General Comparison between AISC LRFD and ASD Hamid Zand GT STRUDL Users Group Las Vegas, Nevada June 22-25, 2005
1
AISC ASD and LRFD • AISC = American Institute of Steel Construction • ASD
= Allowable Stress Design AISC Ninth Edition
• LRFD = Load and Resistance Factor Design AISC Third Edition 2
AISC Steel Design Manuals • • • •
1963 AISC ASD 6th Edition 1969 AISC ASD 7th Edition 1978 AISC ASD 8th Edition 1989 AISC ASD 9th Edition
• 1986 AISC LRFD 1st Edition • 1993 AISC LRFD 2nd Edition • 1999 AISC LRFD 3rd 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 • Static analysis is acceptable for ASD but nonlinear geometric analysis is required for LRFD • Beams and flexural members • Cb computation 4
ASD Load Combinations • 1.0D + 1.0L • 0.75D + 0.75L + 0.75W • 0.75D + 0.75L + 0.75E
D L W E
= = = =
dead load live load wind load earthquake load 5
ASD Load Combinations Or you can use following load combinations with the parameter ALSTRINC to account for the 1/3 allowable increase for the wind and seismic load • • •
1.0D + 1.0L 1.0D + 1.0L + 1.0W 1.0D + 1.0L + 1.0E
•
PARAMETER $ ALSTRINC based on the % increase • ALSTRINC 33.333 LOADINGS 2 3 6
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 L W E
= = = =
dead load live load wind load earthquake load 7
Deflection Load Combinations for ASD and LRFD • 1.0D + 1.0L • 1.0D + 1.0L + 1.0W • 1.0D + 1.0L + 1.0E
D L W E
= = = =
dead load live load wind load earthquake load 8
Forces and Stresses • ASD
= actual stress values are compared to the AISC allowable stress values
• LRFD = actual forces and moments are compared to the AISC limiting forces and moments capacity 9
ASTM Steel Grade • Comparison is between Table 1 of the AISC ASD 9th Edition on Page 1-7 versus Table 2-1 of the AISC LRFD 3rd Edition on Page 2-24 • A529 Gr. 42 of ASD, not available in LRFD • A529 Gr. 50 and 55 are new in LRFD • A441 not available in LRFD • A572 Gr. 55 is new in LRFD • A618 Gr. I, II, & III are new in LRFD • A913 Gr. 50, 60, 65, & 70 are new in LRFD • A992 (Fy = 50, Fu = 65) is new in LRFD (new standard) • A847 is new in LRFD 10
Slenderness Ratio • Compression KL/r ≤ 200
• Tension L/r ≤ 300
11
Tension Members • Check L/r ratio • Check Tensile Strength based on the crosssection’s Gross Area • Check Tensile Strength based on the crosssection’s Net Area
12
Tension Members ASD ft = 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 13
Tension Members ASD Gross Area
Ft = 0.6Fy
Net Area
Ft = 0.5Fu
(ASD Section D1)
LRFD Gross Area
ϕt P n = ϕt F y A g
ϕt = 0.9
Net Area
ϕt Pn = ϕt Fu Ae
ϕt = 0.75
(LRFD Section D1)
14
Compare ASD to LRFD ASD LRFD
1.0D + 1.0L 1.2D + 1.6L
0.6Fy (ASD) × (1.5) = 0.9Fy (LRFD) 0.5Fu (ASD) × (1.5) = 0.75Fu (LRFD) ASD × (1.5) = LRFD 15
Tension Members FIXED JOINT
Y Z
X
o -400.
