unit 3 Introduction to Indeterminate Structures

7/29/2019 unit 3 Introduction to Indeterminate Structures

1/20

216+ @ktrjguft`jk tj @kghthro`kbth Vtrufturhs

Weh ghvhijpohkt jd teh lhkhrbi ohtejg djr `kghthro`kbth strufturhs oby ch

frhg`thg tj `kghphkghkt wjrns cy Mbohs Fihrn Obxwhii %2547) Jttj Ojer

%25


2/20

D`lurh 216+2+ Vtbt`fbi `kghthro`kbfy jd b pibkh truss+

216+3+ Ghthro`kbth vhrsus @kghthro`kbth Vtrufturhs

Fjopbr`sjks oby ch grbwk chtwhhk ghthro`kbth bkg `kghthro`kbth

strufturhs jk teh cbs`s jd hfjkjoy bhsteht`fs fjkstruftbcì`ty bkg sbdhty+

@k jkh shksh ghthro`kbth strufturhs oby ch fbiihg obrl`kbiiy stbcih+ Webt

òpi`hs tebt b ghthro`kbth strufturh fbk chfjoh ukstbcih w`te b s`klih ijfbi

dbìurh sufe bs b ijss jd b s`klih suppjrt rhstrb`kt+ @kghthro`kbth strufturhs

brh fjopbrbt`vhiy ojrh rhgukgbkt `+h+ tehy pjsshss ojrh fjkstrb`kts tebk

o`kòbiiy khfhssbry tj obnh teh strufturh stbcih bkg ghthro`kbth+ Ijfbi

#dbìurhs# `k `kghthro`kbth strufturhs sufe bs djrobt`jk jd b pibst`f e`klh `k

b sthhi ohochr brh tjihrbthg v`b teh rhg`str`cut`jk jd strhsshs tj jtehr pbrts

jd teh strufturh+

Djr ghthro`kbth strufturhs òphrdhft`jks sufe bs `k`t`bi ibfn jd flt jr

dbcr`fbt`jk hrrjrs shtti`kl jd suppjrts bkg thophrbturh febklh %drjo ghs`lk

vbiuh) gj kjt `kgufh bgg`t`jkbi strhsshs `k teh strufturh+ Jk teh jtehr ebkg

sufe s`tubt`jks `kgufh bgg`t`jkbi strhss `k `kghthro`kbth strufturhs+

216+6+ Weh Lhkhrbi Djrfh Ohtejg

Weh lhkhrbi djrfh ohtejg djr `kghthro`kbth strufturhs ebs teh djiijw`kl

sthps=


3/20

2+ @ghkt`dy b sht jd bpprjpr`bth rhgukgbkt djrfhs tehrhcy rhguf`kl teh

strufturh tj b stbcih ghthro`kbth stbth+ We`s `s fbiihg tehpròbry

strufturh+ Weh hxthrkbi ijbgs brh bppi`hg tj teh pròbry strufturh+ Djr teh

pròbry strufturh g`spibfhohkts %ghffihft`jks bkg*jr rjtbt`jks) brh

fjoputhg bt teh ijfbt`jks jd teh rhgukgbkts+

3+ Weh pròbry strufturh %w`tejut ijbgs) `s tehk ijbghg cy uk`t ijbgs

fjrrhspjkg`kl tj teh rhgukgbkts jkh bt b tòh+ Wehsh strufturhs brh

fbiihg teh shfjkgbry strufturhs+ Weus wh ebvh bs obky shfjkgbry

strufturhs bs tehrh brh rhgukgbkts `+h+ teh sboh bs teh ghlrhh jd

`kghthro`kbfy jd teh strufturh+ Ghffihft`jks jr rjtbt`jks brh fjoputhg djr

hbfe jd tehsh shfjkgbry strufturhs bt teh ijfbt`jks jd teh rhgukgbkts+

6+ Fjopbt`cì`ty rhibt`jks brh tehk wr`tthk djr hbfe rhgukgbkt wehrh teh

suo jd teh ghffihft`jks %jr rjtbt`jks) bt b sphf`flf ijfbt`jk `s sht hqubi tj b

prhghthro`khg vbiuh usubiiy zhrj+ We`s rhsuits `k b sht jdk sòuitbkhjus

hqubt`jks `k teh k uknkjwks %rhgukgbkts)+

216+7+ Djrfh Ohtejg @iiustrbt`jk

Weh chbo sejwk `k D`l+ 216+3 `s `kghthro`kbth tj teh flrst jrghr `+h+ `t ebsjkh hxtrb rhbft`jk %chyjkg teh terhh tebt fbk ch sjivhg us`kl hqubt`jks jd

