weld .1. 21

165 inin × sRmab; flange-to-web weblds CamYynwgKMlatdUcbgðaj

enAkñúgrUbTI 10>22.



sRmab; intermediate stiffener welds: TMhMTwkbnSarGb,brma .

163 in= ¬edayQrelIkRmas; .16

5 intw = nig .41 int = ¦

RbEvgGb,brma .5.1.75.01634 inin <=⎟⎠⎞

⎜⎝⎛= yk 5.1

lT§PaBrbs;TwkbnSarkñúg .1in sRmab;TwkbnSar 4 ¬ 2 sRmab; stiffener plate mYy¦ ( )( ) ./70.1645.31

163707.0 inkips=⎟⎠⎞

⎜⎝⎛

lT§PaBkmøaMgkat;rbs; base metal KW ./075.6 inkips ¬emIlkarKNnaxagelIsRmab; .16

5 int = ¦ BIsmIkar !0>3 kmøaMgkat;EdlRtUvKW

( ) ( ) ./539.3290003662045.0045.0

33

inkipsE

Fhf y ===

eRbITwkbnSardac;. lT§PaBrbs;TwkbnSar 4 EdlmYy²manRbEvg .5.1 in ( ) kips112.9075.65.1 = [ersIusþg;kmøaMgkat;kñúg .1in esμ InwgersIusþg;EdlRtUvkar eKTTYl)an ./539.3112.9 inkips

s= b¤ .57.2 ins =

BI AISC Appendix F2.3 clear spacing Gtib,rmaesμ Inwg 16dgkRmas;RTnug b:uEnþminFMCag .10in b¤

.51651616 intw =⎟⎠⎞

⎜⎝⎛=

eRbIKMlatBIG½kSeTAG½kS .5.2 in Edl clear spacing EdleKTTYl)anKW .5.15.15.2 inin <=− (OK)

cemøIy³ eRbI fillet welds 21

163 1× sRmab; intermediate stiffeners

EdlmanKMlatdUcbgðajenAkñúgrUbTI 10>23. sRmab; bearing stiffener welds³

TMhMGb,brma .165 in ¬edayQrelIkRmas; .16

5 intw = nig .43 int = ¦

RbEvgGb,brma .5.1.25.11654 inin <=⎟⎠⎞

⎜⎝⎛= yk 5.1



eRbITwkbnSarBIrsRmab; stiffener mYy dUcenHsrubmanTwkbnSar 4 . dUcKñanwg intermediate

stiffener ersIusþg;kmøaMgkat;rbs; base metal ./075.6 inkips nwgkMNt;ersIusþg;rbs;TwkbnSar b¤ kips112.9 sRmab;TwkbnSarRbEvg .5.1 in .

sRmab; end bearing stiffener bnÞúkEdlGnuvtþkñúg .1in KW ( ) ./662.3

5.02624.223

for weld avaiblelength reaction inkips=

−=

BI 662.3112.9=

s eK)an .49.2 ins =

cemøIy³ eRbI fillet weld 21

163 1× sRmab; bearing stiffener TaMgGs; EdlKMlatRtUv)anbgðajenA

kñúgrUb TI 10>24.

Girder Edl)anKNnaenAkñúg]TahrN_enHminmanlkçN³esdækic©eT. lT§PaBepSgeTotKW girder

EdlmanRTnugesþIgCag ehIyeKeRbI intermediate eRcInCag nigmYyeTotKW girder EdlmanRTnugRkas; Cag ehIyGt;eRbI intermediate stiffener. ktþaEdlb:HBal;dl;lkçN³esdækic©rYmmanTm¶n; ¬maDrbs;



EdkEdlRtUvkar¦ nigtémøkñúgkartMeLIg. eTaHbICa girder Edlman intermedaite EtgEtRtUvkarEdk tick¾eday k¾karbnSMenHGacbEnßmedaytémøénkardMeLIgEdr. kRmas;søabk¾eKGacykmkBicarNa pgEdr. CeRmIsTaMgenHsuT§EtsnSMsMécTm¶n; b:EnþeKk¾RtUvBicarNaBItémøkñúgkartMeLIgEdr. viFIEdleK GnuvtþedIm,ITTYl)annUvkarKNnaEdlmanlkçN³esdækic©KWkarsikSaCeRmIseRcIn ehIyeFVIkareRbob eFobtémørbs;va edayeRbIkar)a:n;s μansMPar³ nigtémøénkartMeLIg. Design of Welded Structures

(Blodgett, 1996) pþl;nUvsMNUmBrEdlmanRbeyaCn_CaeRcInsRmab;karKNna welded plate girder EdlmanlkçN³esdækic©.


T.Chhay 478 Appendix A

Appendix A. karKNna nigkarviPaKedaylkçN³)aøsÞic Plastic Analysis and Design

A>1> esckþIepþIm (Introduction) eyIg)anENnaMBIKMniténkar)ak;eday)aøsÞic (plastic collapse) enAkñúgkfaxNÐ 5>2/“ kug taMgBt; nigm:Um:g; ”)aøsÞic . kar)ak;rbs;eRKOgbgÁúMnwgekIteLIgenAeBlbnÞúkbegáItsnøak;)aøsÞicRKb;RKan; edIm,IbegáItCa mechanism EdlnwgeFVI[manPaBdabedayminmankarekIneLIgbnÞúk. enAkñúgFñwmEdl kMNt;edaysþaTic eKRtUvkarEtsnøak;)aøsÞicmYyEtb:ueNÑaH. dUcbgðajenAkñúgrUbTI A>1 snøak;nwgekIt manenAkEnøgNaEdlmanm:Um:g;Gtibrma ¬krNIenHKWenAkNþalElVg¦. enAeBlEdlm:Um:g;Bt;mantémø FMRKb;RKan;edIm,IeFVI[muxkat;TaMgmUl yield/ enaHvaminGacTb;nwgkarekIneLIgrbs;m:Um:g;EfmeTot ehIy snøak;)aøsÞick¾RtUv)anbegáIteLIg. snøak;)aøsÞicenHRsedogKñanwgsnøak;Fm μtaEdr EtxusRtg;fasnøak; )aøsÞicmanlT§PaBTb;nwgm:Um:g;xøH EdldUcKñay:agxøaMgnwg rusty hinge. lT§PaBm:Um:g;)aøsÞic (plastic moment capacity) EdlsMKal;eday pM Cam:Um:g;Bt;EdlekIt manenARtg;snøak;)aøsÞic. vamantémøes μ Inwgm:Um:g;Tb;xagkñúgEdlekItBIkarEbgEckkugRtaMgEdlbgðaj enAkñúgrUbTI A>1 c EtmanTisedApÞúyKña. eKGackMNt;m:Um:g;)aøsÞicenAeBlEdleKsÁal; yield stress nigrUbragmuxkat; dUcbgðajenAkñúgrUbTI A>2. RbsinebIkarEbgEckkugRtaMgenAkñúglkçxNÐ)aøsÞiceBj RtUv)anCMnYsedaykmøaMgsmmUlsþaTicBIrEdlmantémødUcKña nigTisedApÞúyKña enaHvanwgbegáIt couple. GaMgtg;sIueténkmøaMgnImYy²esμ InwgplKuNrvag yield stress nigBak;kNþalRkLaépÞmuxkat;srub. m:Um:g;EdlbegáIteday couple xagkñúgenHKW xyyp ZFaAFM ==

2

Edl A CaRkLaépÞmuxkat;srub/ a CacMgayrvagTIRbCMuTm¶n;énRkLaépÞBak;kNþalBIr nig xZ Cam:U Dulmuxkat;)aøsÞic. emKuNsuvtßiPaBcenøaHsßanPaB yielding dMbUg nigsßanPaB)aøsÞiceBjRtUv)ansM EdgenAkñúgm:UDulmuxkat;. BIrUbTI A>1 b eKGacsresrm:Um:g;EdlbegáIt yield dMbUg xyy SFM = nig

x

x

xy

xy

y

p

SZ

SFZF

MM

==

pleFobenHCatémøefrsRmab;rUbragmuxkat;EdlsÁal; nigRtUv)aneKehAfa emKuNrUbrag. sRmab;Fñwm EdlKNnaeday allowable stress theory vaCargVas;én reserve capacity ehIymantémømFüm 12.1 sRmab; W-shapes.


]bsm<½n§ A 479 T.Chhay



enAkñúgFñwm b¤eRKagsþaTicminkMNt; eKRtUvkarsnøak;)aøsÞiceRcInCagmYyedIm,IbegáIt collapse

mechanism. snøak;TaMgenHnwgRtUv)anbegáIttamlMdab;lMeday eTaHbICaeKmincaM)ac;dwgBIlMdab;k¾eday. eKnwgBicarNakarviPaKrcnasm<½n§sþaTicminkMNt;eRkayBIkarBiPakSatRmUvkarrbs; Specification.

