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. 1.0D + 1.0L
2. 1.0D + 1.0L + 1.0W
3. 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
ft = FX/Ae ≤ Ft
Gross Area
Net Area
LRFD
Pu = FX ≤ ϕt Pn = ϕt Ag Fy
Pu = FX ≤ ϕt Pn = ϕt Ae Fu
ϕt = 0.9 for Gross Area
ϕt = 0.75 for Net Area
13
Tension Members
ASD
Gross Area
Net Area
LRFD
Gross Area
Net Area
(ASD Section D1)
Ft = 0.6Fy
Ft = 0.5Fu
(LRFD Section D1)
ϕt Pn = ϕt Fy Ag
ϕt Pn = ϕt Fu Ae
ϕt = 0.9
ϕt = 0.75
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
640881
.
10
.
0.989
Area for LRFD  135
. 


 14.395
400.688 15
.
0.989
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
640881
.
10
.
LRFD Ratio computed from ASD  0.928 

 0.989
400.734 15
.
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 = 95 / Fy
h/tw = 253 / Fy
LRFD
b/t = 0.56 E / Fy
h/tw = 149
.
E / Fy
25
Limiting Width-Thickness Ratios
for Compression Elements
Assume E = 29000 ksi
ASD
b/t = 95 / Fy
h/tw = 253 / Fy
LRFD
b/t = 95.36 / Fy
h/tw = 253.74 / Fy
26
Compression Members
ASD
KL/r ≤ C′c
(ASD E2-1 or A-B5-11)
  KL / r  2 
 Fy
Q 1 
2

2Cc 
Fa 
3
5 3 KL / r   KL / r 


3
3
8Cc
8Cc
LRFD
 c Q  15
.

Fcr  Q 0.658
Where
Cc 
2 2 E
QFy
(LRFD A-E3-2)
Q c
2
F
y
Where
KL
c 
r
Fy
E
27
Compression Members
ASD
KL/r > C′c
Fa 
LRFD c
(ASD E2-2)
12 2 E
23 KL / r 
2
Where
Q  15
.
 0.877 
Fcr   2  Fy
 c 
Cc 
2 2 E
QFy
(LRFD A-E3-3)
Where
KL
c 
r
Fy
E
28
Compression Members
LRFD
 0.877 
Fcr   2  Fy
 c 



0.877
Fcr  

  KL Fy
  r E

Fcr 
 KL / r 
Fy
E



 Fy
2
 
 
 
 
0.877 2 E
2
Where
KL
c 
r
Fcr 
20171
. 2E
23 KL / r 
2
29
Compression Members
ASD
Fa 
LRFD
12 2 E
23 KL / r 
2
Fcr 
20171
. 2E
23 KL / r 
2
Fcr / Fa = 1.681
LRFD Fcr = ASD Fa × 1.681
30
Compression Members
ASD
 K y LY K z Lz  KL  
KL / r  
,
,
 
rz  r  e 
 ry
E
 KL 
Where 
 
 r e
Fe
(ASD C-E2-2)
LRFD
λc = Maximum of ( λcy , λcz , λe )
31
Compression Members
LRFD
Where:
 cy 
 cz
K y Ly
Fy
ry 
E
K z Lz

rz 
e 
Fy
E
Fy
Fe
32
Compression Members
Flexural-Torsional Buckling
  2 EC
 10
.
w


Fe 
 GJ
2
  K x Lx 
 I y  I z
33
Qs Computation
ASD
When 95 / Fy / k c  b / t  195 / Fy / k c
Qs  1293
.
 0.00309(b / t ) Fy / k c
kc 
LRFD
4.05
h / t 
0.46
if h / t  70, otherwise k c  10
.
When 0.56 E / Fy  b / t  103
.
E / Fy
Qs  1415
.
 0.74(b / t ) Fy / E
34
Qs Computation
Assume E = 29000 ksi
ASD
When 95 / Fy / k c  b / t  195 / Fy / k c
Qs  1293
.
 0.00309(b / t ) Fy / k c
LRFD
When 95.36 / Fy  b / t  175.4 / Fy
Qs  1415
.
 0.004345(b / t ) Fy
35
Qs Computation
ASD
When b / t  195 / Fy / k c

Qs  26200k c / Fy b / t 
2

LRFD
When b / t  103
.
E / Fy

Qs  0.69 E / Fy b / t 
2

36
Qs Computation
Assume E = 29000 ksi
ASD
When b / t  195 / Fy / k c

Qs  26200k c / Fy b / t 
LRFD
2

When b / t  175.4 / Fy

Qs  20010 / Fy b / t 
2

37
Qa Computation
ASD
253t 
44.3 
be 
1 
  b
f  (b / t ) f 
LRFD
E
0.34
be  191
. t
1


f  (b / t )
Assume E  29000 ksi,
E
  b
f 
325.26t 
57.9 
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
Area for LRFD  14.4 
LRFD
160.967
10
.
10
.
0.941



 16.05
100.734 1681
.
0.85 0.944
W10x54
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
LRFD Ratio computed from ASD  0845
.

LRFD
W10x54
160.967
10
.
10
.