stbt`f hquì`crùo)+ Fjkshquhktiy jkh jd teh hxtrb rhbft`jks `s fejshk bs b

rhgukgbkt djrfh bkg rhojvhg drjo teh strufturh+ Djr ojrh fjopihx

strufturhs tebt brh e`lehr jrghr `kghthro`kbth teh bpprjpr`bth kuochr jd

rhgukgbkts oust ch fejshk+ Djr teh ghojkstrbt`jk chijw iht us fejjsh teh

vhrt`fbi rhbft`jk bt teh rjiihr suppjrt bs teh rhgukgbkt+ Weh rhojvbi jd teh

rhgukgbkt drjo teh jr`l`kbi strufturh rhsuits `k b stbcih ghthro`kbth chbo+

We`s `s fbiihg tehpròbry strufturh + We`s `s sejwk `k D`l+ 216+6+

D`lurh 216+3+ Vtbt`fbiiy `kghthro`kbth chbo+
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch103#ch103fig03http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch103#ch103fig02


4/20

D`lurh 216+6+ Qròbry chbo %rhgukgbkt rhojvhg)+

@k rhojv`kl teh rjiihr suppjrt drjo teh jr`l`kbi chbo wh ebvh v`jibthg b

cjukgbry fjkg`t`jk tehrh+ \ehrhbs teh jr`l`kbi chbo wbs fjkstrb`khg drjo

ghffihft`kl vhrt`fbiiy bt teh rjiihr teh pròbry chbo guh tj teh rhojvbi jd teh

suppjrt `s bcih tj ghffihft+ We`s ghffihft`jk `s sejwk bs `k D`l+ 216+6+ Kjth

tebt guh tj teh pròbry chbo ch`kl ghthro`kbth wh fbk hbsìy sjivh djr teh

ghffihft`jk + Jcv`jusiy teh jkh g`fihrhkfh chtwhhk teh jr`l`kbi chbo bkg

teh pròbry chbo `s tebt teh vhrt`fbi rhbft`jk C `s o`ss`kl+ \h put te`s cbfn

`k b shfjkgbry chbo bs sejwk `k D`l+ 216+7+

D`lurh 216+7+ Vhfjkgbry chbo %rhgukgbkt rh`kshrthg)+

Weus teh jr`l`kbi chbo ebs chhk spi`t `ktj b pròbry chbo bkg b shfjkgbry

chbo+ Djr teh pr`kf`pih jd suphrpjs`t`jk tj ch vbi`g teh strufturh oust ch

i`khbr `k chebv`jr %h+l+ b gjuci`kl jd teh ijbg fbushs b gjuci`kl jd teh

g`spibfhohkts)+ Bisj djr teh suphrpjs`t`jk tj ch vbi`g lhjohtr`fbiiy teh tjtbighffihft`jk bt mj`kt Coust ch zhrj %fjkstrb`khg cy b rjiihr suppjrt)+ Weus wh

ebvh

%216+2)

Weh qubkt`ty `s teh hkg/ghffihft`jk jd b %ghthro`kbth) fbktìhvhr chbo bkgfbk ch fbifuibthg `d teh ijbg`kl jk teh pròbry chbo `s sphf`flhg+ Weh

qubkt`ty jk teh jtehr ebkg ghphkgs jk teh uknkjwk rhgukgbkt C +

Ejwhvhr `d teh rhgukgbkt `s rhpibfhg cy b nkjwk vbiuh %sufe bs 2) teh

Q

Q

y

Q

Vy


5/20

rhsuit`kl ghffihft`jk fbk ch fbifuibthg+ Guh tj i`khbr`ty jd teh strufturh

wh fbk sby tebt teh ghffihft`jk %guh tj teh duii rhgukgbkt C ) `s b i`khbr

ouit`pih jd teh ghffihft`jk %guh tj teh uk`t ijbg)=

%216+3)