A>2> AISC Requirements

AISC Specification GnuBaØat[eRbI plastic analysis and design enAeBleRKOgbgÁúMenArkSa PaBlMnwgTaMg local nigTaMgmUlRtg;cMNuc plastic collapse. edaysareKtRmUv[Fñwm b¤eRKagrgnUvPaB dabFMenAeBlEdlsnøak;)aøsÞicRtUv)anbegáIt eKRtUvkar lateral bracing CaBiess.

edIm,IkarBar local buckling, AISC B5.2 TamTarfaGgát;man compact cross-sectional shape Edl pλλ ≤ sRmab;TaMgRTnug nigsøab. sRmab;Ggát; I-shaped shape dUcCa W nig S-shapes pleFobTTwgelIkRmas;EdlkMNt;BI Table B5.2 KW

yf

f

Ftb 652

≤ (US) yf

f

Ftb 1702

≤ (IS)

nig yw Ft

h 640≤ (US)

yw Fth 1680≤ (IS)

edIm,IkarBar lateral buckling, AISC F1.2d kMNt; unbraced length Gtibrma bL Rtg;TItaMg snøak;)aøsÞicCa pdL EdlsRmab; I-shaped member

( )y

ypd r

FMM

L 21 /22003600 += (US) (AISC Equation F1-17)

( )y

ypd r

FMM

L 21 /1517024820 += (IS)

enAkñúgsmIkarenH 1M Cam:Um:g;EdltUcCagenARtg;cugén unbraced length nig 2M CamU:m:g;EdlFMCag. pleFob 21 / MM KwviC¢manenAeBlEdl 1M nig 2M Bt;Ggát;[mankMeNagDub nigmantémø GviC¢manenAeBlEdlvabegáItkMeNageTal. sRmab; compact shape Edlman lateral bracing RKb;RKan; eKGacyk nM es μ Inwg

pM sRmab; eRbIenAkñúg plastic analysis. b:uEnþ AISC F1.2d kMNt;faenAkñúgtMbn;EdlekItman snøak;)aøsÞiccug eRkay nigenAkñúgtMbn;EdlminEk,rsnøak;)aøsÞiceKRtUveRbIviFIFm μtaedIm,IkMNt; nM . AISC Specification provision epSgeTotEdlTak;Tgnwg plastic analysis and design mandUcxageRkam.



A5.1 Plastic analysis RtUv)anGnuBaØatsRmab;Et ksiFy 65≤ . C2.2 kmøaMgtamG½kSEdlbegáItedaybnÞúkTMnajemKuN nigbnÞúktamTisedkemKuNminRtUvFM

Cag ygc FAφ75.0 . E1.2 sRmab;ssr slenderness parameter cλ minRtUvFMCag K5.1 Edl K CaemKuNRbEvg

RbsiT§PaB.

A>3> karviPaK (Analysis) RbsinebIvaGacman collapse mechanism eRcInCamYy dUcCaFñwmCab;EdlbgðajenAkñúgrUbTI

A>3 eKGacrk)annUv collapse mechanism EdlRtwmRtUv ehIyviPaKCamYynwgCMnYyénRTwsþIeKalcMnYn bIrbs; plastic analysis Edl[enATIenHedayKμankarRsaybBa¢ak;.

!> Lower-bound theorem (static theorem): RbsinebIeKGacrk)annUvkarEbgEckm:Um:g;

d¾mansuvtßiPaB ¬Edlm:Um:g;mYytUcCag b¤es μ Inwg pM RKb;kEnøg¦ ehIyvaGacTTYlbnÞúk edaysþaTic ¬lMnwgRtUv)anbMeBj¦ bnÞab;mkbnÞúkEdlRtUvKñaRtUvtUcCag b¤esμ I collapse

load.



@> Upper-bound theorem (kinetic theorem): bnÞúkEdlRtUvnwg mechanism snμt;RtUvEtFM Cag b¤esμ Inwg collapse load. Cavi)ak RbsinebIeKGegát mechanism EdlGacmanTaMg Gs; mechanism mYyNaEdlRtUvkarbnÞúktUcCageKCa mechanism EdlRtwmRtUv.

#> Uniqueness theorem: RbsineKmankarEbgEckm:Um:g;EdlGacTTYlyk)anedaysþaTic nigmansuvtßiPaB EdlenAkñúgenaH snøak;)aøsÞicRKb;RKan;begáIt collapse mechanism enaH bnÞúkEdlRtUvKñaCa collapse load EdlRbsinebI mechanism bMeBjTaMg upper-boud theorem nig lower-bound theorem vaCa mechanism EdlRtwmRtUv.

karviPaKEdlQrelI lower-bound theorem RtUv)aneKehAfa equilibrium method ehIyRtUv)an bgðajenAkñúg]TahrN_ A>1. ]TahrN_ A>1³ rkbnÞúkcugeRkay (ultimate load) sRmab;FñwmEdlbgðajenAkñúgrUbTI A>4a eday equilibrium method rbs; plastic analysis. snμt;eKeRbI continuous lateral support nig EdlRb ePT 36A .

dMeNaHRsay³ Edk 36A muxkat; 9930×W Ca comapact shape ehIyCamYynwg continuous lateral support, tRmUvkar lateral bracing KWRKb;RKan; dUcenHeKGacTTYlyk plastic analysis.



dMNak;karénkardak;bnÞúkelIFñwmBI working load eTAdl; collapse load RtUv)anKUsbBa¢ak;enA kñúgrUbTI A>4a-d. enAeBl working load muneBl yielding ekIteLIgRKb;TIkEnøg karEbgEckm:Um:g;Bt; RtUv)anbgðajenAkñúgrUbTI A>4a CamYynwgm:Um:g;GtibrmaEdlekItmanRtg;TRmbgáb;. enAeBlEdlbnÞúk ekIneLIgbnþicmþg² yielding cab;epþImekItmanRtg;TRm enAeBlEdlm:Um:g;Bt;eTAdl; xyy SFM = . enA eBlEdlbnÞúkekIneLIgkan;EtFM vanwgekItmansnøak;)aøsÞickñúgeBldMNalKñaenARtg;cugnImYy² enAeBl Edl xyp ZFM = . enARtg;kRmiténkardak;bnÞúkenH eRKOgbgÁúMenAmansißrPaBenAeLIy FñwmRtUv)an ERbkøayeTACasþaTickMNt;edaykarekItmansnøak;)aøsÞicBIr. Mechanism nwgekIt)anEtenAeBlEdl ekItmansnøak;)aøsÞicTIbI. vaGacekItmanenAeBlEdlm:Um:g;viC¢manGtibrmamantémø pM . edayGa Rs½ynwg uniqueness theorem/ bnÞúkEdlRtUvKñaCa collapse load BIeRBaHkarEbgEck m:Um:g;KWsuvtßiPaB ehIyGacTTYlyk)anedaysþaTic. enARKb;dMNak;kalénkardak;bnÞúk plbUkénéldac;xaténm:Um:g;viC¢man nigm:Um:g;GviC¢manGti-brmaKW 8/2wL . enAeBl collapse, plbUkenHkøayeTACa 2

81 LwMM upp =+ b¤ 2

16

L

Mw p

u = eKRtUvEteRbobeFobbnÞúkemKuNCamYynwgersIusþg;emKuN dUcenHeKeRcIneRbI pbMφ Cag pM enAkñúg smIkarBIxagedIm. b:uEnþedIm,IrkSanimitþsBaØa[manlkçN³samBaØ eyIgeRbI pM enARKb;]TahrN_ TaMgGs;rhUtdl;CMhancugeRkayeTIbeyIgCMnYs pbMφ eTAkñúgsmIkar. lT§plEdlRtwmRtUv sRmab; ]TahrN_enHKW 2

16

L

Mw pb

uφ

= sRmab; 9930×W ( ) kipsftZFM xyp −=== 936

1231236

ehIy ( ) kipsftM pb −== 4.8429369.0φ eKk¾GacTTYltémørbs; pbMφ edaypÞal;BI Load Factor Design Selection Table enAkñúg Part 4 of

the Manual. cemøIy³ ( )