16
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 17
Tension Members ASD W18x46
Actual/Allowable Ratio = 0.989
LRFD W10x49
Actual/Limiting Ratio = 0.989 18
Tension Members ASD W18x46 FX = 400.688 kips
Area = 13.5 in.2 Ratio = 0.989
LRFD W10x49 FX = 640.881 kips
Area = 14.4 in.2 Ratio = 0.989
19
Tension Members Load Factor difference between LRFD and ASD 640.881 / 400.688 = 1.599 Equation Factor difference between LRFD and ASD LRFD = (1.5) × ASD Estimate required cross-sectional area for LRFD 6 4 0 .8 8 1 1 . 0 0 . 9 8 9 A r e a f o r L R F D = 1 3 .5 × × × = 1 4 .3 9 5 4 0 0 . 6 8 8 1 .5 0 . 9 8 9
LRFD
W10x49
Area = 14.4 in.2 20
Tension Members Code Check based on the ASD9 and using W10x49
FX = 400.734 kips
Ratio = 0.928
Load Factor difference between LRFD and ASD 640.881 / 400.734 = 1.599 6 4 0 .8 8 1 1 . 0 L R F D R a t i o c o m p u t e d f r o m A S D = 0 .9 2 8 × × = 0 .9 8 9 4 0 0 . 7 3 4 1 .5
LRFD
W10x49
Ratio = 0.989
21
Tension Members ASD Example # 1 Live Load = 400 kips W18x46
Actual/Allowable Ratio = 0.989
LRFD Example # 1 Live Load = 400 kips W10x49 Actual/Limiting Ratio = 0.989 Example # 2 Dead Load = 200 kips Live Load = 200 kips W14x43 Actual/Limiting Ratio = 0.989 Code check W14x43 based on the ASD9 W14x43 Actual/Allowable Ratio = 1.06 22
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 23
Compression Members ASD fa = FX/Ag ≤ Fa LRFD Pu = FX ≤ ϕc Pn = ϕc Ag Fcr Where ϕc = 0.85 24
Limiting Width-Thickness Ratios for Compression Elements ASD b/t = 9 5 /
F
h/tw = 2 5 3 /
y
F
y
LRFD b/t = 0 . 5 6 E / F
y
h/tw = 1 . 4 9 E / F
y
25
Limiting Width-Thickness Ratios for Compression Elements Assume E = 29000 ksi
ASD b/t = 9 5 /
F
h/tw = 2 5 3 /
y
F
y
LRFD b/t = 9 5 . 3 6 /
F
y
h/tw = 2 5 3 . 7 4 /
F
y 26
Compression Members ASD
KL/r ≤ C′c
F
LRFD
a
(ASD E2-1 or A-B5-11)
2 K L / r ( ) F y Q 1 − 2 2 C c′ = 3 5 3(K L / r ) (K L / r ) + − 3 3 8 C c′ 8 C c′
λ c Q ≤ 1 .5
F
cr
(
= Q 0 .6 5 8
W h ere
C c′ =
2π 2E Q Fy
(LRFD A-E3-2) Q λc2
)F
y
W h ere
KL λc = rπ
F E 27
y
Compression Members ASD
KL/r > C′c
F
LRFD
a
=
(ASD E2-2)
12π 2E 2 3(K L / r )
2
W h ere
λ c Q > 1 .5 F
cr
0 .8 7 7 = 2 λc
C c′ =
2π 2E Q Fy
(LRFD A-E3-3)
F
y
W h ere
KL λc = rπ
F
y
E
28
Compression Members LRFD F
F
F
cr
cr
0 .8 7 7 = 2 λc
cr
F
0 .8 7 7 = K L F y r π E
=
0 .8 7 7 π 2 E
(K L
/ r)
2
2
W h ere
y
F
KL λc = rπ
F
y
E
y
F cr =
2 0 .1 7 1 π 2 E
2 2 3(K L / r )
29
Compression Members ASD F
a
=
LRFD
12π 2E 2 3(K L / r
)
2
F cr =
2 0 .1 7 1 π 2 E
2 3(K L / r)
2
Fcr / Fa = 1.681 LRFD Fcr = ASD Fa × 1.681 30
Compression Members ASD
K yL K L / r = ry W h ere
KL r
Y
K zLz KL , , r e rz = π
e
E Fe
(ASD C-E2-2)
LRFD λc = Maximum of ( λcy , λcz , λe ) 31
Compression Members LRFD Where:
λ cy =
λ cz
K yL ryπ
K zL = rzπ
λe =
y
F
y
F
e
F
y
E z
F
y
E
32