 0.944
100806
.
1681
.
085
.
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 / Fy
d / t w  640 / Fy
LRFD
b / t  0.38 E / Fy
h / t w  3.76 E / Fy
Assume E = 29000 ksi
b / t  64.7 / Fy
h / t w  640.3 / Fy
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
Sz = 68.4 in.3
Ratio = 0.959
LRFD
W18x40
MZ = 3462.933 inch-kips
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 for LRFD  68.4  3462.933  0.66  0.959  78.3
2165777
.
LRFD
W18x40
0.9
0.982
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
LRFD Ratio computed from ASD  0.959 
LRFD
W18x40
3462.933 0.66 68.4


 0.981
2165777
.
0.9 78.4
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
Fy  b t  95
d t w  640
Fy
Fy
h t w  760
Fb
LRFD
0.38 E Fy  b / t  0.83 E FL
3.76 E Fy  h t w  5.7 E Fy
59
Limiting Width-Thickness Ratios
for Compression Elements
Assume E = 29000 ksi
ASD
65
Fy  b t  95
d t w  640
Fy
Fy
h t w  760
Fb
LRFD
64.7 / Fy  b / t  1413
. / FL
640.3 / Fy  h t w  970.7 / Fy
60
Flexural Members
Noncompact Section
ASD

bf
Fb  Fy 0.79  0.002
2t f

If
 76b f
Lb  Lc  minimum
 F
y

or

Fy 


(ASD F1-3)
20000 
d A f Fy 

(ASD F1-2)
ASD Equations F1-6, F1-7, and F1-8 must to be checked.
61
Flexural Members
Noncompact Section
ASD
When
102  10 3 Cb
510  10 3 Cb
l


Fy
rT
Fy
2
2
Fy l / rT  
 Fy  0.6 Fy Qs
Fb   
3
 3 1530  10 Cb 


(ASD F1-6)
62
Flexural Members
Noncompact Section
ASD
When
510  10 3 Cb
l

rT
Fy
Fb 
170  10 3 Cb
l / rT 
2
 0.6 Fy Qs
(ASD F1-7)
63
Flexural Members
Noncompact Section
ASD
For any value of l/rT
12  10 3 Cb
Fb 
 0.6 Fy Qs
ld / A f
(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
(Table A-F1.1)

   p 
   M p
M n  Cb  M p  M p  M r 
(LRFD A-F1-2)
  r   p  

Where:
Mp = Fy Zz ≤ 1.5Fy Sz
Mr = FLSz
FL = Smaller of (Fyf − Fr) or Fyw
λ = Lb/ry


.
E Fyf
λp = 176
67
Flexural Members
Noncompact Section
LRFD
LTB
(Table A-F1.1)
Where:
λr
X1
1  1  X 2 FL2
=
FL
X1 =
X2

Sz
EGJA
2
C S 
= 4 w z
I y  GJ 
2
68
Flexural Members
Noncompact Section
LRFD
For
FLB
(Table A-F1.1)
λp < λ ≤ λ r

   p 
 
M n   M p  M p  M r 
  r   p  



(LRFD A-F1-3)
Where:
Mp
Mr
λ
λp
λr
=
=
=
=
=
Fy Zz ≤ 1.5Fy Sz
FLSz
b/t
FL = Smaller of (Fyf − Fr) or Fyw
0.38 E Fy
0.83 E FL
69
Flexural Members
Noncompact Section
LRFD
WLB
For λp < λ ≤ λr
(Table A-F1.1)

   p 
 
M n   M p  M p  M r 
  r   p  



(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
λ
(Table A-F1.1)
= h/tw
λp = 3.76 E Fy
λr
= 5.7 E Fy
71
Flexural Members
Noncompact Section
ASD
Cb  175
.  105
.  M 1 M 2   0.3 M 1 M 2   2.3
2
M1  M 2
If M max between M 1 and M 2 , Cb  10
.
LRFD
Cb 
2.5 M max
12.5 M max
 3M A  4 M B  3MC
M A  absolute value of moment at quarter point
M B  absolute value of moment at centerline
M C  absolute value of moment at three  quarter point
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
h / t w  380
ASD
Fy
fv = FY/Aw ≤ Fv = 0.4Fy
LRFD
(ASD F4-1)
h / t w  2.45 E / Fyw
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw
(LRFD F2-1)
Where ϕv = 0.9
77
Design for Shear
Assume E = 29000 ksi
ASD
h / t w  380 Fy
fv = FY/Aw ≤ Fv = 0.4Fy
LRFD
(ASD F4-1)
h / t w  417.2 / Fyw
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw
(LRFD F2-1)
Where ϕv = 0.9
78
Design for Shear
ASD
h / t w  380
Fy
fv = FY/Ay ≤ Fv 
LRFD
Fy
2.89
Cv  
0.4 Fy
(ASD F4-2)
2.45 E / Fyw  h / t w  3.07 E / Fyw
 2.45 E / Fyw
Vu = FY ≤ ϕvVn = ϕv 0.6 Fyw Aw 
h / tw





(LRFD F2-2)
Where ϕv = 0.9
79
Design for Shear
LRFD
3.07 E / Fyw  h / t w  260
 4.52 E 

Vu = FY ≤ ϕvVn = ϕv Aw 
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
Ay = 5.638 in.2
Ratio = 0.8
LRFD
W18x40
FY = 144.289 kips
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
LRFD Ratio computed from ASD  08
. 
LRFD
W18x40
144.289 0.4 10
.


 0.948
90.241 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
Cmy f by
fa
Cmz f bz


 10
.
Fa 

fa 
fa 
1 
 Fby  1 



Fez 

Fey 

f by
fa
f

 bz  10
.
0.6 Fy Fby Fbz
LRFD
(ASD H1-1)
(ASD H1-2)
Pu /ϕPn ≥ 0.2
Pu
M uz 
8  M uy
  10
 

.
Pn 9   b M ny  b M nz 
(LRFD H1-1a)
87
Combined Forces
ASD
fa /Fa ≤ 0.15
f by
fa
f bz


 10
.
Fa Fby Fbz
LRFD
(ASD H1-1)
Pu /ϕPn < 0.2
 M uy
Pu
M uz 
  10
 

.
2Pn   b M ny  b M nz 
(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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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