So sanh cac ly thuyet tinh toan KC thep

1. 1
General Comparison between
AISC LRFD and ASD
Hamid Zand
GT STRUDL Users Group
Las Vegas, Nevada
June 22-25, 2005

2. 2
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

3. 3
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

4. 4
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

5. 5
ASD Load Combinations
• 1.0D + 1.0L
• 0.75D + 0.75L + 0.75W
• 0.75D + 0.75L + 0.75E
D = dead load
L = live load
W = wind load
E = earthquake load

6. 6
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

7. 7
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 load
L = live load
W = wind load
E = earthquake load

8. 8
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 load
L = live load
W = wind load
E = earthquake load

9. 9
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

10. 10
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

11. 11
Slenderness Ratio
• Compression
KL/r ≤ 200
• Tension
L/r ≤ 300

12. 12
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

13. 13
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

14. 14
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 = 0.9
Net Area ϕt Pn = ϕt Fu Ae ϕt = 0.75

15. 15
Compare ASD to LRFD
ASD 1.0D + 1.0L
LRFD 1.2D + 1.6L
0.6Fy (ASD) × (1.5) = 0.9Fy (LRFD)
0.5Fu (ASD) × (1.5) = 0.75Fu (LRFD)
ASD × (1.5) = LRFD

16. 16
Tension Members
X
Y
Z
FIXED JOINT
-400.
o

17. 17
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

18. 18
Tension Members
ASD
W18x46 Actual/Allowable Ratio = 0.989
LRFD
W10x49 Actual/Limiting Ratio = 0.989

19. 19
Tension Members
ASD
W18x46 Area = 13.5 in.2
FX = 400.688 kips Ratio = 0.989
LRFD
W10x49 Area = 14.4 in.2
FX = 640.881 kips Ratio = 0.989

20. 20
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
LRFD W10x49 Area = 14.4 in.2
A r e a f o r L R F D = × × × =
1 3 5
6 4 0 8 8 1
4 0 0 6 8 8
1 0
1 5
0 9 8 9
0 9 8 9
1 4 3 9 5
.
.
.
.
.
.
.
.

21. 21
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
LRFD W10x49 Ratio = 0.989
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
6 4 0 8 8 1
4 0 0 7 3 4
1 0
1 5
0 9 8 9
.
.
.
.
.
.

22. 22
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

23. 23
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

24. 24
Compression Members
ASD
fa = FX/Ag ≤ Fa
LRFD
Pu = FX ≤ ϕc Pn = ϕc Ag Fcr
Where ϕc = 0.85

25. 25
Limiting Width-Thickness Ratios
for Compression Elements
ASD
b/t = h/tw =
LRFD
b/t = h/tw =
9 5 / F y
0 5 6
. /
E F y
2 5 3 / F y
1 4 9
. /
E F y

26. 26
Limiting Width-Thickness Ratios
for Compression Elements
Assume E = 29000 ksi
ASD
b/t = h/tw =
LRFD
b/t = h/tw =
9 5 / F y
9 5 3 6
. / F y
2 5 3 / F y
2 5 3 7 4
. / F y

27. 27
Compression Members
ASD KL/r ≤ C′c (ASD E2-1 or A-B5-11)
LRFD (LRFD A-E3-2)
( )
( ) ( )
F
Q
K L r
C
F
K L r
C
K L r
C
a
c
y
c c
=
−
′








+
′
−
′
1
2
5
3
3
8 8
2
2
3
3
/
/ /
( )
F Q F
c r
Q
y
c
= 0 6 5 8
2
. λ
W h e r e ′ =
C
E
Q F
c
y
2 2
π
W h e r e λ
π
c
y
K L
r
F
E
=
λ c Q ≤ 1 5
.

28. 28
Compression Members
ASD KL/r > C′c (ASD E2-2)
LRFD (LRFD A-E3-3)
( )
F
E
K L r
a =
1 2
2 3
2
2
π
/
W h e r e ′ =
C
E
Q F
c
y
2 2
π
λ c Q > 1 5
.
F F
c r
c
y
=






0 8 7 7
2
.
λ
W h e r e λ
π
c
y
K L
r
F
E
=

29. 29
Compression Members
LRFD
F F
c r
c
y
=






0 8 7 7
2
.
λ
W h e r e λ
π
c
y
K L
r
F
E
=
F
K L
r
F
E
F
c r
y
y
=
























0 8 7 7
2
.
π
( )
F
E
K L r
c r =
0 8 7 7 2
2
.
/
π
( )
F
E
K L r
c r =
2 0 1 7 1
2 3
2
2
.
/
π

30. 30
Compression Members
ASD LRFD
Fcr / Fa = 1.681
LRFD Fcr = ASD Fa × 1.681
( )
F
E
K L r
a =
1 2
2 3
2
2
π
/ ( )
F
E
K L r
c r =
2 0 1 7 1
2 3
2
2
.
/
π