Compression Members Flexural-Torsional Buckling π 2EC Fe = ( K x L x
w
)
2
1 .0 + G J I y + I
z
33
Qs Computation ASD W h en
95 / Q
s
W h en s
c
4 .0 5
(h
0 .5 6 Q
/ k
y
< b / t < 195 /
F
= 1 .2 9 3 − 0 .0 0 3 0 9 ( b / t ) F
kc =
LRFD
F
/ t)
/ k
/ k
c
c
if h / t > 7 0 , o th e rw ise k
0 .4 6
E / F
y
y
y
< b / t < 1 .0 3 E / F
= 1 .4 1 5 − 0 .7 4 ( b / t ) F
y
c
= 1 .0
y
/ E
34
Qs Computation Assume E = 29000 ksi
ASD W h en
95 /
Q
LRFD
F
y
/ k
< b / t <195 /
F
9 5 .3 6 / s
F
y
/ k
y
= 1 .2 9 3 − 0 .0 0 3 0 9 ( b / t ) F
s
W h en Q
c
y
c
/ k
c
< b / t < 1 7 5 .4 /
= 1 .4 1 5 − 0 .0 0 4 3 4 5 ( b / t ) F
F
y
y
35
Qs Computation ASD b / t ≥ 195 /
W h en Q
= 26200k
s
c
F
[
/ F
/ k
y
y
c
(b / t )
]
2
LRFD b / t ≥ 1 .0 3 E / F
W h en
Q
s
[
= 0 .6 9 E / F
y
y
(b / t )
2
] 36
Qs Computation Assume E = 29000 ksi
ASD
b / t ≥ 195 /
W h en Q
LRFD
s
= 26200k
c
F
[
/ F
W h en
b / t ≥ 1 7 5 .4 /
Q
= 20010 / F
s
[
/ k
y
y
(b / t ) F
y
c
]
2
y
(b / t )
2
] 37
Qa Computation ASD 253t 4 4 .3 be = 1 − f ( b / t ) f
LRFD b e = 1 .9 1 t
E f
0 .3 4 1 − (b / t)
A ssu m e E = 2 9 0 0 0 k si ,
≤
E f
b
≤
b
3 2 5 .2 6 t 5 7 .9 be = 1 − f ( b / t ) f 38
Compression Members o -100.
Y Z
X
FIXED JOINT 39
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 • Load combinations based on the ASD and LRFD codes • Steel grade is A992 • Design based on the ASD and LRFD codes 40
Compression Members ASD W10x49
Actual/Allowable Ratio = 0.941
LRFD W10x54
Actual/Limiting Ratio = 0.944 41
Compression Members ASD W10x49 FX = 100.734 kips
Area = 14.4 in.2 Ratio = 0.941
LRFD W10x54 FX = 160.967 kips
Area = 15.8 in.2 Ratio = 0.944 42
Compression Members Load Factor difference between LRFD and ASD 160.967 / 100.734 = 1.598 Equation Factor difference between LRFD and ASD LRFD Fcr = (1.681) × ASD Fa Estimate required cross-sectional area for LRFD 1 6 0 .9 6 7 1 .0 1 .0 0 .9 4 1 A r e a f o r L R F D = 1 4 .4 × × × × = 1 6 .0 5 1 0 0 .7 3 4
LRFD
W10x54
1 .6 8 1
0 .8 5
0 .9 4 4
Area = 15.8 inch 43
Compression Members Code Check based on the ASD9 and use W10x54
FX = 100.806 kips
Ratio = 0.845
Load Factor difference between LRFD and ASD 160.967 / 100.806 = 1.597 L R F D R a t i o c o m p u t e d f r o m A S D = 0 .8 4 5 ×
LRFD
W10x54
1 6 0 .9 6 7 1 .0 1 .0 × × = 0 .9 4 4 1 0 0 .8 0 6 1 . 6 8 1 0 .8 5
Ratio = 0.944
44
Compression Members ASD Example # 1 Live Load = 100 kips W10x49 Actual/Allowable Ratio = 0.941 LRFD Example # 1 Live Load = 100 kips W10x54 Actual/Limiting Ratio = 0.944 Example # 2 Dead Load = 50 kips Live Load = 50 kips W10x49 Actual/Limiting Ratio = 0.921 Code check W10x49 based on the ASD9 W10x49 Actual/Allowable Ratio = 0.941 45
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 46
Flexural Members ASD fb = MZ/SZ ≤ Fb LRFD Mu = MZ ≤ ϕb Mn Where ϕb = 0.9 47
