ASD vs LRFD - · PDF file01/06/2016 · 3 ASD and LRFD Major Differences • Load Combinations and load factors • ASD results are based on the stresses and LRFD results are based

1

AISC

LRFD and ASD

Source: GT

STRUDL Users GroupLas Vegas, Nevada, 2005

Hamid Zand

2

AISC ASD and LRFD

•

AISC =

American Institute of SteelConstruction

•

ASD =

Allowable Stress DesignAISC Ninth Edition

•

LRFD

=

Load and Resistance Factor DesignAISC Third Edition

3

ASD and LRFD Major Differences

•

Load

Combinations and load factors•

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

•

Cb

computation

4

ASD Load Combinations

•

1.0D

+ 1.0L•

0.75D

+ 0.75L

+ 0.75W

•

0.75D

+ 0.75L

+ 0.75E

D

=

dead loadL

=

live loadW

=

wind loadE

=

earthquake load

5

LRFD Load Combinations

•

1.4D•

1.2D

+ 1.6L

•

1.2D

+ 1.6W + 0.5L•

1.2D

±

1.0E

+ 0.5L

•

0.9D

±

(1.6W or 1.0E)

D

=

dead loadL

=

live loadW

=

wind loadE

=

earthquake load

6

Deflection Load Combinations for ASD and LRFD

•

1.0D

+ 1.0L•

1.0D

+ 1.0L

+ 1.0W

•

1.0D

+ 1.0L

+ 1.0E

D

=

dead loadL

=

live loadW

=

wind loadE

=

earthquake load

7

Forces and Stresses

•

ASD =

actual stress values are compared to the AISCallowable stress values

•

LRFD

=

actual forces and momentsare compared to the AISClimiting forces and momentscapacity

8

Slenderness Ratio

•

CompressionKL/r

≤

200

•

TensionL/r

≤

300

9

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

10

Tension Members

ASDft

= FX/Ag

≤

Ft

Gross Area

ft

= FX/Ae

≤

Ft

Net Area

LRFD

Pu

= FX

≤

ϕt Pn

= ϕt Ag Fy

ϕt

= 0.9 for Gross Area

Pu

= FX

≤

ϕt Pn

= ϕt Ae

Fu

ϕt

= 0.75 for Net Area

11

Tension Members

ASD (ASD Section D1)

Gross Area Ft

= 0.6Fy

Net Area

Ft

= 0.5Fu

LRFD (LRFD Section D1)

Gross Area ϕt Pn

= ϕt Fy

Ag

ϕt

= 0.9Net Area

ϕt Pn

= ϕt Fu Ae

ϕt

= 0.75

12

Compare ASD to LRFD

ASD

1.0D

+ 1.0LLRFD

1.2D

+ 1.6L

0.6Fy

(ASD)

×

(1.5)

= 0.9Fy

(LRFD)

0.5Fu

(ASD)

×

(1.5)

= 0.75Fu

(LRFD)

ASD ×

(1.5)

= LRFD

13

Tension Members

X

Y

Z

FIXED JOINT

-400.

o

14

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

15

Tension Members

ASD

W18x46

Actual/Allowable Ratio = 0.989

LRFD

W10x49

Actual/Limiting Ratio = 0.989

16

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

17

Tension MembersLoad Factor difference between LRFD and ASD

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

LRFD = (1.5) ×

ASD

Estimate required cross-sectional area for LRFD

LRFD W10x49 Area = 14.4 in.2

Area for LRFD 135 640881400 688

1015

0 9890 989

14 395. ..

.

...

.

18

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

1015

0 989. ..

.

..