( )ftkipswu /0.15

304.84216

2 ==



]TahrN_ A>2³RbsinebIFñwmenAkñúg]TahrN_ A>1 minman continuous lateral support cUrkMNt;TItaMg EdlRtUvBRgwg. dMeNaHRsay³ snøak;)aøsÞicenAxagcugekIteLIgkñúgeBldMNalKña ehIymuneBlsnøak;enAkNþalElVg ekIteLIg. dUcenHeKKYrEtRtYtBinitü unbraced length GtibrmaedayeFobeTAnwgcug ¬snøak;cugeRkay EdlekIteLIgmintRmUvkar bracing sRmab; plastic analysis eT¦. edayeFobnwgsnøak;enAcugxageqVg snμt;facMNucBRgwgKWenAkNþalElVg. kñúgkrNIenH =1M

pMM =2 dUcenHFñwmmankMeNagDub ¬m:Um:g;TaMgBIrmansBaØadUcKña¦ dUcenH 1/ 21 +=MM BI AISC

Equation F1-17, unbraced length GtibrmaKW ( ) ( ) ( ) ftinr

FMML y

ypd 2.28.3.33810.2

360.122003600/22003600 21 ==

+=

+=

cMNaMfa FñwmenHesÞIrEtRKb;RKan;edayminRtUvkar lateral bracing. CamYynwg lateral mYyTl;enAkNþalElVg ftftLp 2.2815 <= (OK)

Unbraced length EdlRtUvBicarNarYmKWrYbbBa©ÚlTaMgsnøak;enAkNþalElVg. vaminmantMbn;Edlmin enACab;nwgsnøak;)aøsÞiceT dUcenHvaminRtUvkarkarKNna design strength eT. cemøIy³ eRbI lateral brace mYyenAkNþalElVg. Mechanism method KWQrelI upper-bound theorem nigRtUvakrGegátRKb; collapse

mechanism EdlGacekItman. Collapse mechanism NaEdlRtUvkarbnÞúktUcCageKnwglub eyIy bnÞúkEdlRtUvKñaCa collapse laod. eKRtUvGnuvtþeKalkarN_rbs; virtual work sRmab;viPaK mechanism nImYy². Mechanism snμt;RtUvrgnUv virtual displacement RsbeTAtamclnaEdlGac ekItmanrbs; mechanism ehIyeK[kmμnþxageRkA nigkm μnþxagkñúgesμIKña. bnÞab;mkeKGacrkTMnak; TMngrvagbnÞúk niglT§PaBTb;m:Um:g;)aøsÞic pM . bec©keTsenHRtUv)anbgðajenAkñúg]TahrN_ A>3 nig A>4. ]TahrN_ A>3³ FñwmCab;EdlRtUv)anbgðajenAkñúgrUbTI A>5 man compact cross section Edlman design strength kipsftM pb −=1040φ . eRbI mechanism method edIm,Irk collapse load uP . snμt; continuous lateral support.



dMeNaHRsay³ eKman failure mechanism sRmab;FñwmenHBIry:ag. dUcEdlbgðajenAkñúgrUbTI A>5 vamanlkçN³RsedogKñaEdlkMNat;Ggát;nImYy²rgnUv rigid-body motion. edIm,IGegát mechanism enAkñúgElVg AB dak; vitual rotation θ Rtg; A. karvilEdlRtUvKñaenARtg;snøak;)aøsÞicRtUv)anbgðaj enAkñúgrUbTI A>5b ehIybMlas;TItamTisQrébnÞúkKW θ10 . BIeKalkarN_rbs; virtual work kmμnþxageRkA = kmμnþxagkñúg

( ) ( ) θθθ pp MMP += 210 ¬vaminmankmμnþxagkñúgenARtg; A eT eRBaHvaminmansnøak;)aøsÞic¦

collapse load KW

103 p

uM

P = Mechanism sRmab;ElVg AB manlkçN³xusKñabnþic³ RKb;snøak;TaMgbICasnøak;)aøsÞic. Virtual work xagkñúg nig virtual work xageRkAkñúgkrNIKW



( ) ( ) θθθθ pppu MMMP ++= 2152 enaH pu MP

152

= lT§PaBTIBIrenHRtUvkarbnÞúktUcCag dUcenHvaCa mechanism EdlRtwmRtUv. Collapse load Edlnwg TTYl)anedayeRbI pbMφ CMnYs[ pM cemøIy³ ( ) kipsMP pbu 1391040

152

152

=== φ

]TahrN_ A>4³ kMNt; collapse load uP sRmab; rigid frame EdlbgðajenAkñúgrUbTI A>6. Ggát; nImYy²rbs;eRKagKW 14721×W Edlman ksiFy 50= . snμt; lateral support Cab;.



dMeNaHRsay³ 14721×W Ca compact shape sRmab; ksiFy 50= nigman lateral support Cab; dUc enHvabMeBjlkçxNÐkñúgkareRbIR)as; plastic analysis. dUcbgðajenAkñúgrUbTI A>6 eKman failure mode cMnYnbIsRmab;eRKagenH³ Fñwm mechanism enA kñúgGgát; BC / sway mechanism nigmYyeTotCabnSMén mechanism BIrdMbUg. eyIgcab;epþImkarviPaK mechanism nImYy²edaydak; virtual rotation θ enARtg;snøak;mYy ehIysresrsmIkarCaGnuKmn_ eTAnwgmMuenH. Virtual displacement rbs;Fñwm mechanism RtUv)anbgðajenAkñúgrUbTI A>6 b. BIsmPaBén kmμnþxageRkA nigkm μnþxagkñúg ( ) ⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+= θθθθ

32

3510 pppu MMMP

EdleKeRbI pM CMnYs[ pbMφ . edaHRsayrk uP pu MP 3333.0= RbsinebIeKminKit axial strain enAkñúgGgát; BC / sway mechanism nwgxUcRTg;RTaydUcbgðaj enAkñúgrUbTI A>6 c CamYynwgbMlas;TItamTisedkdUcKñaRtg; B nig C . Cavi)ak muMrgVilénRKb;snøak; TaMgGs;KWlkçN³RsedogKña³ ( ) ( )θθ 415 pu MP = b¤ pu MP 2667.0= BIrUbTI A>6d/ eKalkarN_én virtual work sRmab; combined mechanism [ ( ) ( ) θθθθθθθ ppppuu MMMMPP +⎟

⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛+=+

32

351015

pu MP 2133.0= ¬lub¦ cemøIy³ Collapse load sRmab;eRKagKW ( ) kipsMP pbu 29914002133.02133.0 === φ cMNaMfa vamancMNucdUcKñaxøHrvagviFIénkarviPaKTaMgBIr. eTaHbICa equilibrium method min RtUvkarBicarNaRKb; mechanism k¾eday k¾vaRtUvkar[eyIgdwgBI mechanism enAeBlEdlkarEbg Ecgm:Um:g;snμt;RsbeTAnwg mechanism mYy. viFITaMgBIrRtUvkarkarsnμt; failure mechanism b:uEnþenA kñúg equilibrium method eKRtUvRtYtBinitükarsnμt;nImYy²sRmab;suvtßiPaB nigkarEbgEck m:Um:g;Edl GacTTYlyk)anedaysþaTic ehIyvaminRtUvkarkarGegátRKb; mechanism eT.



A>4> karKNnamuxkat; (Design) dMeNIrkarénkarKNnaKWRsedogKñanwgkarviPaKEdr EtvaxusKñaRtg;faGBaØatEdlRtUvrkCalT§ PaBm:Umg;)aøsÞicEdlRtUvkar pM . eKsÁal; collapse load EdlTTYl)anBIkarKuN service load nwgem KuNbnÞúk. ]TahrN_ A>4³ FñwmCab;bIElVgdUcbgðajenAkñúgrUbTI A>7 RtUvRTnUv gravity service load. bnÞúknI- mYy²pSMeLIgedaybnÞúkefr %25 nigbnÞúkGefr %75 . eKeRbI cover plate enAkñúgElVg BC nig CD edIm,ITTYl)an moment strength dUcEdl)anbgðaj. snμt; continuous lateral support nigeRCIs erIsrUbragEdksRmab;RbePT 36A .



dMeNaHRsay³ Collapse load EdlTTYl)anedaykarKuN service load edayemKuNbnÞúksmRsb. sRmab; service load kips45 ( ) ( ) kipsPu 5.674575.060.14525.02.1 =×+×= sRmab; service load kips75 ( ) ( ) kipsPu 5.857575.060.17525.02.1 =×+×= eKRtUvGegát mechanism bIEdlman mechanism mYyenAelIElVgmYy. rUbTI A>7 c-e bgðajBI mechanism nImYy²eRkayBIrgnUv virtual displacement. enAeBlEdlsnøak;)aøsÞicekIteLIgenARtg; TRmEdlGgát;nImYy²minmanersIusþg;esμ IKña vanwgekIteLIgenAeBlEdlm:Um:g;Bt;esμ InwglT§PaBm:Um:g;)aø-sÞic rbs;Ggát;EdlexSayCag. sRmab;ElVg AB kmμnþxageRkA = kmμnþxagkñúg ( ) ( )θθθ += 255.67 pM b¤ kipsftM p −= 5.112 sRmab;ElVg BC