Weh tjtbi ghffihft`jk `s tehk l`vhk cy

%216+6)

Weh vbiuh jd teh rhgukgbkt djrfh `s tehk l`vhk cy

%216+7)

Weh prhfhg`kl bpprjbfe `s bisj fbiihg teh uk`t/ijbg ohtejg +

216+8+ Fbst`li`bkj,s Ohtejg

Fbst`li`bkj,s ohtejg jr teh ohtejg jd ihbst wjrn `s cbshg jk Fbst`li`bkj,s

shfjkg tehjrho+ Weh tehjrho `s cbshg jk teh djiijw`kl bssuopt`jksteh

strufturh `s obgh drjo b i`khbr hibst`f obthr`bi tehrh brh kj tehrobi

strhsshs %thophrbturh `s fjkstbkt) jr suppjrt shttihohkts+ Bky bppi`fbt`jk jd

Fbst`li`bkj,s ohtejg `s rhstr`fthg tj s`tubt`jks wehrh tehsh fjkg`t`jks ejig

truh+

216+8+2+ Fbst`li`bkj,s Vhfjkg Wehjrho

Weh ghffihft`jk fjopjkhkt jd teh pj`kt jd bppi`fbt`jk jd bk bft`jk jk b

strufturh `k teh g`rhft`jk jd tebt bft`jk w`ii ch jctb`khg cy hvbiubt`kl teh

flrst pbrt`bi ghr`vbt`vh jd teh tjtbi `kthrkbi strb`k hkhrly jd teh strufturh w`te

rhsphft tj teh bppi`hg bft`jk+

216+4+ Fbst`li`bkj,s Ohtejg Bppi`hg tj Wrusshs

Fjks`ghr teh `kghthro`kbth truss sejwk `k D`l+ 216+8+ Weh truss `s

V

Vy

V
http://accessengineeringlibrary.com/browse/civil-engineering-all-in-one-pe-exam-guide-breadth-and-depth-second-edition/c9780071787727ch103#ch103fig05


6/20

`kghthro`kbth tj teh flrst jrghr+ Weh `kghthro`kbfy `k te`s fbsh `s `kthrkbi

s`kfh tehrh brh terhh hxthrkbi rhbft`jks we`fe brh sjivbcih us`kl teh terhh

hqubt`jks jd stbt`f hquì`crùo+ Weh hxtrb uknkjwk br`shs guh tj teh

prhshkfh jd jkh rhgukgbkt `kthrkbi ohochr+ Shohochr tebt bky jd teh truss

ohochrs fjuig ch ghs`lkbthg bs b rhgukgbkt+ Weh shihft`jk jd teh

rhgukgbkt ohochr `s ljvhrkhg cy teh rhqu`rhohkt tj obnh teh pròbry

strufturh stbcih+ \h brh lj`kl tj rhojvh teh rhgukgbkt truss ohochr %FD)

tehrhcy frhbt`kl b stbcih ghthro`kbth truss bkg tehk rh`kshrt teh #hfihft# jd

teh rhojvhg ohochr `ktj b shfjkgbry strufturh %shh D`ls+ 216+4 bkg 216+


7/20

D`lurh 216+


8/20

Fbst`li`bkj,s shfjkg tehjrho oby ch stbthg bs #`k bk `kghthro`kbth

strufturh teh vbiuhs jd teh rhgukgbkts oust ch sufe tebt teh tjtbi `kthrkbi

hibst`f strb`k hkhrly rhsuit`kl drjo b l`vhk systho jd ijbgs `s o`kòuo+# Djr

bk `ghbi truss wehrh teh ohochr djrfhs brh purhiy bx`bi teh bx`bi strb`k

hkhrly `s l`vhk cy b suoobt`jk jd teh bx`bi strb`k hkhrly djr bii truss

ohochrs=

%216+8)

Djr te`s strb`k hkhrly tj ch o`kòuo `ts pbrt`bi ghr`vbt`vh w`te rhsphft tj

teh rhgukgbkt Q `s zhrj=

@d bii ohochrs ebvh hqubi frjss/shft`jkbi brhb %B) bkg teh sboh ojguius jd

hibst`f`ty %H) teh prhfhg`kl hqubt`jk fbk ch sòpi`flhg tj

Bppiy`kl teh bcjvh hqubt`jk tj teh sphf`flf truss sejwk wh ebvh

1+438Q 1+60Q .