19

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


20

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

21

Compression Members

ASD

fa

= FX/Ag

≤

Fa

LRFD

Pu

= FX

≤

ϕc Pn

= ϕc Ag FcrWhere

ϕc

= 0.85

22

Limiting Width-Thickness Ratios for Compression Elements

ASD

b/t

=

h/tw

=

LRFD

b/t

=

h/tw

=

95 / Fy

056. /E Fy

253 / Fy

149. /E Fy

23


Assume E

= 29000 ksiASD

b/t

=

h/tw

=

LRFD

b/t

=

h/tw

=

95 / Fy

9536. / Fy

253 / Fy

25374. / Fy

24

Compression Members

ASD KL/r

≤

C′c

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

LRFD (LRFD A-E3-2)

F

QKL r

CF

KL rC

KL r

C

ac

y

c c

12

53

38 8

2

2

3

3

/

/ /

F Q FcrQ

yc 0 658

2

.

Where C EQFc

y

2 2

Where c

yKLr

FE

c Q 15.

25

Compression Members

ASD KL/r

> C′c

(ASD E2-2)

LRFD (LRFD A-E3-3)

F E

KL ra

1223

2

2

/Where C E

QFcy

2 2

c Q 15.

F Fcrc

y

08772

.

Where c

yKLr

FE

26

Compression Members

LRFDF Fcr

cy

08772

. Where

cyKL

rFE

FKLr

FE

Fcr

y

y

08772

.

F E

KL rcr

0877 2

2.

/

F

EKL rcr

2017123

2

2

./

27

Compression Members

ASD LRFD

Fcr

/ Fa

= 1.681

LRFD Fcr

= ASD Fa

×

1.681

F E

KL ra

1223

2

2

/ F

EKL rcr

2017123

2

2

./

28

Compression Members

ASD

(ASD C-E2-2)

LRFD

λc

= Maximum of

( λcy

, λcz

, λe )

KL rK L

rK L

rKLr

y Y

y

z z

z e/ , ,

WhereKLr

EFe e

29

Compression Members

LRFDWhere:

cy

y y

y

yK Lr

FE

cz

z z

z

yK Lr

FE

ey

e

FF

30

Compression Members

Flexural-Torsional Buckling

F

EC

K LGJ

I Iew

x x y z

2

210.

31

Qs

Computation

ASD

LRFD

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. . ( / ) /

k

h th t kc c

4 05 70 100.46.

// , .if otherwise

32

Qs

Computation

Assume E

= 29000 ksiASD

LRFD

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. . ( / )

33

Qs

Computation

ASD

LRFD

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. / /

34

Qs

Computation

Assume E

= 29000 ksiASD

LRFD

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/ /

35

Qa

Computation

ASD

LRFD

b tf b t f

be

253 1 44 3.

( / )

b t Ef b t

Ef

be

191 1 0 34. .

( / )

Assume ksiE b tf b t f

e

29000 32526 1 57 9, . .( / )

36

Compression Members

X

Y

Z FIXED JOINT

-100.o

37

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

•


•



38

Compression Members

ASD

W10x49


LRFD

W10x54


39

Compression Members

ASDW10x49

Area = 14.4 in.2

FX

= 100.734 kips

Ratio = 0.941

LRFDW10x54

Area = 15.8 in.2

FX

= 160.967 kips

Ratio = 0.944

40

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

10085

0 9410 944

16 05. ..

..

..

.

..

41

Compression MembersCode Check based on the ASD9 and use W10x54

FX

= 100.806 kips

Ratio = 0.845


LRFD W10x54

Ratio = 0.944

LRFD Ratio computed from ASD 0845 160 967100806

101681

10085

0 944. ..

..

..

.

42

Compression MembersASD


W10x49



W10x54


Dead Load = 50 kipsLive Load = 50 kips

W10x49


W10x49


43

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

. Lb

is the laterally unbraced

length of the compression flange

44

Flexural Members

ASD

fb

= MZ/SZ

≤

Fb

LRFD

Mu

= MZ

≤

ϕb Mn

Where ϕb

= 0.9

45


ASD

LRFD

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

46

Flexural Members Compact Section

ASD (ASD F1-1)

Fb

= 0.66Fy

LRFD (LRFD A-F1-1)