( ) ( ) θθθθ ppp MMM3522105.85 ++= b¤ kipsftM p −= 2.128

sRmab;ElVg CD ( ) ( )θθθθ ++= 2

35105.85 pM b¤ kipsftM p −= 2.128

Upper-bound theorem RtUv)anbkRsaydUcxageRkam³ témøénm:Um:g;)aøsÞicEdlRtUvKñanwg mechanism Edlsnμt;KWtUcCag b¤esμ Inwgm:Um:g;)aøsÞicsRmab; collapse load. dUcenH mechanism EdlTamTar lT§PaBm:Um:g;FMCageKCa mechanism EdlRtwmRtUv. Mechanism TaMgBIrcugeRkaymantémø pM dUcKña ehIyGacnwgekIteLIgkñúgeBldMNalKña. CaTUeTAersIusþg;EdlRtUvkarCa design strength Edl RtUvkar dUcenH kipsftM pb −= 2.128φ BI Load Factor Design Selection Table, rUbragEdlRsalCageKKW 3116×W Edlman design strength kipsftM pb −=146θ sakl,g 3116×W ehIyRtYtBinitükmøaMgkat; ¬eyagtamrUbTI A>8¦ sRmab;ElVg AB ( ) ( ) 02.12855.6710 =+−=∑ AB VM



kipsVA 93.20= kipsVB 57.465.6793.20 −=−= sRmab;ElVg BC ( ) ( ) 020

35105.85 =−⎟⎠⎞

⎜⎝⎛++−=∑ CppB VMMM

( ) ( ) ( )( ) kipsM

V pC 02.47

202.1283/2855

203/2105.85

=+

=+

=

kipsVB 48.3802.475.85 =−= sRmab;ElVg CD ( ) ( ) 020105.85

35

35

=−++−=∑ DppC VMMM CD VkipsV == 75.42 dUcenH kmøaMgkat;TTwgGtibrma CV KW)anmkBIElVg BC b¤esμ IKña kips02.47 . BItaragbnÞúkBRgayesμ IemKuNenAkñúg Part 4 of the Manual, shear design strength rbs;

3116×W KW kipskipsVnv 02.479.84 >=φ (OK) cemøIy³ eRbI 3116×W . A>5> karsnñidæan (Conclusion Remark) karviPaKén mechanism EdlrgbnÞúkBRgaybgðajBIPaBsμ úKs μajbEnßmeTotEdlmin)anerob rab;enATIenH. bBaðaCak;EsþgenAkñúg plastic analysis or design rYmbBa©ÚlnUvkardak;bnÞúkEbbenH y:agCak;Esþg. elIsBIenH eKKYrGegátGnþrGMeBIén\T§iBlrbs;kmøaMgtamG½kS nigm:Um:g;Bt;sRmab;Ggát; EdlrgTaMgkmøaMgtamG½kS nigm:Um:g;Bt; dUcenA rigid frame enAkñúg]TahrN_ A>4 . cMeBaHviFIviPaKEdlmanlkçN³TUeTAdUcCa equilibrium method manniyayy:aglMGitenAkñúg the plastic methods of structural analysis (Neal, 1977). ehIyvamanrUbmnþEdlmanlkçN³ s μ úKsμajsRmab; mechanism method eTotpg. CamYynwgviFIenH EdleKsÁal;faCa method of

inequalities eKGackMNt; mechanism EdlRtwmRtUveday linear programming technique eday pÞal;. eKGaceRbI plastic design FmμtasRmab;KNnaeRKOgbgÁúMPaKeRcIn b:uEnþCaTUeTA mechanism

method EdlbgðajenAkñúg]bsm<½n§enHKWRKb;RKan;ehIy.


]bsm<½n§ B 491 T.Chhay

Appendix B. karKNnaeRKOgbgÁúMEdkedayQrelIkugRtaMgGnuBaØat Structural Steel Design Based on Allowable Stress

B>1> esckþIepþIm (Introduction) PaBxusKñacMbgrvag allowable stress design nig loads and resistance factor design KW emKuNsuvtßiPaB. * enAkñúg LRFD eKGnuvtþemKuNbnÞúkeTAelIbnÞúk nigemKuNersIusþg;eTAelIersIusþg;. elIsBIenH témørbs;emKuNbnÞúkGaRs½ynwgRbePTrbs;bnÞúk nigkarbnSMbnÞúk. enAkñúg allowable

stress design (ASD) eKeRbIEtemKuNsuvtßiPaBmYyKt; ehIyvaRtUv)anGnuvtþeTAelIkugRtaMgEdlman enAkñúgsßanPaBkMNt;. sßanPaBkMNt;rbs; ASD KWRsedogKñasRmab; LEFD KW yielding, fracture nig buckling. eKalkarN_rbs; allowable stress analysis and design KWmandUcteTA³ kugRtaMgenAkñúg sßanPaBkMNt;RtUv)anEckCamYynwgemKuNsuvtßiPaBedIm,ITTYl)ankugRtaMgGnuBaØat ehIykugRtaMg Gb,brmaEdlekIteLIgeday service load dac;xatminRtUvFMCagkugRtaMgGnuBaØatenH eT. ]TahrN_ sRmab;kmøaMgTajtamG½kS tt F

APf ≤= (B.1)

Edl =tf kugRtaMgTajKNna =P bnÞúkTajtamG½kSeFVIkar =tF kugRtaMgTajGnuBaØat kugRtaMgTajGnuBaØatGacCaplEckrvag yield stress CamYynwgemKuNsuvtßiPaB b¤CaplEckrvag ultimate tensile stress CamYynwgemKuNsuvtßiPaBepSgeTot. eyIgnwgerobrab;BIGgát;rgkarTajlMGit enAkñúgEpñk B>2. eKeRbI ASD sRmab;eRKOgbgÁúMEdkmuneBlEdlmankarENnaMBI LRFD Specification enAkñúgqñaM 1989. kare)aHBum<elIkcugeRkayrbs; ASD Specification (AISC, 1989b) ehIynig Manual of

steel Construction (AISC, 1989a) RtUv)anpSBVpSayenAkñúgqñaM 1989. karerobcMÉksarrbs;Éksar TaMgBIrxagelImanlkçN³RsedogKñanwgkarerobcMÉksarrbs; LRFD Edr. eKEbgEck Specification

* snμt;faeyIgsÁal; nigyl;BI AISC LRFD Specification nig Manual


T.Chhay 492 Appendix B

CaCMBUk ¬]TahrN_ “Chapter D, Tension members”¦ ehIy Manual RtUv)anEbgEckCaEpñk ¬dUcCa “Part 2, Beam and Girder Design”¦. enAkñúg Specification mankarENnaM eday Commentary. nimitþsBaØaenAkñúgsmIkar B.1 manlkçN³RsedogKñaeTAnwgkareRbIR)as;enAkñúg Specification. eKeRbIGkSr f sRmab;kugRtaMgEdlKNnaCak;Esþg nigeKeRbIGkSr F sRmab;kugRtaMgGnuBaØat. snÞsSn_R)ab;BIRbePTkugRtaMg. edaysar]bsm<½n§enHRKan;EtCaesckþIENnaM dUcenHeyIgminRtUvkareRbIelxEpñkrbs; AISC

Specification b¤elxsmIkareT. smIkarenAkñúg]bsm<½n§enHykecjBI Specification EtelxsmIkar RtUv)andak;eTAedayxøÜneyIg. elIsBIenH enAeBlEdleyIgeRbIBakü Specification b¤ Manual enA kñúg]bsm<½n§enH )ann½faeyIgeRbI allowable stress elIkElgEtmankarENnaM. Ggát;CaeRcInénkarKNnaeRKOgbgÁúMEdkKWRsedogKñasRmab; ASD nig LRFD. ]TahrN_ net area sRmab;Ggát;rgkarTajKWdUcKña rYmbBa©ÚlTaMg gs 4/2 sRmab; staggered holed ¬karteRmob rn§qøas;¦ nigemKuN U sRmab; shear leg ¬eTaHbICa ASD Specification eRbItémømFümrbs; U nigdak;smIkarsRmab; U enAkñúg Commentary k¾eday k¾eKeRbIGVIEdlmanenAkñúg LRFD

