ASD vs LRFD - · PDF file01/06/2016 · 3 ASD and LRFD Major Differences • Load...

LRFD and ASD

Source: GT

STRUDL Users GroupLas Vegas, Nevada, 2005

Hamid Zand

AISC ASD and LRFD

AISC =

American Institute of SteelConstruction

Allowable Stress DesignAISC Ninth Edition

Load and Resistance Factor DesignAISC Third Edition

ASD and LRFD Major Differences

Combinations and load factors•

ASD results are based on the stresses and LRFD results are based on the forces and moments capacity

computation

ASD Load Combinations

+ 1.0L•

+ 0.75L

+ 0.75W

+ 0.75L

+ 0.75E

dead loadL

live loadW

wind loadE

earthquake load

LRFD Load Combinations

1.4D•

+ 1.6L

+ 1.6W + 0.5L•

+ 0.5L

(1.6W or 1.0E)

dead loadL

live loadW

wind loadE

earthquake load

Deflection Load Combinations for ASD and LRFD

+ 1.0L•

+ 1.0L

+ 1.0W

+ 1.0L

+ 1.0E

dead loadL

live loadW

wind loadE

earthquake load

Forces and Stresses

actual stress values are compared to the AISCallowable stress values

actual forces and momentsare compared to the AISClimiting forces and momentscapacity

Slenderness Ratio

CompressionKL/r

TensionL/r

Tension Members

Check L/r

ratio•

Check Tensile Strength based on the cross-

section’s Gross Area•

Check Tensile Strength based on the cross-

section’s Net Area

Tension Members

= FX/Ag

Gross Area

= FX/Ae

Net Area

ϕt Pn

= ϕt Ag Fy

= 0.9 for Gross Area

ϕt Pn

= ϕt Ae

= 0.75 for Net Area

Tension Members

ASD (ASD Section D1)

Gross Area Ft

= 0.6Fy

Net Area

= 0.5Fu

LRFD (LRFD Section D1)

Gross Area ϕt Pn

= ϕt Fy

= 0.9Net Area

ϕt Pn

= ϕt Fu Ae

= 0.75

Compare ASD to LRFD

+ 1.0LLRFD

+ 1.6L

= 0.9Fy

(LRFD)

= 0.75Fu

(LRFD)

ASD ×

= LRFD

Tension Members

FIXED JOINT

Tension Members•

Member is 15 feet long

Fixed at the top of the member and free at the bottom•

Loadings are:

Self weight•

400 kips tension force at the free end

Load combinations based on the ASD and LRFD codes

Steel grade is A992•

Design based on the ASD and LRFD codes

Tension Members

W18x46

Actual/Allowable Ratio = 0.989

W10x49

Actual/Limiting Ratio = 0.989

Tension Members

ASDW18x46

Area = 13.5 in.2

FX = 400.688 kips

Ratio = 0.989

LRFDW10x49

Area = 14.4 in.2

FX = 640.881 kips

Ratio = 0.989

Tension MembersLoad Factor difference between LRFD and ASD

640.881 / 400.688 = 1.599Equation Factor difference between LRFD and ASD

LRFD = (1.5) ×

Estimate required cross-sectional area for LRFD

LRFD W10x49 Area = 14.4 in.2

Area for LRFD 135 640881400 688

0 9890 989

14 395. ..

Tension MembersCode Check based on the ASD9 and using W10x49

FX = 400.734 kips

Ratio = 0.928

Load Factor difference between LRFD and ASD640.881 / 400.734 = 1.599

LRFD W10x49

Ratio = 0.989

LRFD Ratio computed from ASD 0 928 640881400 734

0 989. ..

Tension MembersASD

Example # 1Live Load = 400 kips

W18x46

Actual/Allowable Ratio = 0.989LRFD

W10x49

Actual/Limiting Ratio = 0.989Example # 2

Dead Load = 200 kipsLive Load = 200 kips

W14x43

Actual/Limiting Ratio = 0.989Code check W14x43 based on the ASD9

W14x43

Compression Members

Check KL/r

ratio•

Compute Flexural-Torsional Buckling and Equivalent (KL/r)e

Find Maximum of KL/r

and (KL/r)e

Compute Qs

and Qa

based on the b/t

and h/tw

ratios•

Based on the KL/r

ratio, compute allowable

stress in ASD or limiting force in LRFD

Compression Members

= FX/Ag

ϕc Pn

= ϕc Ag FcrWhere

= 0.85

Limiting Width-Thickness Ratios for Compression Elements

95 / Fy

056. /E Fy

253 / Fy

149. /E Fy

Assume E

= 29000 ksiASD

95 / Fy

9536. / Fy

253 / Fy

25374. / Fy

Compression Members

ASD KL/r

(ASD E2-1 or A-B5-11)

LRFD (LRFD A-E3-2)

F Q FcrQ

yc 0 658

Where C EQFc

Where c

c Q 15.