ϕb Mn

= ϕb Mp

= ϕb Fy ZZ

≤ 1.5Fy SZ

Where ϕb

= 0.9

47


X

Y

Z

FIXED JOINT

-15.00

-15.00

o

o

FIXED JOINT

Braced at 1/3 Points

48


•

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

•


49


ASD

W18x40


LRFD

W18x40


50


ASDW18x40

Sz

= 68.4 in.3

MZ

= 2165.777 inch-kips

Ratio = 0.959

LRFDW18x40

Zz

= 78.4 in.3

MZ


Ratio = 0.982

51



Equation Factor difference between LRFD and ASDLRFD = (0.66Sz

)(1.5989) / (0.9Zz

) ×

ASD

Zz

LRFD W18x40

Zz

= 78.4 in.3

for LRFD 68 4 3462 9332165777

0 660 9

0 9590 982

78 3. ..

..

.

..

52


Code Check based on the ASD9, Profile W18x40MZ


Ratio = 0.959


LRFD W18x40 Ratio = 0.982


0 660 9

68 478 4

0 981. ..

..

.

..

53


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


W18x40


54

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

55

Flexural Members Noncompact Section

ASD

fb

= MZ/SZ

≤

Fb

LRFD

Mu

= MZ

≤

ϕb Mn

Where ϕb

= 0.9

56


ASD

LRFD

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

57


Assume E

= 29000 ksiASD

LRFD

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

58


ASD

(ASD F1-3)

(ASD F1-2)

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

F Fbt

Fb yf

fy

0 79 0 0022

. .

If minimum orL L

b

F d A Fb cf

y f y

76 20000

59


ASD

When

(ASD F1-6)

102 10 510 103 3

CF

lr

CF

b

y T

b

y

F

F l r

CF F Qb

y T

by y s

23 1530 10

0 62

3

/.

60


ASD

When

(ASD F1-7)

lr

CFT

b

y

510 103

F

C

l rF Qb

b

Ty s

170 100 6

3

2/.

61


ASD

For any value of l/rT

(ASD F1-8)FC

ld AF Qb

b

fy s

12 100 6

3

/.

62


LRFD

1. LTB, Lateral-Torsional Buckling

2. FLB, Flange Local Buckling

3. WLB, Web Local Buckling

63


Section

LRFD–

LTB

•

Compute Cb•

Based on the Lb

, compute limiting moment capacity. Lb

is the lateral unbraced

length of the compression flange,λ

= Lb

/ry•

Lb

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–

WLB

•

Compute limiting moment capacity based on the h/tw

ratio of the web, λ

= h/tw

64


LRFD LTB (Table A-F1.1)

For λp

< λ

≤

λr

(LRFD A-F1-2)

Where:Mp

= Fy

Zz

≤

1.5Fy Sz

Mr

= FL

Sz

FL

= Smaller of (Fyf

−

Fr

) or Fyw

λ

= Lb

/ry

λp

=

M C M M M Mn b p p rp

r pp

176. E Fyf

65


LRFD LTB (Table A-F1.1)

Where:

λr

=

X1

=

X2

=

XF

X FL

L1

221 1

S

EGJA

z 2

42C

ISGJ

w

y

z

66


LRFD FLB (Table A-F1.1)

For λp

< λ

≤

λr

(LRFD A-F1-3)Where:

Mp

= Fy

Zz

≤

1.5Fy Sz

Mr

= FL

Sz

FL

= Smaller of (Fyf

−

Fr

) or Fyw

λ

= b/tλp

=λr

=

M M M Mn p p rp

r p

0 38. E Fy

083. E FL

67


LRFD WLB (Table A-F1.1)

For λp

< λ

≤

λr

(LRFD A-F1-3)Where:

Mp

= Fy

Zz

≤

1.5Fy Sz

Mr

= Re Fy

Sz

Re

= 1.0

for non-hybrid girder

M M M Mn p p rp

r p

68


LRFD WLB (Table A-F1.1)

λ = h/tw

λp

=

λr

=

376. E Fy

57. E Fy

69


ASD

LRFD

C M M M MM M

M M M C

b

b

175 105 0 3 2 3

10

1 2 1 22

1 2

1 2

. . . .