Specification Edr¦. niymn½yrbs; compact member, noncompact member nig slender member KWdUcKña b:uEnþ LRFD Specication cugeRkaymankarEklMGeRcIn. CaTUeTA enAeBlmanPaBminRtUvKña rvag ASD nig LRFD provision eKKYredaHRsayedayQrelI LRFD Specification eRBaHvaTan; sm½ykal. eTaHCavaminmanemKuNbnÞúkenAkñúg allowable stress design k¾eday eKenAEtGacKitbnÞúk sMxan;epSg²enAkñúgkarbnSMbnÞúkEdr. ]TahrN_ CaTUeTAeKeRbIbnSMbnÞúksRmab;eRKOgbgÁúMdMbUldUct eTA³ SD + / WD + / ( ) WSD ++ 2/ nig ( )3/WSD ++ . elIsBIenH Specification GnuBaØat [ allowable stress ekIneLIgmYyPaKbIenAeBleKrab;bBa©ÚlbnÞúkxül; nigbnÞúkrBa¢ÜydI. Building

code CaeRcInk¾mankarpþl;EbbenHEdr. ASD Manual k¾mantarag nigdüaRkamCaeRcInRsedogKñanwg LRFD Manual Edr. eyIgnwg elIkykEttarag b¤düaRkamNaEdlsMxan;mkbkRsayenAkñúgkarENnaMd¾segçbenH.



B>2> Ggát;rgkarTaj (Tension members) BIsmIkar B.1 kugRtaMgTajtamG½kSEdlKNnaKW APft /= . Allowable stress KWQrelI sßanPaBkMNt; yielding nig fracture EdleRKaHfñak;CageK. sRmab; yielding rbs; gross section kugRtaMgGnuvtþn_KW

gt A

Pf = (B.2)

Edl gA Ca gross cross-sectional area. The factor of safety sRmab;sßanPaBkMNt;enHKW 3/5 ehIykugRtaMgGnuBaØatKW y

yyt F

FSF

FF 6.0

3/5..=== (B.3)

sRmab; fracture rbs; net section

e

t APf = (B.4)

Edl eA Ca effective net area. emKuNsuvtßiPaBKW 0.2 EdllT§plrbs;kugRtaMgGnuBaØatKW u

uut FF

SFFF 5.0

2.=== (B.5)

]TahrN_ B>1³ RtYtBinitükugRtaMgenAkñúgGgát;rgkarTajEdlbgðajenAkñúgrUbTI B>1 EdlekItBIbnÞúk eFIVkar kips50 . eKeRbIEdkRbePT 36A nigb‘ULúgGgát;p©it .8

7 in .

dMeNaHRsay³ BIsmIkar B.2 nig B.3 kugRtaMgGnuvtþn_enAelI gross section KW ksi

APfg

t 2.2048.2

50===



ehIykugRtaMgGnuBaØatKW ( ) ksiksiFF yt 2.206.213660.05.0 >=== (OK) kugRtaMgenAelI net area KW ( )diameter hole thickness×−= gn AA

2.105.281

87

8348.2 in=⎟

⎠⎞

⎜⎝⎛ +−=

RbsinebIeyIgeRbItémømFüm U enaH effective net area KW ( ) 2.789.1105.285.085.0 inAUAA nne ==== sRmab;smIkar B.4 nig B.5 ksi

APf

et 9.27

789.150

=== ( ) ksiksiFF ut 9.27295850.050.0 >=== (OK) cemøIy³ Ggát;KWmanlkçN³RKb;RKan;. B>3> Ggát;rgkarsgát; (Compression members) kugRtaMgenAkñúgGgát;Edlrgkarsgát;tamG½kSKW

ga A

Pf =

kugRtaMgGnuBaØat EdlsMKal;eday aF RtUv)anTTYledayEck critical buckling load CamYy nwgemKuNsuvtßiPaB. emKuNsuvtßiPaBsRmab;ssreGLasÞic (slender column) mantémøefr ehIyem KuNsRmab;ssr inelastic mantémøERbRbYl. enAkñúg ASD ersIusþg;rgkarsgát;RtUv)ansresrCa GnuKmn_én slenderness ratio rKL / b:uEnþenAkñúg LRFD ersIusþg;CaGnuKmn_eTAnwg =cλ ( ) EFrKL y // π . enAkñúgtMbn;eGLasÞic kugRtaMgeRKaHfñak;KWplEckrvag Euler buckling load nwgRkLaépÞ b¤

( ) ( )22

2

2

// rKLEA

rKL

EAAPF g

g

g

crcr

ππ=÷== (B.6)

sRmab;tMbn; elastic EdnsmamaRtRtUv)ansnμt;es μ Inwg 2/yF eKnwgeRbIsmIkarEdl)anBIkarBiesaFdUc xageRkamCMnYs[ tangent modulus formula³



( )⎥⎥⎦

⎤

⎢⎢⎣

⎡−= 2

2

2/1c

ycrC

rKLFF (B.7)

Edl cC témørbs; rKL / EdlRtUvKñanwgkugRtaMg 2/yF . smIkar B.7 bgðajBIExS)a:ra:bUlEdlb:H nwgExSekag Euler enARtg; cCrKL =/ ehIyb:HeTAnwgbnÞat;edkenARtg; 0/ =rKL . eyIgGacrk smIkarsRmab; cC edayEpñkxagsþaMrbs;smIkar B.6 esμ Inwg 2/yF ³

( ) 2

2

2

2

/2 c

y

CE

rKLEF ππ

==

eyIgTTYl)an y

c FEC

22π= (B.8)

munnwgkarGnuvtþemKuNsuvtßiPaB ersIusþg;ssrelItMbn; slenderness eBj RtUv)anbgðajedayRkaPic enAkñúgrUbTI B>2.

edIm,ITTYlnUvkugRtaMgsgát;GnuBaØat eyIgEcksmIkar B.6 nig B.7 CamYynwgemKuNsuvtßiPaB. emKuNsuvtßiPaBsRmab;ssreGLasÞicKW 12/23 . sRmab;ssr inelastic eKeRbIemKuNEdlERbRbYl dUcxageRkam³ ( ) ( )

3

3

8/

8/3

35..

cc CrKL

CrKLSF −+=



smIkarenHmantémø 3/5 enAeBl 0/ =rKL ¬dUcKñasRmab; yielding rbs;Ggát;rgkarTaj¦ ehIy témø 12/23 enAeBl cCrKL =/ ¬RbEhl %15 eRcInCag 3/5 ¦. edayEcksmIkarersIusþg;CamYy emKuNsuvtßiPaBEdlsmRsb eyIgTTYl)ankugRtaMgGnuBaØatdUcxageRkam³ sRmab; cCrKL </

( )

( ) ( )3

3

2

2

8/

8/3

35

2/1

cc

cy

a

CrKL

CrKL

CrKLF

F−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

= (B.9)

sRmab; cCrKL >/

( ) ( )22

2

2

/2312

1223

/ rKLE

rKLEFa

ππ=÷= (B.10)

sRmab;Ggát;Edlmanmuxkat; slender eKRtUveFVIkarkat;bnßykugRtaMgGnuBaØatedIm,IKitBIlT§PaBEdl GacekItman local buckling. eKTTYl emKuNkat;bnßyenHBI appendix EdlmanenAkñúg Specifica-

tion. ]TahrN_ B>2³ kMNt;bnÞúkeFVIkarGnuBaØat P sRmab;Ggát;rgkarsgát;EdlbgðajenAkñúgrUbTI B>3.

dMeNaHRsay³ RtYtBinitüemIlfaetIGgát;CaGgát;Edlmanmuxkat; slender b¤Gt;. pleFobTTwgelI kRmas;sRmab;Ggát;rgkarsgát;Edl[enAkñúg ASD Specification manlkçN³dUcKñaenAkñúg LRFD Specification:



4.62

=f

f

tb ¬BI properties table EdlmanenAkñúg Manual¦

4.68.1536

9595>==

yF (OK)

3.25=wth

3.252.4236

253253>==

yF (OK)

kugRtaMgKW ga APf /= dUcenHbnÞúkEdlRtUvKñaKW ga AfP = ehIybnÞúksgát;GnuBaØtKW ga AF . BI smIkar B.8

( ) 1.126362900022 22

===ππ

yc F

EC

pleFob slenderness GtibrmaKW ( )( ) 77.96

48.212200.1

min====

yrKL

rKL

rKL

lT§plEdlTTYl)antUcCag cC dUcenHeKGacrk aF BIsmIkar B.9:

( )

( ) ( )

( )( )

( )( )

( )( )

ksi

CrKL

CrKL

CrKLF

F

cc

cy

a 38.13

1.126877.96

1.126877.963

35

1.126277.96136

8/

8/3

35

2/1

3

3

2

2

3

3

2

2

=

−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=

−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=

cemøIy³ ( ) kipsAFP ga 2928.2138.13 === Design Aids ASD manual man column design aids EdlmanTRmg;RsedogKñaenAkñúg LRFD Manual. kñúgcMeNam aids TaMgenHPaKeRcInCataragsRmab;bnÞúktamG½kSGnuBaØat. enAeBleKbBa©ÚlRbEvg RbsiT§PaB KL niglT§PaBRTbnÞúkeFVIkarEdlTamTareTAkñúgtarag eKGacrk)annUvmuxkat;Edlman lT§PaBRKb;RKan;)any:agelOn. dUcKñanwg LRFD column load table Edr eKKYeRbIRbEvgRbsiT§PaB

LK y eFobnwgkaMniclPaBGb,brma yr . müa:geToteKGacbBa©Úl ( )yxx rrLK // . enAeBlEdleKrkemKuNRbEvgRbsiT§PaB K BI Jackson-Mooreland alignment chart eK



Gac GnuvtþemKuNkat;bnßy stiffness RbsinebIssrCa inelastic enAeBl)ak; ( )cCrKL </ .