Compression Members

ASD KL/r

> C′c

(ASD E2-2)

LRFD (LRFD A-E3-3)

/Where C E

c Q 15.

F Fcrc

Where c

Compression Members

LRFDF Fcr

. Where

KL rcr

0877 2

EKL rcr

2017123

Compression Members

ASD LRFD

= 1.681

LRFD Fcr

= ASD Fa

EKL rcr

2017123

Compression Members

(ASD C-E2-2)

= Maximum of

( λcy

, λcz

, λe )

KL rK L

z e/ , ,

WhereKLr

Compression Members

LRFDWhere:

Compression Members

Flexural-Torsional Buckling

x x y z

Computation

When 95 195/ / / / /F k b t F ky c y c

Q b t F ks y c 1293 0 00309. . ( / ) /

When 056 103. / / . /E F b t E Fy y

Q b t F Es y 1415 0 74. . ( / ) /

h th t kc c

4 05 70 100.46.

// , .if otherwise

Computation

Assume E

= 29000 ksiASD

When 95 195/ / / / /F k b t F ky c y c

Q b t F ks y c 1293 0 00309. . ( / ) /

When 9536 1754. / / . /F b t Fy y

Q b t Fs y 1415 0 004345. . ( / )

Computation

When b t F ky c/ / / 195

Q k F b ts c y 26200 2/ /

When b t E Fy/ . / 103

Q E F b ts y 0 69 2. / /

Computation

Assume E

= 29000 ksiASD

When b t F ky c/ / / 195

Q k F b ts c y 26200 2/ /

When b t Fy/ . / 1754

Q F b ts y 20010 2/ /

Computation

b tf b t f

253 1 44 3.

b t Ef b t

191 1 0 34. .

Assume ksiE b tf b t f

29000 32526 1 57 9, . .( / )

Compression Members

Z FIXED JOINT

-100.o

Compression Members•

Member is 15 feet long

Fixed at the bottom of the column and free at the top•

Loadings are:

Self weight•

100 kips compression force at the free end

Compression Members

W10x49

W10x54

Compression Members

ASDW10x49

Area = 14.4 in.2

= 100.734 kips

Ratio = 0.941

LRFDW10x54

Area = 15.8 in.2

= 160.967 kips

Ratio = 0.944

Compression MembersLoad Factor difference between LRFD and ASD

LRFD Fcr

= (1.681) ×

ASD Fa

Estimate required cross-sectional area for LRFD

LRFD W10x54 Area = 15.8 inch

Area for LRFD 14 4 160 967100 734

101681

0 9410 944

16 05. ..

Compression MembersCode Check based on the ASD9 and use W10x54

= 100.806 kips

Ratio = 0.845

LRFD W10x54

Ratio = 0.944

LRFD Ratio computed from ASD 0845 160 967100806

101681

0 944. ..

Compression MembersASD

W10x49

W10x54

Dead Load = 50 kipsLive Load = 50 kips

W10x49

Flexural Members•

Based on the b/t

and h/tw

ratios determine the compactness of the cross-section

Classify flexural members as Compact, Noncompact, or Slender

When noncompact

section in ASD, allowable stress Fb

is computed based on the l/rt

ratio. l

is the laterally unbraced length of the compression flange. Also, Cb

has to be computed•

When noncompact

or slender section in LRFD, LTB, FLB,

and WLB are checked•

LTB for noncompact

or slender sections is computed using Lb

and Cb

is the laterally unbraced

length of the compression flange

Flexural Members

= MZ/SZ

ϕb Mn

Where ϕb

Assume E

= 29000 ksi

d t Fw y/ / 640

b t E Fy/ . / 0 38 h t E Fw y/ . / 376

b t Fy/ / 65

b t Fy/ . / 64 7 h t Fw y/ . / 640 3

Flexural Members Compact Section

ASD (ASD F1-1)

= 0.66Fy

LRFD (LRFD A-F1-1)

ϕb Mn

= ϕb Mp

= ϕb Fy ZZ

≤ 1.5Fy SZ

Where ϕb

FIXED JOINT

-15.00

FIXED JOINT

Braced at 1/3 Points

Member is 12 feet long•

Fixed at both ends of the member

Loadings are:•

Self weight

15 kips/ft uniform load•

Braced at the 1/3 Points

W18x40

ASDW18x40

= 68.4 in.3

= 2165.777 inch-kips

Ratio = 0.959

LRFDW18x40

= 78.4 in.3

Ratio = 0.982

Equation Factor difference between LRFD and ASDLRFD = (0.66Sz

)(1.5989) / (0.9Zz

LRFD W18x40

= 78.4 in.3

for LRFD 68 4 3462 9332165777

0 660 9

0 9590 982

78 3. ..