, .maxIf between and

CM

M M M MMMM

bA B C

A

B

C

12 52 5 3 4 3

..

max

max

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

70


X

Y

Z

Roller

-12.00

-12.00

o

o

Pin

71


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

72


ASDW12x65

Cb

= 1.0Actual/Allowable Ratio = 0.988

LRFDW12x65

Cb

= 1.136Actual/Limiting Ratio = 0.971

Code check is controlled by FLB.Cb

= 1.0


73


Section

ASDExample # 1

Live Load = 12 kips/ftW12x65



W12x65


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

W12x65


W12x65


74

Design for Shear

ASD

fv

= FY/Aw

≤

Fv

= 0.4Fy

(ASD F4-1)

LRFD

Vu

= FY

≤

ϕv

Vn

= ϕv

0.6Fyw Aw

(LRFD F2-1)

Where ϕv

= 0.9

h t Fw y/ 380

h t E Fw yw/ . / 2 45

75

Design for ShearAssume E

= 29000 ksi

ASD

fv

= FY/Aw

≤

Fv

= 0.4Fy

(ASD F4-1)

LRFD

Vu

= FY

≤

ϕv

Vn

= ϕv

0.6Fyw Aw

(LRFD F2-1)Where ϕv

= 0.9

h t Fw y/ 380

h t Fw yw/ . / 417 2

76

Design for ShearASD

fv

= FY/Ay

≤

(ASD F4-2)

LRFD

Vu

= FY

≤

ϕv

Vn

= ϕv

(LRFD F2-2)

Where ϕv

= 0.9

h t Fw y/ 380

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

FF

C Fvy

v y 2 89

0 4.

.

0 62 45

.. /

/F A

E F

h tyw wyw

w

77

Design for Shear

LRFD

Vu

= FY

≤

ϕv

Vn

= ϕv

(LRFD F2-3)

Where ϕv

= 0.9

307 260. / /E F h tyw w

A E

h tw

w

4 522

./

78

Design for Shear

X

Y

Z

FIXED JOINT

-15.00

-15.00

o

o

FIXED JOINT

Braced at 1/3 Points

79

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

•


80

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


81

Design for Shear

ASDW18x40

Ay

= 5.638 in.2

FY

= 90.241 kips

Ratio = 0.8

LRFDW18x40

Ay

= 5.638 in.2

FY

= 144.289 kips

Ratio = 0.948

82

Design for ShearCode Check based on the ASD9, Profile W18x40

FY

= 90.241 kips

Ratio = 0.8Load Factor difference between LRFD and ASD


LRFD = (0.4)(1.5989) /(0.6)(0.9) ×

ASD

LRFD W18x40 Ratio = 0.948


0 40 6

100 9

0 948. ..

.

...

.

83

Design for ShearASD


W18x40



W18x40


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

W18x40


W18x40


84

Combined Forces

ASD fa

/Fa

> 0.15

(ASD H1-1)

(ASD H1-2)

LRFD Pu

/ϕPn

≥ 0.2

(LRFD H1-1a)

fF

C f

fF

F

C ffF

a

a

my by

a

eyby

mz bz

a

ez

1 110.

fF

fF

fF

a

y

by

by

bz

bz0 610

..

PP

MM

MM

u

n

uy

b ny

uz

b nz

89

10.

85

Combined Forces

ASD fa

/Fa

≤

0.15

(ASD H1-1)

LRFD Pu

/ϕPn

< 0.2

(LRFD H1-1a)

fF

fF

fF

a

a

by

by

bz

bz

10.

PP

MM

MM

u

n

uy

b ny

uz

b nz210

.

86

Combined Forces

X

Y

Z

87

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

88

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 ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

89

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 >< ><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


90

Combined Forces

ASD

WEIGHT = 46.566 kips

LRFD

WEIGHT = 33.874 kips

91

Deflection Design ASD



92

Deflection Design LRFD



Documents

ASD vs LRFD - · PDF file01/06/2016 · 3 ASD and LRFD Major Differences • Load Combinations and load factors • ASD results are based on the stresses and LRFD results are based