Manual k¾pþl;taragsRmab;karcg;)anenHEdr. B>4> Fñwm (Beams) kugRtaMgBt;GtibrmaenAkñúg homogeneous beam EdlminmankugRtaMgeRkABIEdnsmamaRt RtUv)an[eday flexural formula³

SM

cIM

IMcfb ===

/

Edl =M m:Um:g;Bt;GtibrmaenAkñúgFñwm =c cMgayBIG½kSNWteTAsréseRkAeKbMput =I m:Um:g;niclPaBeFobG½kSBt; =S m:UDulmuxkat;eGLasÞic karBN’nakñúgEpñkenHRtUv)ankMNt;Rtwm hot-rolled I nig H-shaeped cross section EdlrgkarBt; eFobG½kSEkgeTAnwgRTnug ¬G½kS x ¦. kugRtaMgBt;GnuBaØatRtUv)ansMKal;eday bF nigQrelIsßanPaBkMNt;dUcteTA³ yilding, local

buckling b¤ lateral-torional buckling. enAkñúg ASD eKnwgmanPaBgayRsYlRbsinebI eKbMEbkFñwm CaBIrKW³ FñwmEdlmanTRmxag (laterally supported beam) nigFñwmEdlminmanTRmxag (laterally

unsupported beam). RbsinebIFñwmman lateral support RKb;RKan; kugRtaMgGnuBaØatnwgQrelI yielding kñúgkrNImuxkat; compact ehIyvanwgQrelI local buckling kñúgkrNImuxkat; uncompact. kugRtaMgBt;GnuBaØatsRmab; laterally unsupported beams nwgQrelI lateral-torsional buckling. Lateral support eKKitfaFñwmEdlman unbraced length bL man lateral support RKb;RKan;edIm,IkarBar lateral-

torsional buckling enAeBlEdl cb LL ≤ Edl cL CatémøtUcCageKkñúgcMeNam ( ) yfy

fc FAdF

bL

/2000076

≤= (US) (B.12)

( ) yfy

fc FAdF

bL

/137900200

≤= (IS)



eyIgeRbIlkçxNÐenHedIm,IkMNt;cMNat;fñak;rbs;FñwmfaCa laterally supported b¤ laterally

unsupported. Laterally Supported Beams RbsinebI laterally supported beam GacrgkugRtaMgdl;cMnuc yield edayK μan local buckling enaHem KuNsuvtßiPaBKW 3/5 ehIykugRtaMgGnuBaØatKW y

yyb F

FSF

FF 60.0

3/5..===

lkçxNÐenHRtUvnwgrUbragEdlmanpleFobTTwgelIkRmas;sßitenAEdnkMNt;x<s;bMputsRmab; noncom-

pactness Edl yff Ftb /952/ = (US) b¤ yff Ftb /2502/ = (IS). ¬EdnkMNt;enHxusKña BIEdnkMNt;rbs; LRFD b:uEnþeKeRbIvaenATIenH edaysarvaminTak;TgenAkñúgsmIkar AISC sRmab; ASD¦. RbsinebImuxkat;enH compact eKGacTTYllkçxNÐ)aøsÞiceBjedayKμan local buckling ehIyeKGnuBaØat[bEnßm %10 sRmab;kugRtaMgGnuBaØat. dUcenHkñúgkrNIenH kugRtaMgGnuBaØatKW ( ) yyb FFF 66.060.010.1 == sRmab; noncompact shape, AISC eRbI linear transition cenøaH yF6.0 nig yF66.0 edayQrelItémø ff tb 2/ . RKb; hot-rolled I- and H-shapes TaMgGs;enAkñúg Manual man compact

web. kugRtaMg GnuBaØatsRmab;krNIenH[enAkúñsmIkarxageRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛−= y

f

fyb F

tb

FF2

002.079.0

rUbTI B>4 bgðajBITMnak;TMngrvagpleFoTTwgelIkRmas;CamYynwgkugRtaMgGnuBaØatsRmab; laterally

supported beams. eKedaHRsay slender shape enAkñúg appendix EdlmanenAkñúg Specification b:uEnþvaminman hot-rolled I- and H-shapes enAkñúg Manual Ca slender eT. kugRtaMgsRmab; laterally supported beam mandUcxageRkam³ RbsinebIrUbragCa compact yb FF 66.0= (B.13)

RbsinebIrUbragCa noncompact

⎟⎟⎠

⎞⎜⎜⎝

⎛−= y

f

fyb F

tb

FF2

002.079.0 (B.14)



Laterally Unsupported Beams ersIusþg;rbs; lateral unsupported beam KWQrelIsßanPaBkMNt;rbs; lateral-torsional

buckling. enAkñúg ASD, sßanPaBenHmanBIry:agKW³ uniform warping nig nonuniform warping. Uniform warping KWmanlkçN³eGLasÞic ehIysßanPaBkMNt;KW

fbu AdL

Ef/

65.0= (B.15)

Edl =d km<s;srubrbs;Fñwm =fA RkLaépÞrbs;søabrgkarsgát; cMENk nonuniform warping GacCa inelastic b¤k¾eGLasÞic. sRmab;eGLasÞic warping, failure

stress KW ( )2

2

/ ybnu

rLEf π

= (B.16)

sRmab; inelastic warping, eKeRbIsmIkarEdl)anmkBIkarBiesaFEdlmanlkçN³RsedogKñanwg smIkarsRmab;Ggát;rgkarsgát;

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡−= 2

2

2

/1

910

C

rLFf yb

ynu (B.17)

Edl =C témøGtibrmarbs; bL sRmab; nonuniform warping Ca inelastic ¬RbsinebI CLb > / warping Ca elastic¦

yF

E5

3π=



Buckling stress Edl[edaysmIkar B.15-B.17 RtUv)ankMNt;RtwmEdnx<s;bMputrbs; yF . rUbTI B.5 bgðajBI uniform warping stress CaGnuKmn_eTAnwg bL nigrUbTI B.6 bgðajBI nonuniform warping

stress.

edIm,ITTYl)ansmIkar AISC sRmab;kugRtaMgBt;GnuBaØatEdlQrelI lateral-torsional

buckling, eKRtUveFVIkarEktRmUveTAelIsmIkarEdl)anerobrab;BImundUcteTA³ !> eKRtUvEck failure stress TaMgGs;CamYynwgemKuNsuvtßiPaB 3/5

@> eKCMnYskaMniclPaB yr eday Tr EdlCakaMniclPaBeFobG½kSexSaysRmab; cMENkrbs; muxkat;Edlmansøabrgkarsgát; nigmYyPaKbIénEpñksgát;rbs;RTnug. témøenHminCaxusKña BI yr EdlmanenAkñúgtaragrbs; ASD Manual eT.