31. 31
Compression Members
ASD
(ASD C-E2-2)
LRFD
λc = Maximum of ( λcy , λcz , λe )
K L r
K L
r
K L
r
K L
r
y Y
y
z z
z e
/ , ,
=














W h e r e
K L
r
E
F
e e





 = π

32. 32
Compression Members
LRFD
Where:
λ
π
c y
y y
y
y
K L
r
F
E
=
λ
π
c z
z z
z
y
K L
r
F
E
=
λ e
y
e
F
F
=

33. 33
Compression Members
Flexural-Torsional Buckling
( )
F
E C
K L
G J
I I
e
w
x x y z
= +







 +
π 2
2
1 0
.

34. 34
Qs Computation
ASD
LRFD
W h e n 9 5 1 9 5
/ / / / /
F k b t F k
y c y c
< <
Q b t F k
s y c
= −
1 2 9 3 0 0 0 3 0 9
. . ( / ) /
W h e n 0 5 6 1 0 3
. / / . /
E F b t E F
y y
< <
Q b t F E
s y
= −
1 4 1 5 0 7 4
. . ( / ) /
( )
k
h t
h t k
c c
= > =
4 0 5
7 0 1 0
0 .4 6
.
/
/ , .
i f o t h e r w i s e

35. 35
Qs Computation
Assume E = 29000 ksi
ASD
LRFD
W h e n 9 5 1 9 5
/ / / / /
F k b t F k
y c y c
< <
Q b t F k
s y c
= −
1 2 9 3 0 0 0 3 0 9
. . ( / ) /
W h e n 9 5 3 6 1 7 5 4
. / / . /
F b t F
y y
< <
Q b t F
s y
= −
1 4 1 5 0 0 0 4 3 4 5
. . ( / )

36. 36
Qs Computation
ASD
LRFD
W h e n b t F k
y c
/ / /
≥ 1 9 5
( )
[ ]
Q k F b t
s c y
= 2 6 2 0 0
2
/ /
W h e n b t E F y
/ . /
≥ 1 0 3
( )
[ ]
Q E F b t
s y
= 0 6 9
2
. / /

37. 37
Qs Computation
Assume E = 29000 ksi
ASD
LRFD
W h e n b t F k
y c
/ / /
≥ 1 9 5
( )
[ ]
Q k F b t
s c y
= 2 6 2 0 0
2
/ /
W h e n b t F y
/ . /
≥ 1 7 5 4
( )
[ ]
Q F b t
s y
= 2 0 0 1 0
2
/ /

38. 38
Qa Computation
ASD
LRFD
b
t
f b t f
b
e = −








≤
2 5 3
1
4 4 3
.
( / )
b t
E
f b t
E
f
b
e = −





 ≤
1 9 1 1
0 3 4
.
.
( / )
A ssu m e k si
E b
t
f b t f
e
= = −








2 9 0 0 0
3 2 5 2 6
1
5 7 9
,
. .
( / )

39. 39
Compression Members
X
Y
Z FIXED JOINT
-100.
o

40. 40
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

41. 41
Compression Members
ASD
W10x49 Actual/Allowable Ratio = 0.941
LRFD
W10x54 Actual/Limiting Ratio = 0.944

42. 42
Compression Members
ASD
W10x49 Area = 14.4 in.2
FX = 100.734 kips Ratio = 0.941
LRFD
W10x54 Area = 15.8 in.2
FX = 160.967 kips Ratio = 0.944

43. 43
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
LRFD W10x54 Area = 15.8 inch
A r e a f o r L R F D = × × × × =
1 4 4
1 6 0 9 6 7
1 0 0 7 3 4
1 0
1 6 8 1
1 0
0 8 5
0 9 4 1
0 9 4 4
1 6 0 5
.
.
.
.
.
.
.
.
.
.

44. 44
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 W10x54 Ratio = 0.944
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
1 6 0 9 6 7
1 0 0 8 0 6
1 0
1 6 8 1
1 0
0 8 5
0 9 4 4
.
.
.
.
.
.
.
.