Code Check based on the ASD9, Profile W18x40MZ

Ratio = 0.959

LRFD W18x40 Ratio = 0.982

0 660 9

68 478 4

0 981. ..

ASDExample # 1

Live Load = 15 kips/ftW18x40

Example # 1Live Load = 15 kips/ft

W18x40

Dead Load = 7.5 kips/ftLive Load = 7.5 kips/ft

W18x40

Flexural Members Noncompact

Section

ASD•

Based on b/t, d/tw

and h/tw

determine if the section is noncompact

Compute Cb

Compute Qs

Based on the l/rt

ratio, compute allowable stress Fb

Laterally unbraced

length of the compression flange (l) has a direct effect on the equations of the noncompact

section

Flexural Members Noncompact Section

= MZ/SZ

ϕb Mn

Where ϕb

65 95F b t Fy y

d t Fw y 640

0 38 083. / .E F b t E Fy L

376 57. .E F h t E Fy w y

h t Fw b 760

Assume E

= 29000 ksiASD

65 95F b t Fy y

d t Fw y 640

64 7 1413. / / . /F b t Fy L

640 3 970 7. / . /F h t Fy w y

h t Fw b 760

(ASD F1-3)

(ASD F1-2)

ASD Equations F1-6, F1-7, and F1-8 must to be checked.

0 79 0 0022

If minimum orL L

F d A Fb cf

76 20000

(ASD F1-6)

102 10 510 103 3

CF F Qb

by y s

23 1530 10

(ASD F1-7)

510 103

l rF Qb

170 100 6

For any value of l/rT

(ASD F1-8)FC

ld AF Qb

12 100 6

1. LTB, Lateral-Torsional Buckling

2. FLB, Flange Local Buckling

3. WLB, Web Local Buckling

Section

LRFD–

Compute Cb•

Based on the Lb

, compute limiting moment capacity. Lb

is the lateral unbraced

length of the compression flange,λ

/ry•

has a direct effect on the LTB equations for noncompactand slender sections

FLB•

Compute limiting moment capacity based on the b/t

ratio of the flange, λ

= b/t–

Compute limiting moment capacity based on the h/tw

ratio of the web, λ

= h/tw

LRFD LTB (Table A-F1.1)

For λp

(LRFD A-F1-2)

Where:Mp

1.5Fy Sz

= Smaller of (Fyf

) or Fyw

M C M M M Mn b p p rp

176. E Fyf

LRFD LTB (Table A-F1.1)

Where:

LRFD FLB (Table A-F1.1)

For λp

(LRFD A-F1-3)Where:

1.5Fy Sz

= Smaller of (Fyf

) or Fyw

= b/tλp

M M M Mn p p rp

0 38. E Fy

083. E FL

LRFD WLB (Table A-F1.1)

For λp

(LRFD A-F1-3)Where:

1.5Fy Sz

= Re Fy

for non-hybrid girder

M M M Mn p p rp

LRFD WLB (Table A-F1.1)

λ = h/tw

376. E Fy

57. E Fy

C M M M MM M

M M M C

175 105 0 3 2 3

1 2 1 22

. . . .

, .maxIf between and

M M M MMMM

bA B C

12 52 5 3 4 3

absolute value of moment at quarter pointabsolute value of moment at centerlineabsolute value of moment at three quarter point

Roller

-12.00

Section

Pin at the start of the member

Roller at the end of the member•

Cross-section is W12x65

Loadings are:•

Self weight

Check code based on the ASD and LRFD codes

ASDW12x65

= 1.0Actual/Allowable Ratio = 0.988

LRFDW12x65

= 1.136Actual/Limiting Ratio = 0.971

Code check is controlled by FLB.Cb

Section

ASDExample # 1

Live Load = 12 kips/ftW12x65

W12x65

Dead Load = 6 kips/ftLive Load = 6 kips/ft

W12x65

Design for Shear

= FY/Aw

= 0.4Fy

(ASD F4-1)