#> RKb;smIkarTaMgGs;RtUv)ansresredaymanpleFob Tb rL /



$> emKuN bC RtUv)anKitbBa©ÚlsRmab;bMErbMrYlrbs;m:Um:g;Bt;elI unbraced length ¬smIkar warping KWQrelIm:Um:g;BRgayes μ I¦

%> eTaHbICa lateral-torsional buckling strength RtUv)anbMEbkecjBIbgÁúM uniform nig nonuniform warping k¾eday k¾ AISC eRbIbgÁúMNaEdlmantémøFMCag.

eKGacsegçbsmIkar AISC sRmab;kugRtaMgBt;GnuBaØatsRmab; laterally unsupported beam dUcxageRkam³ sRmab;

y

b

T

bF

CrL 102000

< (US) y

b

T

bF

CrL 703300

< (IS)

yb FF 60.0= sRmab;

y

b

T

b

y

bF

CrL

FC 510000102000

≤≤

yktémøEdlFMCageKkñúgcMeNam

( )yy

b

Tbyb FF

CrLF

F 60.01530000

/32

2

≤⎥⎥⎦

⎤

⎢⎢⎣

⎡−= (US) (inelastic nonuniform warping) (B.18)

( )yy

b

Tbyb FF

CrLF

F 60.010550000

/32

2

≤⎥⎥⎦

⎤

⎢⎢⎣

⎡−= (IS)

nig yfb

bb F

AdLCF 60.0

/12000

≤= (US) (uniform warping) (B.19)

yfb

bb F

AdLCF 60.0

/82750

≤= (IS)

sRmab; y

b

T

bF

CrL 510000

> (US) y

b

T

bF

CrL 3516500

> (IS)

yktémøFMCageKkñúgcMeNam

( ) yTb

bb F

rLCF 60.0

/170000

2 ≤= (US) (elastic nonuniform warping) (B.20)

( ) y

Tb

bb F

rLCF 60.0

/1172150

2 ≤= (IS)

nig yfb

bb F

AdLC

F 60.0/

12000≤= (US) (uniform warping) (B.19)

yfb

bb F

AdLCF 60.0

/82750

≤= (IS)



ASD Specification [nUvsmIkarsRmab; bC EdlxusBI bC Edl[eday LRFD

Specification b:uEnþeKGaceRbImYyNak¾)an. cMNaMfa eTaHbICa flexural strength Edleyagtam LRFD KWsmamaRtedaypÞal;eTAnwg bC k¾eday k¾vaminEmnCakrNIsRmab; allowable stress Edl [edaysmIkar B.18 - B.20 Edr. vamankars μ úKs μajxøHkñúgkarKNna allowable stress rbs;Fñwm. Shear

kugRtaMgkmøaMgRtUv)anKNnaedayykbnÞúkkmøaMgkat;eFVIkarGtibrmaEcknwgRkLaépÞRTnug.

dtV

AVf

wwv ≈=

kugRtaMgkmøaMgkat;KWQrelI shear yielding ehIyRtUv)anykesμ InwgBIrPaKbIénkugRtaMgTaj GnuBaØatelI gross section. ( ) yytv FFFF 40.060.0

32

32

=== (B.21)

]TahrN_ B>3³ eKeRbI 10016×W sRmab;FñwmTRmsamBaØEdlrgbnÞúkBRgayesμIehIyman lateral

bracing EtenAxagcugrbs;va. RbsinebIeKeRbIEdkRbePT 36A kMNt;m:Um:g;Bt;eFVIkarGtibrmaEdlFñwm enHGacTb;)ansRmab;ElVgEdlmanRbEvg (a) ft10 (b) ft15 nig (c) ft40 . dMeNaHRsay³ dMbUg kMNt; cL BIsmIkar B.12 ( ) ftin

F

b

y

f 1113236

42.107676===

( )( ) ( )

ftinFAd yf

280.33636

985.042.1097.16

20000/20000

===

eKyktémøEdltUcCageK dUcenH ftLc 0.11= a) sRmab;ElVgEdlmanRbEvg ft10

cb LftL <=10 dUcenHFñwmCa laterally supported beam.



eday 10016×W Ca compact shape sRmab;Edk 36A / kugRtaMgGnuBaØatEdl)anBIsmIkar B.13 KW ( ) ksiFF yb 76.233666.066.0 === kugRtaMgBt;GtibrmasRmab;m:Um:g; M Edl[edaysmIkar B.11 KW SMfb /= dUcenHm:Um:g; GtibrmaEdlekIteLIgenAeBlkugRtaMg af esμ InwgkugRtaMgGnuBaØat bF ( ) kipsftkipsinSFM b −=−=== 346.415817576.23

cemøIy³ a) m:Um:g;Gtibrma kipsft −= 346 b) sRmab;ElVgEdlmanRbEvg ft15

ftLftL cb 0.1115 =>= dUcenHFñwmCa laterally unsupported beam. .81.2 inrT = ¬témøenHRtUv)an[enAkñúg properties table enAkñúg ASD Manual¦ ( ) 06.64

81.21215

==T

brL

sRmab;FñwmTRmsamBaØrgbnÞúgBRgayes μIEdlman lateral bracing enAxagcug/ 14.1=bC ¬Edl KNnaCamYynwg LRFD Specification equation b:uEnþeKk¾GaceRbIvaCamYynwg ASD equation pgEdr¦. kMNt;EdnkMNt;sRmab; Tb rL / ( ) 8.56

3614.1102000102000

==y

bF

C

( ) 12736

14.1510000510000==

y

bF

C

edaysar 127/8.56 << Tb rL eKeRbIsmIkar B.18 nig B.19

( )yy

b

Tbyb FF

CrLF

F 60.01530000

/32

2

≤⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

( )( ) ksi95.2036

14.1153000006.6436

32 2

=⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

b¤ yfb

bb F

AdLCF 60.0

/12000

≤= ( )

( )( ) ( ) ksi97.45985.042.10/97.161215

14.112000=

××=

lT§plxagelImantémøFMCag ( ) ksiFy 6.213660.060.0 == . dUcenHyk



ksiFF yb 6.2160.0 == m:Um:g;Bt;GtibrmaKW ( ) kipsftkipsinSFM b −==== 315.37801756.21 cemøIy³ b) m:Um:g;Gtibrma kipsft −= 315

c) sRmab;ElVgEdlmanRbEvg ft40 ( ) 1275100008.17081.21240

=>==y

b

T

bF

CrL

eRbIsmIkar B.19 nig B.20:

( )( )

( ) yTb

bb Fksi

rLCF 6.0643.6

8.17014.1170000

/170000

22 <===

b¤ ( )( )( ) ( ) y

fb

bb Fksi

AdLCF 60.024.17

985.042.10/97.16124014.112000

/12000

<=××

==

yk ksiFb 24.17= . m:Um:g;GtibramKW ( ) kipsftkipsinSFM b −=−=== 251.301717524.17 cemøIy³ c) m:Um:g;Gtibrma kipsft −= 251 . Design Aids Design aids sRmab;FñwmPaKeRcInEdlmanenAkñúg LRFD Manual k¾manenAkñúg ASD Manual Edr. varYmmanTaMg design chart Edl[ allowable bending moment CaGnuKmn_én unbraced length sRmab;rUbragEdleKeRbIsRmab;FñwmCaTUeTA. ExSekagTaMgenHQrelI 0.1=bC b:uEnþeKminGaceRbIvaeday pÞal;sRmab;témøepSgeTotrbs; bC eT edaysar allowable stress bF minsmamaRtedaypÞal;eTAnwg

bC . B>5> Beam-Columns eKviPaKGgát;eRKOgbgÁúMEdlrgTaMgkugRtaMgBt; nigkugRtaMgtamG½kSCamYynwgsmIkarGnþrGMeBI edayKitpleFobkugRtaMgCak;EsþgelIkugRtaMgGnuBaØat. ASD Specification equation KW 0.1≤++

by

by

bx

bx

a

aFf

Ff

Ff



Edl x nig y sMKal;karBt;tamG½kS. eKeRbIsmIkarBIrenAkñúg Specification³ EdlmYyKNnaCamYy nwgkugRtaMgBt;EdlQrelIm:Um:g;Gtibrmadac;xatenAkñúgGgát; nigmYyeTotCamYykugRtaMgBt;EdlQrelI m:Um:g;cugGtibrma. eKeRbI amplification factor EtmYy vaminmanemKuNdac;edayELkkñúgkarKit sway nig nonsway components. Amplification factor enHmanTRmg;dUcxageRkam³ ( )ea

mFf

C'/1−

Edl mC RtUv)ankMNt;es μ Inwg³ sRmab;Ggát;RbQmnwg sidesway 85.0=mC sRmab;Ggát;EdlminRbQmnwg sidesway ehIynigminman transverse load ( )21 /4.06.0 MMCm − (B.22)

Edl 1M nig 2M Cam:Um:g;enAxagcugrbs;Ggát; ehIyEdltémødac;xatrbs; 1M tUcCag. pleFob 21 / MM viC¢manRbsinebIGgát;ekagDub ehIyvamantémøGviC¢mansRmab;kMeNageTal. sRmab;Ggát;EdlTb;RbqaMgnwg sidesway ehIyman transverse load 85.0=mC RbsinebIcugRtUv)anTb;min[vil 0.1=mC RbsinebIcugminRtUv)anTb; emKuN eF ' CaplEckrvag Euler buckling stress CamYynwgemKuNsuvtßiPaB 12/23 ³