45. 45
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

46. 46
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

47. 47
Flexural Members
ASD
fb = MZ/SZ ≤ Fb
LRFD
Mu = MZ ≤ ϕb Mn
Where ϕb = 0.9

48. 48
Limiting Width-Thickness Ratios
for Compression Elements
ASD
LRFD
Assume E = 29000 ksi
d t F
w y
/ /
≤ 6 4 0
b t E F y
/ . /
≤ 0 3 8 h t E F
w y
/ . /
≤ 3 7 6
b t F y
/ /
≤ 6 5
b t F y
/ . /
≤ 6 4 7 h t F
w y
/ . /
≤ 6 4 0 3

49. 49
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

50. 50
Flexural Members
Compact Section
X
Y
Z
FIXED JOINT
-15.00
-15.00
o
o
FIXED JOINT
Braced at 1/3 Points

51. 51
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

52. 52
Flexural Members
Compact Section
ASD
W18x40 Actual/Allowable Ratio = 0.959
LRFD
W18x40 Actual/Limiting Ratio = 0.982

53. 53
Flexural Members
Compact Section
ASD
W18x40 Sz = 68.4 in.3
MZ = 2165.777 inch-kips Ratio = 0.959
LRFD
W18x40 Zz = 78.4 in.3
MZ = 3462.933 inch-kips Ratio = 0.982

54. 54
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
LRFD W18x40 Zz = 78.4 in.3
f o r L R F D = × × × =
6 8 4
3 4 6 2 9 3 3
2 1 6 5 7 7 7
0 6 6
0 9
0 9 5 9
0 9 8 2
7 8 3
.
.
.
.
.
.
.
.

55. 55
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 W18x40 Ratio = 0.982
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
3 4 6 2 9 3 3
2 1 6 5 7 7 7
0 6 6
0 9
6 8 4
7 8 4
0 9 8 1
.
.
.
.
.
.
.
.

56. 56
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

57. 57
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

58. 58
Flexural Members
Noncompact Section
ASD
fb = MZ/SZ ≤ Fb
LRFD
Mu = MZ ≤ ϕb Mn
Where ϕb = 0.9

59. 59
Limiting Width-Thickness Ratios
for Compression Elements
ASD
LRFD
6 5 9 5
F b t F
y y
< ≤
d t F
w y
> 6 4 0
0 3 8 0 8 3
. / .
E F b t E F
y L
< ≤
3 7 6 5 7
. .
E F h t E F
y w y
< ≤
h t F
w b
≤ 7 6 0

60. 60
Limiting Width-Thickness Ratios
for Compression Elements
Assume E = 29000 ksi
ASD
LRFD
6 5 9 5
F b t F
y y
< ≤
d t F
w y
> 6 4 0
6 4 7 1 4 1 3
. / / . /
F b t F
y L
< ≤
6 4 0 3 9 7 0 7
. / . /
F h t F
y w y
< ≤
h t F
w b
≤ 7 6 0

61. 61
Flexural Members
Noncompact Section
ASD
(ASD F1-3)
(ASD F1-2)
ASD Equations F1-6, F1-7, and F1-8 must to be checked.
F F
b
t
F
b y
f
f
y
= −








0 7 9 0 0 0 2
2
. .
( )
I f m i n i m u m o r
L L
b
F d A F
b c
f
y f y
> =








7 6 2 0 0 0 0

62. 62
Flexural Members
Noncompact Section
ASD
When
(ASD F1-6)
1 0 2 1 0 5 1 0 1 0
3 3
×
≤ ≤
×
C
F
l
r
C
F
b
y T
b
y
( )
F
F l r
C
F F Q
b
y T
b
y y s
= −
×








≤
2
3 1 5 3 0 1 0
0 6
2
3
/
.

63. 63
Flexural Members
Noncompact Section
ASD
When
(ASD F1-7)
l
r
C
F
T
b
y
≥
×
5 1 0 1 0 3
( )
F
C
l r
F Q
b
b
T
y s
=
×
≤
1 7 0 1 0
0 6
3
2
/
.

64. 64
Flexural Members
Noncompact Section
ASD
For any value of l/rT
(ASD F1-8)
F
C
l d A
F Q
b
b
f
y s
=
×
≤
1 2 1 0
0 6
3
/
.

65. 65
Flexural Members
Noncompact Section
LRFD
1. LTB, Lateral-Torsional Buckling
2. FLB, Flange Local Buckling
3. WLB, Web Local Buckling

66. 66
Flexural Members
Noncompact 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 noncompact
and 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

67. 67
Flexural Members
Noncompact Section
LRFD LTB (Table A-F1.1)
For λp < λ ≤ λr
(LRFD A-F1-2)
Where:
Mp = Fy Zz ≤ 1.5Fy Sz
Mr = FLSz FL = Smaller of (Fyf − Fr) or Fyw
λ = Lb/ry
λp =
( )
M C M M M M
n b p p r
p
r p
p
= − −
−
−
















≤
λ λ
λ λ
1 7 6
. E F y f

68. 68
Flexural Members
Noncompact Section
LRFD LTB (Table A-F1.1)
Where:
λr =
X1 =
X2 =
X
F
X F
L
L
1
2
2
1 1
+ +
π
S
E G J A
z 2
4
2
C
I
S
G J
w
y
z