0.6Fyw Aw

(LRFD F2-1)

Where ϕv

h t Fw y/ 380

h t E Fw yw/ . / 2 45

Design for ShearAssume E

= 29000 ksi

= FY/Aw

= 0.4Fy

(ASD F4-1)

0.6Fyw Aw

(LRFD F2-1)Where ϕv

h t Fw y/ 380

h t Fw yw/ . / 417 2

Design for ShearASD

= FY/Ay

(ASD F4-2)

(LRFD F2-2)

Where ϕv

h t Fw y/ 380

2 45 307. / / . /E F h t E Fyw w yw

v y 2 89

0 62 45

h tyw wyw

Design for Shear

(LRFD F2-3)

Where ϕv

307 260. / /E F h tyw w

Design for Shear

FIXED JOINT

-15.00

FIXED JOINT

Braced at 1/3 Points

Design for Shear•

Same as example # 3 which is used for design of flexural member with compact section

Fixed at both ends of the member

Loadings are:•

Self weight

Braced at the 1/3 Points

Design for Shear

ASD (Check shear at the end of the member, equation “F4-1 Y”)

W18x40

LRFD (Check shear at the end of the member, equation “A-F2-1 Y”)

W18x40

Design for Shear

ASDW18x40

= 5.638 in.2

= 90.241 kips

Ratio = 0.8

LRFDW18x40

= 5.638 in.2

= 144.289 kips

Ratio = 0.948

Design for ShearCode Check based on the ASD9, Profile W18x40

= 90.241 kips

Ratio = 0.8Load Factor difference between LRFD and ASD

LRFD = (0.4)(1.5989) /(0.6)(0.9) ×

LRFD W18x40 Ratio = 0.948

0 40 6

0 948. ..

Design for ShearASD

W18x40

Dead Load = 7.5 kips/ftLive Load = 7.5 kips/ft

W18x40

Combined Forces

ASD fa

> 0.15

(ASD H1-1)

(ASD H1-2)

LRFD Pu

≥ 0.2

(LRFD H1-1a)

1 110.

bz0 610

Combined Forces

ASD fa

(ASD H1-1)

LRFD Pu

(LRFD H1-1a)

b nz210

Combined Forces

Combined Forces•

3D Simple Frame

3 Bays in X direction

3 @ 15 ft•

2 Bays in Z direction

2 @ 30 ft•

2 Floors in Y direction

2 @ 15 ft

• Loadings

Self weight of the Steel•

Self weight of the Slab

62.5 psf•

Other dead loads

15.0 psf•

Live load on second floor

50.0 psf•

Live load on roof

20.0 psf•

Wind load in the X direction

20.0 psf•

Wind load in the Z direction

20.0 psf

Combined Forces ASD

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 2.1600E+03 2.0974E+04 5.9418E+00 12 >< W12x58 1.4400E+03 2.4480E+04 6.9352E+00 4 >< W12x65 1.4400E+03 2.7504E+04 7.7919E+00 4 >< W12x72 2.1600E+03 4.5576E+04 1.2912E+01 12 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 >< W8x40 1.4400E+03 1.6848E+04 4.7730E+00 4 >< W8x48 1.4400E+03 2.0304E+04 5.7521E+00 4 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< ACTIVE UNITS WEIGHT KIP LENGTH INCH >< >< TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS >< >< LENGTH = 1.3320E+04 WEIGHT = 4.6566E+01 VOLUME = 1.6437E+05 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Combined Forces LRFD

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>< Active Units Weight Unit = KIP Length Unit = INCH >< >< Steel Take Off Itemize Based on the PROFILE >< Total Length, Volume, Weight, and Number of Members >< >< Profile Names Total Length Total Volume Total Weight # of Members >< W10x33 3.6000E+03 3.4956E+04 9.9030E+00 16 >< W10x39 1.4400E+03 1.6560E+04 4.6914E+00 4 >< W10x49 7.2000E+02 1.0368E+04 2.9373E+00 4 >< W12x45 1.4400E+03 1.9008E+04 5.3850E+00 4 >< W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 >< W8x31 1.4400E+03 1.3147E+04 3.7246E+00 4 >< W8x40 1.4400E+03 1.6848E+04 4.7730E+00 8 >< ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Combined Forces

WEIGHT = 46.566 kips

WEIGHT = 33.874 kips

Deflection Design ASD

Deflection Design LRFD

ASD vs LRFD - · PDF file01/06/2016 · 3 ASD and LRFD Major Differences • Load...

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