( )22

/2312'

bbe

rKLEF π

= (B.23)

GkSr b sMedAelIG½kSénkarBt;. RbsinebIeKBicarNakarBt;eFobnwgG½kS x enaH exe FF '' = nig xxbb rKLrKL // = . dUcKñasRmab; eyF ' eRbI yy rLK / .

eKRtUvRtYtBinitüsmIkarGnþrGMeBIxageRkam³ RbsinebI 15.0/ ≤aa Ff / eKminRtUvkar moment amplification ehIy 0.1≤++

by

by

bx

bx

a

aFf

Ff

Ff (B.24)

RbsinebI 15.0/ >aa Ff / eKRtUvRtYtBinitüsmIkarTaMgBIrxageRkam³ 0.1

'1'

1≤

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+

byey

a

bymy

bxex

a

bxmx

a

a

FF

f

fC

FF

ffC

Ff (B.25)



nig 0.16.0

≤++by

by

bx

bx

a

aFf

Ff

Ff (B.26)

smIkar B.25 CakarRtYtBinitüesßrPaB ehIyeKeRbIm:Um:g;Bt;GtibrmaedIm,IKNna bxf nig byf . smIkar B.26 EdlmineRbI amplification factor CakarRtYtBinitükugRtaMg ehIyeKeRbIm:Um:g;cugGtibrma edIm,IKNna bxf nig byf . cMNaMfa eKeRbI yF60.0 CMnYs[ aF enAkñúgsmIkar B.26 edaysar sßanPaBkMNt;Ca yielding CaCag buckling. sRmab;mUlehtudUcKña eKGacBicarNaGgát;Ca laterally

supported member sRmab;karKNna bxF enAkñúgsmIkar B.26 b:uEnþeKRtUvKitlkçxNÐ lateral bracing Cak;EsþgenAeyIgeRbIsmIkar B.25 edIm,IRtYtBinitü. eKalbMNgrbs;emKuN mxC enAkñúgsmIkar 25.B KWedIm,IKitBI gradient m:Um:g;eFobG½kS x rbs;Ggát;. enAkñúg laterally supported member eKeRbIemKuN bC kñúgkarKNna bxF k¾edIm,IKitBI gradient Edr. dUcenH Specification yk bC esμ ImYyenAeBlEdleKKit bxF sRmab;eRbIenAkñúgsmIkar B.25 sRmab;Ggát;EdlBRgwgRbqaMgnwgkarrMkiltMN (members braced againt joint translation). ]TahrN_ B>4³ Beam-column EdlbgðajenAkñúgrUbTI B.7 CaEpñkrbs; braced frame. karBt;KWeFob nwgG½kS x ehIycugrbs;vaRtUvman lateral bracing. snμt;fa 0.1== yx KK cUrviPaKGgát;eday eKarBtam AISC Specification.

dMeNaHRsay³ kugRtaMgrgkarsgát;tamG½kS ksi

APfg

a 944.64.14

100===



KNnakugRtaMgsgát;GnuBaØat Slenderness ration GtibrmaKW ( )( ) 87.70

54.212150.1

==y

y

rLK

BIsmIkar B.8

( ) 1.126362900022 22

===ππ

yc F

EC

edaysar cCrKL ≤/ / kMNt;kugRtaMgsgát;GtibrmaCamYysmIkar B.9

( )

( ) ( )

( )( )

( )( )

( )( )

ksi

CrKL

CrKL

CrKLF

F

cc

cy

a 34.16

1.126887.70

1.126887.703

35

1.126287.70136

8/

8/3

35

2/1

3

3

2

2

3

3

2

2

=

−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=

−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=

15.04250.034.16

944.6>==

a

aFf

dUcenHRtYtBinitüsmIkar B.25 nig B.26 ( ) ksi

SMf

x

xbx 19.13

6.541260

===

0=bvf KNnakugRtaMgBt;GnuBaØat BIsmIkar B.12 ( ) ftin

F

b

y

f 6.10.7.12636

00.107676===

( )( ) ( )

ftinFAd yf

0.26.7.31136

00.10560.098.9

20000/20000

===

témøEdltUcCaglub dUcenH ftLc 6.10= . RbEvgenHKWtUcCag unbraced length ftLb 15= dUcenH Ggát;enHRtUv)aneKKitCa laterally unsupported beam. edaysarGgát;enHRtUv)anTb;nwg sidesway dUcenHyk 0.1=bC ( ) 2.53

360.1102000102000

==y

bF

C



( ) 11936

0.1510000510000==

y

bF

C

( ) 69.6574.21215

==T

brL ¬ Tr RtUv)anerobCataragenAkñúg Manual¦

edaysar 119/2.53 << Tb rL yktémøEdlKNnaCamYynwgsmIkar B.18 nig B.19 EdlFMCagEtmin RtUvFMCagEdnkMNt;x<s;bMputén ( ) ksiFy 6.213660.060.0 == BIsmIkar B.18

( ) ( )( ) ksiF

CrLF

yb

Tby 34.200.11530000

69.653632

1530000/

32 22

=⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

BIsmIkar B.19 ( )

( )( ) ( ) ksiAdlC

fb

b 4.3700.10560.0/98.91215

0.112000/

12000=

××=

témøEdl)ansmIkarTaMgBIrxagelIFMCag yF6.0 dUcenH ksiFF ybx 6.2160.0 == dMbUgRtYtBinitüsmIkar B.26. enAkñúgsmIkarenH GVIEdlRtUvRtYtBinitüKWlkçxNÐkugRtaMgenARtg;TRm dUcenHeKRtUvKNnakugRtaMgBt;GnuBaØatrbs;Ggát;enH RbsinebIGgát;rgkarsgát;rbs;vaman full lateral

support. 4916×W Ca compact sRmab;Edk 36A dUcenHeKGacykkugRtaMgGnuBaØat yF66.0 . eday karBt;eFobnwgG½kS x dUcenHeKecaltYEdlTak;TgnwgkarBt;eFobG½kS y . dUcenHeK)an ( ) ( ) 0.1877.0

3666.019.13

3660.0944.6

60.0<=+=+

bx

bx

y

aFf

Ff (OK)

RtYtBinitüsmIkar B.25 BIsmIkar B.22

8333.060354.06.04.06.0

2

1 =⎟⎠⎞

⎜⎝⎛−−=−=

MMCm

Slenderness ratio EdleRbIkñúgkarKNna exF ' KW ( )( ) 38.41

35.412150.1

===x

x

b

br

LKr

KL

ehIy ( )

( )( )

ksirLK

EFxx

ex 21.8738.4123

2900012/23

12' 2

2

2

2===

ππ



( ) 0.1978.06.21

21.87944.61

19.138333.04250.0

'1

<=⎟⎠⎞

⎜⎝⎛ −

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+

bxex

a

bxmx

a

a

FFf

fCFf (OK)

cemøIy³ 4910×W RKb;RKan; Design Aids eRkABItarag nigdüaRkamsRmab;KNnassr nigFñwm principal Manual design aid sRmab; beam-column CataragéntémøefrsRmab;eRbIkñúgkareRCIserIsmuxkat;dMbUg (Burgett, 1973). témøefr TaMgenH Gac[GñkKNnabMElgm:Um:g;Bt;[eTACabnÞúktamG½kSsmmUlEdlGacpSMCamYynwgbnÞúkCak; EsþgedIm,ITTYl)anbnÞúktamG½kSRbsiT§PaBsrub. bnÞab;mkeKGacbBa©ÚlbnÞúktamG½kSRbsiT§PaBenH eTAkñúg Column allowable load table eKnwgTTYl)anmuxkat;sakl,gEdleKGacykvaeTAsikSa epÞógpÞat;)an. B>6> snñidæan (Concluding Remarks) eTaHbICa ASD RtUv)anCMnYsy:agelOneday LRFD k¾eday k¾vaenAEtRtUv)anGnuBaØat [eRbIeday AISC dEdl ehIyeBlxøHk¾eKenAEteRbIvaEdr. sRmab;GñksikSaEdlmanbMNgcg;dwg lMGitBI ASD elIsBIGVIEdl)anerobrab;kñúg]bsm<½n§enHGacrk)anenAkñúg Design of Steel structure

(Gaylord and stallmeyer, 1992) EdlenAkñúgenaHk¾manerobrab;BI AISC Specification provision pgEdr.

Education

Structure analysis LRFD steel design