2+84Q

DH 7+1 27+5 1 27+5 1 1 1

DF 4+7 1+1 .Q .Q .2+1 .Q 4+7Q

61+7

.

33+13


9/20

We`s vbiuh jdQ fbk tehk ch ushg tj fbifuibth teh djrfhs `k bii truss ohochrs+

216+


10/20

Drjo teh drhh/cjgy g`blrbo jd teh pr`obry chbo jkh fbk wr`th teh djiijw`kl

hxprhss`jks djr teh rhbft`jks btB+ Wehsh brh bt te`s stblh jd teh bkbiys`s

dukft`jks jd teh ijbgs Q bkg R+

Xs`kl tehsh hxprhss`jks djr S bkg O jkh oby tehk durtehr wr`th teh

djiijw`kl hxprhss`jks djr teh `kthrkbi chkg`kl/ojohkt dukft`jks `k shlohkts

2 3 bkg 6+

Djr fjopbt`c`i ty w`te teh suppjrts teh vhrt`fbi ghffihft`jks bt teh rjiihr

ijfbt`jks oust ch zhrj+ Wurk`kl tj Fbst`li`bkj,s shfjkg tehjrho tj fbifuibth

tehsh ghffihft`jks wh ebvh

Fbrry`kl jut tehsh `kthlrbt`jks wh jctb`k teh djiijw`kl pb`r jd hqubt`jks=

B B


11/20

Ehkfh teh rhbft`jks bt Cbkg F brh l`vhk cy 27+46 n`ps %upwbrg) bkg 4+76

n`ps %upwbrg)+

216+5+ G`spibfhohkt Ohtejgs

B crjbg fbthljry jd ohtejgs nkjwk bs g`spibfhohkt ohtejgs djros b obmjr

pbrt jd teh strufturbi bkbiys`s tehjry ushdui djr `kghthro`kbth strufturhs+

Wwj jd teh ojst prjo`khkt jd tehsh ohtejgs brh teh sijph/ghffihft`jk ohtejg

bkg teh ojohkt/g`str`cut`jk ohtejg+ Wehsh brh cr`hffiy g`sfusshg ibthr+

\ehrhbs `t `s e`leiy uki`nhiy tebt teh furrhkt djrobt jd teh Q+H+ hxbo`kbt`jk

wjuig rhqu`rh tehsh ohtejgs tj ch bppi`hg `k duii nkjwihglh jd nhy hihohkts

jd tehsh ohtejgs oby ch ushdui pbrt`fuibriy djr teh strufturbi ghpte

hxbo`kbt`jk+

216+0+ Ojohkt/G`str`cut`jk Ohtejg

Weh ojohkt/g`str`cut`jk ohtejg ebs chhk rhihlbthg tj e`stjr`fbi opjrtbkfh

jkiy guh tj teh bgvhkt jd e`le/sphhg fjoput`kl bkg teh db`riy hbsy

bppi`fbt`jk jd teh st`fikhss ohtejg jk teh g`l`tbi fjoputhr+ Weh cbs`f `ghb jd

teh ojohkt/g`str`cut`jk ohtejg `s tj ijfn bii suppjrts sj tebt tehy chebvh

i`nh flxhg suppjrts bkg tehk tj ukijfn teho jkh cy jkh bkg g`str`cuth teh

rhsuit`kl #ukijfn ojohkts# terjulejut teh strufturhs+

Vthp 2= D`x`kl Bii Kjghs

D`x`kl bii kjghs ukfjupihs teh vbr`jus pbrts jd teh strufturh `ktj

`kghphkghkt flxhg/flxhg spbks+ Weh hxthrkbiiy bppi`hg ijbg tehk frhbths flxhg/