Limiting Width-Thickness Ratios for Compression Elements ASD b / t ≤ 65 /
F
d / tw ≤ 640 /
F
y
h / t w ≤ 3 .7 6
E / F
F
h / t w ≤ 6 4 0 .3 /
F
y
LRFD
b / t ≤ 0 .3 8
E / F
Assume E = 29000 ksi
b / t ≤ 6 4 .7 /
y
y
y
y 48
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 49
-15.00
Flexural Members Compact Section
o
FIXED JOINT Y Z
X
-15.00
Braced at 1/3 Points o FIXED JOINT
50
Flexural Members Compact Section • Member is 12 feet long • Fixed at both ends of the member • Loadings are: • Self weight • 15 kips/ft uniform load • Load combinations based on the ASD and LRFD codes • Steel grade is A992 • Braced at the 1/3 Points • Design based on the ASD and LRFD codes 51
Flexural Members Compact Section ASD W18x40
Actual/Allowable Ratio = 0.959
LRFD W18x40
Actual/Limiting Ratio = 0.982 52
Flexural Members Compact Section ASD W18x40 MZ = 2165.777 inch-kips LRFD W18x40 MZ = 3462.933 inch-kips
Sz = 68.4 in.3 Ratio = 0.959
Zz = 78.4 in.3 Ratio = 0.982 53
Flexural Members Compact Section Load Factor difference between LRFD and ASD 3462.933 / 2165.777 = 1.5989 Equation Factor difference between LRFD and ASD LRFD = (0.66Sz)(1.5989) / (0.9Zz) × ASD Zz
f o r L R F D = 6 8 .4 ×
LRFD
3 4 6 2 .9 3 3 0 .6 6 0 .9 5 9 × × = 7 8 .3 2 1 6 5 .7 7 7 0 .9 0 .9 8 2
W18x40
Zz = 78.4 in.3 54
Flexural Members Compact Section Code Check based on the ASD9, Profile W18x40
MZ = 2165.777 inch-kips
Ratio = 0.959
Load Factor difference between LRFD and ASD 3462.933 / 2165.777 = 1.5989 L R F D R a t i o c o m p u t e d f r o m A S D = 0 .9 5 9 ×
LRFD
W18x40
3 4 6 2 .9 3 3 0 .6 6 6 8 .4 × × = 0 .9 8 1 2 1 6 5 .7 7 7 0 .9 7 8 .4
Ratio = 0.982 55
Flexural Members Compact Section ASD Example # 1 Live Load = 15 kips/ft W18x40 Actual/Allowable Ratio = 0.959 LRFD Example # 1 Live Load = 15 kips/ft W18x40 Actual/Limiting Ratio = 0.982 Example # 2 Dead Load = 7.5 kips/ft Live Load = 7.5 kips/ft W18x40 Actual/Limiting Ratio = 0.859 Code check W18x40 based on the ASD9 W18x40 Actual/Allowable Ratio = 0.959 56
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 57
Flexural Members Noncompact Section ASD fb = MZ/SZ ≤ Fb LRFD Mu = MZ ≤ ϕb Mn Where ϕb = 0.9 58
Limiting Width-Thickness Ratios for Compression Elements ASD 65
F
y
< b t ≤ 95
d tw > 640
F
F
y
h tw ≤ 760
y
Fb
LRFD 0 .3 8
E F
y
< b / t ≤ 0 .8 3 E F
3 .7 6
E F
y
< h t w ≤ 5 .7
E F
L y 59
Limiting Width-Thickness Ratios for Compression Elements Assume E = 29000 ksi
ASD
65
F
< b t ≤ 95
y
d tw > 640
F
F
y
y
h tw ≤ 760
Fb
LRFD 6 4 .7 /
F
y
< b / t ≤ 1 4 1 .3 /
6 4 0 .3 /
F
y
< h t w ≤ 9 7 0 .7 /
F
L
F
y 60
Flexural Members Noncompact Section ASD b f F b = F y 0 .7 9 − 0 .0 0 2 2tf If
76b f L b > L c = m in im u m F y
or
Fy
(d
(ASD F1-3)
20000 A
f
)
F y
(ASD F1-2)
ASD Equations F1-6, F1-7, and F1-8 must to be checked.
61
Flexural Members Noncompact Section ASD When
102 × 103C Fy
b
≤
l rT
≤
510 × 103C Fy
2 2 F y (l / rT ) Fb = − 3 1530 × 103C
b
F
y
b
≤ 0 .6 F y Q
s
(ASD F1-6)
62
Flexural Members Noncompact Section ASD When
l rT
≥
Fb =
510 × 103C Fy
170 × 103C
(l
/ rT
)
2
b
b
≤ 0 .6 F y Q
s
(ASD F1-7)
63
Flexural Members Noncompact Section ASD For any value of l/rT
12 × 103C Fb = ld / A f
b
≤ 0 .6 F y Q
s
(ASD F1-8)
64
Flexural Members Noncompact Section LRFD 1. 2. 3.
LTB, Lateral-Torsional Buckling FLB, Flange Local Buckling WLB, Web Local Buckling
65
Flexural Members Noncompact Section LRFD –
LTB • •
•
–
FLB •
–
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 noncompact and slender sections 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 66
Flexural Members Noncompact Section LRFD LTB For λp < λ ≤ λr M
n
= C b M
p
(Table A-F1.1)
(
− M
p
− M
r
)
λ − λp λr − λp
≤ M
p
(LRFD A-F1-2)
Where: Mp = Fy Zz ≤ 1.5Fy Sz Mr = FLSz λ λp
FL = Smaller of (Fyf − Fr) or Fyw
= Lb/ry =
1 .7 6
E F
yf
67
Flexural Members Noncompact Section LRFD
LTB
(Table A-F1.1)
Where: λr
X = F
1 +
1
1 + X 2F
L
2
L
π X1 = Sz
E G JA 2
C X2 = 4 I
Sz G J
w y
2
68
Flexural Members Noncompact Section LRFD
FLB
(Table A-F1.1)
For λp < λ ≤ λr M
n
= M
p
(
− M
p
− M
r
)
λ − λp λr − λp
(LRFD A-F1-3)
Where: Mp = Fy Zz ≤ 1.5Fy Sz Mr = FLSz λ = b/t λp = 0 . 3 8 E F λr
=
0 .8 3 E F
FL = Smaller of (Fyf − Fr) or Fyw y L
69
Flexural Members Noncompact Section LRFD WLB For λp < λ ≤ λr M
n
= M
p
(Table A-F1.1)
(
− M
p
− M
r
)
λ − λp λr − λp
(LRFD A-F1-3)
Where: Mp = Fy Zz ≤ 1.5Fy Sz Mr = Re Fy Sz Re = 1.0
for non-hybrid girder
70
Flexural Members Noncompact Section LRFD
WLB
(Table A-F1.1)
λ
= h/tw
λp
= 3 .7 6 E F
λr = 5 . 7 E F
y
y
71
Flexural Members Noncompact Section ASD C
= 1 .7 5 + 1 .0 5 ( M
b
M
< M
1
If M
m ax
=
b
1
2 ) +
0 .3 ( M
M
1
)2 2
≤ 2 .3
2
b e tw e e n M
LRFD C
M
2 .5 M
m ax
and M
2
1 2 .5 M m a x + 3M A + 4 M
B
1
,
C
b
+ 3M
= 1 .0
C
M M
B
= a b so lu te v a lu e o f m o m e n t a t q u a rte r p o in t = a b so lu te v a lu e o f m o m e n t a t c e n te rlin e
M
C
= a b so lu te v a lu e o f m o m e n t a t th re e − q u a rte r p o in t
A
72
-12.00
Flexural Members Noncompact Section
o Pin
Y Z
X
-12.00
o Roller
73
Flexural Members Noncompact Section • • • • •
Member is 12 feet long Pin at the start of the member Roller at the end of the member Cross-section is W12x65 Loadings are: • Self weight • 12 kips/ft uniform load • Load combinations based on the ASD and LRFD codes • Steel grade is A992 • Check code based on the ASD and LRFD codes 74
Flexural Members Noncompact Section ASD W12x65 Cb = 1.0 Actual/Allowable Ratio = 0.988 LRFD W12x65 Cb = 1.136 Actual/Limiting Ratio = 0.971 Code check is controlled by FLB. Cb = 1.0 Actual/Limiting Ratio = 0.973 75