hkg djrfhs jk hbfe spbk+ We`s bisj ohbks tebt bt hvhry kjgh tehrh oby hx`st

b ojohkt òcbibkfh+ Cut s`kfh teh kjgh `s fibophg hquì`crùo gjhs kjt

khhg tj ch sbt`sflhg+ D`x`kl bii kjghs ukfjupihs teh vbr`jus pbrts jd teh

strufturh `ktj `kghphkghkt flxhg/flxhg spbks+ Weh hxthrkbiiy bppi`hg ijbg

tehk frhbths flxhg/hkg djrfhs %ojohkts) jk hbfe spbk+

Vthp 3= Shihbs`kl KjghsJkh bt b Wòh

\ehk b pbrt`fuibr kjgh `s rhihbshg teh ojohkt òcbibkfh bt tebt kjgh

khhgs tj ch fjrrhfthg cy bppiy`kl b ojohkt jd teh jppjs`th g`rhft`jk+ Webt

fjrrhft`jk ojohkt `s tehk g`str`cuthg tj bii ohochrs fjkkhfthg tj teh kjgh

`k prjpjrt`jk tj teh`r ffihxurbi st`fikhsshs+ Weh rhsuit`kl ohochr hkg ojohkt

fbk bisj frhbth b fbrry/jvhr/ojohkt bt teh dbr hkg jd teh ohochr `d tebt dbr


12/20

hkg `s r`l`g+ Weh ojohkt/g`str`cut`jk ohtejg `s teus bk `thrbt`vh fjkvhrlhkt

prjfhss fjks`st`kl jd teh djiijw`kl sthps=

2+ Fbifuibth flxhg/hkg ojohkts bt hbfe kjgh guh tj teh hxthrkbi ijbgs+

3+ Bt hbfe kjgh bppiy b fjrrhft`jk ojohkt tj hbfe ohochr sufe tebt teh

ohochr fjrrhft`jk ojohkts brh prjpjrt`jkbi tj ohochr chkg`kl st`fikhss

bkg kjgh sbt`sflhs ojohkt hquì`crùo hqubt`jk+

6+ Djr bky ohochr tebt ebs b r`l`g dbr kjgh %kjt p`kkhg) bppiy b fbrry/jvhr/

ojohkt bt teh dbr kjgh hqubi tj ebid teh fjrrhft`jk ojohkt bt teh khbr

kjgh+

7+ Shphbt sthps 3 bkg 6 uktì fjrrhft`jk ojohkts chfjoh bffhptbciy sobii+

Kjth tebt flxhg/hkg ojohkts djr vbr`jus stbkgbrg ijbg`kl fjkg`t`jks brh

suoobr`zhg bt teh hkg jd te`s febpthr+ Wehsh sthps brh ìiustrbthg `k Hxbopih

216+2+

Hxbopih 216+2

Fjks`ghr teh strufturh sejwk chijw+ @t ebs b flxhg suppjrt btB bkg rjiihrs bt

Cbkg F+ VpbkBCfbrr`hs b uk`djroiy g`str`cuthg ijbg bkg spbk CF fbrr`hs bfjkfhktrbthg ijbg+ Weh drhh/cjgy g`blrbo w`te teh flvh uknkjwk suppjrt

rhbft`jks `s bisj sejwk+

Kuochr jd uknkjwks ? 8

Kuochr jd hqubt`jks jd stbt`f hquì`crùo ? 6


13/20

Ghlrhh jd `kghthro`kbfy ? 3

Iht H@ch fjkstbkt+

Wrhbt`kl cjte spbks BCbkgCFbs flxhg/flxhg

Ohochr Vt`fikhsshs %N ? 7H@*I)

G`str`cut`jk Dbftjrs bt Mj`kt C

D`xhg/Hkg Ojohkts %Fijfnw`sh Qjs`t`vh)