Flexural Members Noncompact Section ASD Example # 1 Live Load = 12 kips/ft W12x65 Actual/Allowable Ratio = 0.988 LRFD Example # 1 Live Load = 12 kips/ft W12x65 Actual/Limiting Ratio = 0.971 Example # 2 Dead Load = 6 kips/ft Live Load = 6 kips/ft W12x65 Actual/Limiting Ratio = 0.85 Code check W12x65 based on the ASD9 W12x65 Actual/Allowable Ratio = 0.988 76
Design for Shear ASD
h / tw ≤ 380
F
y
fv = FY/Aw ≤ Fv = 0.4Fy LRFD
h / t w ≤ 2 .4 5 E / F
(ASD F4-1)
yw
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw
(LRFD F2-1)
Where ϕv = 0.9 77
Design for Shear Assume E = 29000 ksi ASD h / tw ≤ 380 F y fv = FY/Aw ≤ Fv = 0.4Fy LRFD
h / t w ≤ 4 1 7 .2 /
F
(ASD F4-1)
yw
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw
(LRFD F2-1)
Where ϕv = 0.9 78
Design for Shear ASD
h / tw > 380
F
fv = FY/Ay ≤ F v =
LRFD
2 .4 5 E / F
yw
y
F
y
2 .8 9
(C v ) ≤
< h / t w ≤ 3 .0 7
Vu = FY ≤ ϕvVn = ϕv 0 . 6 F
yw
0 .4 F
(ASD F4-2)
y
E / F
yw
2 .4 5 E / F Aw h / tw
yw
(LRFD F2-2)
Where ϕv = 0.9 79
Design for Shear LRFD
3 .0 7
E / F
yw
< h / tw ≤ 260
4 .5 2 E Vu = FY ≤ ϕvVn = ϕv A w 2 ( h / t w )
(LRFD F2-3)
Where ϕv = 0.9
80
-15.00
Design for Shear
o
FIXED JOINT Y Z
X
-15.00
Braced at 1/3 Points o FIXED JOINT
81
Design for Shear • Same as example # 3 which is used for design of flexural member with compact section • Member is 12 feet long • Fixed at both ends of the member • Loadings are: • Self weight • 15 kips/ft uniform load • Load combinations based on the ASD and LRFD codes • Steel grade is A992 • Braced at the 1/3 Points • Design based on the ASD and LRFD codes 82
Design for Shear ASD W18x40 LRFD W18x40
(Check shear at the end of the member, equation “F4-1 Y”)
Actual/Allowable Ratio = 0.8 (Check shear at the end of the member, equation “A-F2-1 Y”)
Actual/Limiting Ratio = 0.948 83
Design for Shear ASD W18x40 FY = 90.241 kips LRFD W18x40 FY = 144.289 kips
Ay = 5.638 in.2 Ratio = 0.8
Ay = 5.638 in.2 Ratio = 0.948 84
Design for Shear Code Check based on the ASD9, Profile W18x40 FY = 90.241 kips Ratio = 0.8 Load Factor difference between LRFD and ASD 144.289 / 90.241 = 1.5989 Equation Factor difference between LRFD and ASD LRFD = (0.4)(1.5989) /(0.6)(0.9) × ASD L R F D R a t i o c o m p u t e d f r o m A S D = 0 .8 ×
LRFD
W18x40
1 4 4 .2 8 9 0 .4 1 .0 × × = 0 .9 4 8 9 0 .2 4 1 0 .6 0 .9
Ratio = 0.948 85
Design for Shear ASD Example # 1 Live Load = 15 kips/ft W18x40 Actual/Allowable Ratio = 0.8 LRFD Example # 1 Live Load = 15 kips/ft W18x40 Actual/Limiting Ratio = 0.948 Example # 2 Dead Load = 7.5 kips/ft Live Load = 7.5 kips/ft W18x40 Actual/Limiting Ratio = 0.83 Code check W18x40 based on the ASD9 W18x40 Actual/Allowable Ratio = 0.8 86
Combined Forces ASD
fa /Fa > 0.15
C m y f by fa C m z f bz + + ≤ 1 .0 Fa fa fa 1 − F by 1 − F ez F ey
fa 0 .6 F
LRFD
+ y
f by F by
+
f bz ≤ 1 .0 F bz
(ASD H1-1)
(ASD H1-2)
Pu /ϕPn ≥ 0.2
Pu M uz 8 M uy + + φPn 9 φ b M ny φ b M nz
≤ 1 . 0
(LRFD H1-1a)
87
Combined Forces ASD
fa /Fa ≤ 0.15
f by fa f bz + + ≤ 1 .0 Fa F by F bz
LRFD
(ASD H1-1)
Pu /ϕPn < 0.2
M uy Pu M uz + + 2 φP n φ b M ny φ b M nz
≤ 1 . 0
(LRFD H1-1a)
88
Combined Forces
Y Z
X
89
Combined Forces •
3D Simple Frame • • •
•
3 Bays in X direction 2 Bays in Z direction 2 Floors in Y direction
3 @ 15 ft 2 @ 30 ft 2 @ 15 ft
Loadings • • • • • • •
Self weight of the Steel Self weight of the Slab Other dead loads Live load on second floor Live load on roof Wind load in the X direction Wind load in the Z direction
62.5 15.0 50.0 20.0 20.0 20.0
psf psf psf psf psf psf 90
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 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
91
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 > < > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> < ACTIVE UNITS WEIGHT KIP LENGTH INCH > < > < TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS > < > < LENGTH = 1.3320E+04 WEIGHT = 3.3874E+01 VOLUME = 1.1957E+05 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
92
Combined Forces ASD WEIGHT = 46.566 kips
LRFD WEIGHT = 33.874 kips 93
Deflection Design 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 > < W14x43 1.4400E+03 1.8144E+04 5.1402E+00 4 > < W14x48 1.4400E+03 2.0304E+04 5.7521E+00 4 > < W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> < ACTIVE UNITS WEIGHT KIP LENGTH INCH > < > < TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS > < > < LENGTH = 1.3320E+04 WEIGHT = 4.6933E+01 VOLUME = 1.6566E+05 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
94
Deflection Design 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 2.1600E+03 2.0974E+04 5.9418E+00 12 > < W10x49 1.4400E+03 2.0736E+04 5.8745E+00 8 > < W10x54 7.2000E+02 1.1376E+04 3.2228E+00 4 > < W12x40 1.4400E+03 1.6992E+04 4.8138E+00 4 > < W14x43 2.8800E+03 3.6288E+04 1.0280E+01 8 > < W14x48 1.4400E+03 2.0304E+04 5.7521E+00 4 > < W6x9 3.2400E+03 8.6832E+03 2.4600E+00 18 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> < ACTIVE UNITS WEIGHT KIP LENGTH INCH > < > < TOTAL LENGTH, WEIGHT AND VOLUME FOR SPECIFIED MEMBERS > < > < LENGTH = 1.3320E+04 WEIGHT = 3.8345E+01 VOLUME = 1.3535E+05 > <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
95
Deflection Design ASD WEIGHT = 46.933 kips
LRFD WEIGHT = 38.345 kips 96
Compare Design without and with Deflection Design ASD Without Deflection Design With Deflection Design
WEIGHT = 46.566 kips WEIGHT = 46.933 kips
LRFD Without Deflection Design With Deflection Design
WEIGHT = 33.874 kips WEIGHT = 38.345 kips
97
Design same example based on Cb = 1.0 Code and deflection design with Cb = 1.0 ASD Compute Cb Specify Cb = 1.0
WEIGHT = 46.933 kips WEIGHT = 51.752 kips
LRFD Compute Cb Specify Cb = 1.0
WEIGHT = 38.345 kips WEIGHT = 48.421 kips 98
Design Similar example based on Cb = 1.0 and LL×5 • Code and deflection design with Cb = 1.0 and increase the live load by a factor of 5. • Area loads are distributed using two way option instead of one way • Also change the 2 bays in the Z direction from 30 ft to 15 ft. ASD