D`lurh 216+5 sejws teh ojohkt/g`str`cut`jk ohtejg bppi`hg tj te`s

strufturh+


14/20

D`lurh 216+5+ Ojohkt/g`str`cut`jk ìiustrbt`jkohtejg jkh+

Kjth tebt teh `thrbt`vh prjfhss `s kjt yht fjopihthbs teh khxt fbrry/jvhr/

ojohkts wìi fjkt`kuh tj gò`k`se cut kjt hqubi tj zhrj+ Fjktrbst te`s w`te

teh khxt bpprjbfe wehrh teh prjfhss fjkvhrlhs `k b s`klih `thrbt`jk+

Wrhbt`kl spbkBCbs flxhg/flxhg bkgCFbs flxhg/p`kkhg

Ohochr Vt`fikhsshs %N ? 7H@*I djr D`xhg/D`xhg N ? 6H@*I djr D`xhg/Q`kkhg)

Kjth tebt teh ohochr st`fikhss jdCF `s g`fihrhkt drjo chdjrh+

G`str`cut`jk Dbftjrs bt Mj`kt C

D`xhg/Hkg Ojohkts


15/20

Weh ojohkt g`str`cut`jk prjfhss `s sejwk `k D`l+ 216+0+

D`lurh 216+0+ Ojohkt/g`str`cut`jk `iiustrbt`jkohtejg 3+

216+21+ Weh Vijph/Ghffihft`jk Ohtejg

Weh sijph/ghffihft`jk hqubt`jks djr b strufturbi ohochr chtwhhk b #khbr

kjgh# %k) bkg b #dbr kjgh# %d) oby ch wr`tthk `k thros jd teh kjgbi

g`spibfhohkts bs djiijws+ Ehrh bkg brh kjgbi rjtbt`jks bkg `s teh

trbksvhrsh g`spibfhohkt jd teh dbr kjgh rhibt`vh tj teh khbr kjgh bs `k D`l+

216+21+

k d


16/20

D`lurh 216+21+ Vijph/ghffihft`jk vbr`bcihs+

Wehsh hqubt`jks sejw tebt teh ojohkt bt b kjgh `s fjopjshg jd

fjktr`cut`jks jd tehsh kjgbi g`spibfhohkts bkg teh flxhg/hkg ojohkts we`fe

brh teh kjgh/iuophg hfihft jd teh hxthrkbi ijbg`kl+

Hxbopih 216+3

Iht us rhphbt teh sboh hxbopih bs fjks`ghrhg hbri`hr us`kl teh sijph/

ghffihft`jk ohtejg+

D`xhg/Hkg Ojohkts %Fijfnw`sh Qjs`t`vh)


17/20

Vijph/Ghffihft`jk Hqubt`jks %Fijfnw`sh Qjs`t`vh)

VpbkBC=

Vpbk CF=

Hqu`i`cr`uo hqubt`jks brh

Vjiv`kl tehsh hqubt`jks wh lht

Vucst`tut`kl tehsh cbfn `ktj teh ojohkt hxprhss`jks wh lht

Wehsh rhsuits brh db`riy fijsh tj tejsh jctb`khg drjo ojohkt g`str`cut`jk

hbri`hr+

216+22+ Xs`kl Shsuits drjo Ojohkt/G`str`cut`jk jr Vijph/

Ghffihft`jk Ohtejgs


18/20

Vthp 2= Grbw`kl teh Drhh/Cjgy G`blrbos

Weh sjiut`jk jd teh ghffihft`jk ohtejgs fjks`sts jd teh kjgbi ojohkts O

O O bkg sj jk+ Nkjwihglh jd tehsh ojohkts biijws teh #ghfjupi`kl#

jd teh `kg`v`gubi spbks bs sejwk chijw+

Vthp 3= \r`t`kl teh Hquì`crùo Hqubt`jks

Djr teh ihdt sucstrufturh teh djiijw`kl brh teh twj hquì`crùo hqubt`jks=

Djr teh r`let sucstrufturh teh djiijw`kl brh teh twj hquì`crùo hqubt`jks=

Wehrhdjrh teh tjtbi vhrt`fbi rhbft`jk bt C `s

Shbft`jk btB `sB ? 3+513 n`ps

Shbft`jk bt F `s F ? 2+664 n`ps

216+23+ D`xhg/Hkg Ojohkts

D`lurh 216+22 sejws flxhg/hkg ojohkts djr b vbr`hty jd ijbgs jk b flxhg/flxhg

chbo+

BC

CB CF

y

y


19/20

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Documents

unit 3 Introduction to Indeterminate Structures