WEIGHT = 25.677 kips
LRFD
WEIGHT = 22.636 kips Difference = 3.041 kips 99
Design Similar example based on Cb = 1.0 and LL×10 • Code and deflection design with Cb = 1.0 and increase the live load by a factor of 10. • Area loads are distributed using two way option instead of one way • Also change the 2 bays in the Z direction from 30 ft to 15 ft. ASD
WEIGHT = 31.022 kips
LRFD
WEIGHT = 29.051 kips Difference = 1.971 kips 100
Stiffness Analysis versus Nonlinear Analysis • Stiffness Analysis – Load Combinations or Form Loads can be used. • Nonlinear Analysis – Form Loads must be used. Load Combinations are not valid. • Nonlinear Analysis – Specify type of Nonlinearity. • Nonlinear Analysis – Specify Maximum Number of Cycles. • Nonlinear Analysis – Specify Convergence Tolerance. 101
Nonlinear Analysis Commands • NONLINEAR EFFECT • TENSION ONLY • COMPRESSION ONLY • GEOMETRY AXIAL
• MAXIMUM NUMBER OF CYCLES • CONVERGENCE TOLERANCE • NONLINEAR ANALYSIS 102
Design using Nonlinear Analysis Input File # 1 • • • • • • • • • • • •
Geometry, Material Type, Properties, Loading ‘SW’, ‘LL’, and ‘WL’ FORM LOAD ‘A’ FROM ‘SW’ 1.4 FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6 FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5 FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6 DEFINE PHYSICAL MEMBERS PARAMETERS MEMBER CONSTRAINTS LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ $ Activate only the FORM loads STIFFNESS ANALYSIS SAVE 103
Design using Nonlinear Analysis Input File # 2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
RESTORE LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ SELECT MEMBERS SMOOTH PHYSICAL MEMBERS DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’ SELF WEIGHT LOADING RECOMPUTE FORM LOAD ‘A’ FROM ‘SW’ 1.4 FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6 FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5 FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6 LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ STIFFNESS ANALYSIS CHECK MEMBERS STEEL TAKE OFF SAVE 104
Design using Nonlinear Analysis Input File # 3 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
RESTORE LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ SELECT MEMBERS SMOOTH PHYSICAL MEMBERS DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’ SELF WEIGHT LOADING RECOMPUTE FORM LOAD ‘A’ FROM ‘SW’ 1.4 FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6 FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5 FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6
105
Design using Nonlinear Analysis Input File # 3 (continue) 1. 2. 3. 4. 5. 6. 7. 8. 9.
NONLINEAR EFFECT GEOMETRY ALL MEMBERS MAXIMUM NUMBER OF CYCLES CONVERGENCE TOLERANCE DISPLACEMENT LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ NONLINEAR ANALYSIS CHECK MEMBERS STEEL TAKE OFF SAVE 106
General Comparison between AISC LRFD and ASD
Questions
107