69. 69
Flexural Members
Noncompact Section
LRFD FLB (Table A-F1.1)
For λp < λ ≤ λr
(LRFD A-F1-3)
Where:
Mp = Fy Zz ≤ 1.5Fy Sz
Mr = FLSz FL = Smaller of (Fyf − Fr) or Fyw
λ = b/t
λp =
λr =
( )
M M M M
n p p r
p
r p
= − −
−
−
















λ λ
λ λ
0 3 8
. E F y
0 8 3
. E F L

70. 70
Flexural Members
Noncompact Section
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 M
n p p r
p
r p
= − −
−
−
















λ λ
λ λ

71. 71
Flexural Members
Noncompact Section
LRFD WLB (Table A-F1.1)
λ = h/tw
λp =
λr =
3 7 6
. E F y
5 7
. E F y

72. 72
Flexural Members
Noncompact Section
ASD
LRFD
( ) ( )
C M M M M
M M
M M M C
b
b
= + + ≤
<
=
1 7 5 1 0 5 0 3 2 3
1 0
1 2 1 2
2
1 2
1 2
. . . .
, .
m a x
I f b e t w e e n a n d
C
M
M M M M
M
M
M
b
A B C
A
B
C
=
+ + +
=
=
= −
1 2 5
2 5 3 4 3
.
.
m a x
m a x
a b s o l u t e v a l u e o f m o m e n t a t q u a r t e r p o i n t
a b s o l u t e v a l u e o f m o m e n t a t c e n t e r l i n e
a b s o l u t e v a l u e o f m o m e n t a t t h r e e q u a r t e r p o i n t

73. 73
Flexural Members
Noncompact Section
X
Y
Z
Roller
-12.00
-12.00
o
o
Pin

74. 74
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

75. 75
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

76. 76
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

77. 77
Design for Shear
ASD
fv = FY/Aw ≤ Fv = 0.4Fy (ASD F4-1)
LRFD
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw (LRFD F2-1)
Where ϕv = 0.9
h t F
w y
/ ≤ 3 8 0
h t E F
w y w
/ . /
≤ 2 4 5

78. 78
Design for Shear
Assume E = 29000 ksi
ASD
fv = FY/Aw ≤ Fv = 0.4Fy (ASD F4-1)
LRFD
Vu = FY ≤ ϕvVn = ϕv0.6Fyw Aw (LRFD F2-1)
Where ϕv = 0.9
h t F
w y
/ ≤ 3 8 0
h t F
w y w
/ . /
≤ 4 1 7 2

79. 79
Design for Shear
ASD
fv = FY/Ay ≤ (ASD F4-2)
LRFD
Vu = FY ≤ ϕvVn = ϕv (LRFD F2-2)
Where ϕv = 0.9
h t F
w y
/ > 3 8 0
2 4 5 3 0 7
. / / . /
E F h t E F
y w w y w
< ≤
( )
F
F
C F
v
y
v y
= ≤
2 8 9
0 4
.
.
0 6
2 4 5
.
. /
/
F A
E F
h t
y w w
y w
w









80. 80
Design for Shear
LRFD
Vu = FY ≤ ϕvVn = ϕv (LRFD F2-3)
Where ϕv = 0.9
3 0 7 2 6 0
. / /
E F h t
y w w
< ≤
( )
A
E
h t
w
w
4 5 2
2
.
/









81. 81
Design for Shear
X
Y
Z
FIXED JOINT
-15.00
-15.00
o
o
FIXED JOINT
Braced at 1/3 Points

82. 82
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

83. 83
Design for Shear
ASD (Check shear at the end of the member, equation “F4-1 Y”)
W18x40 Actual/Allowable Ratio = 0.8
LRFD (Check shear at the end of the member, equation “A-F2-1 Y”)
W18x40 Actual/Limiting Ratio = 0.948

84. 84
Design for Shear
ASD
W18x40 Ay = 5.638 in.2
FY = 90.241 kips Ratio = 0.8
LRFD
W18x40 Ay = 5.638 in.2
FY = 144.289 kips Ratio = 0.948

85. 85
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 W18x40 Ratio = 0.948
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
1 4 4 2 8 9
9 0 2 4 1
0 4
0 6
1 0
0 9
0 9 4 8
.
.
.
.
.
.
.
.

86. 86
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

87. 87
Combined Forces
ASD fa /Fa > 0.15
(ASD H1-1)
(ASD H1-2)
LRFD Pu /ϕPn ≥ 0.2
(LRFD H1-1a)
f
F
C f
f
F
F
C f
f
F
a
a
m y b y
a
e y
b y
m z b z
a
e z
+
−








+
−






≤
1 1
1 0
.
f
F
f
F
f
F
a
y
b y
b y
b z
b z
0 6
1 0
.
.
+ + ≤
P
P
M
M
M
M
u
n
u y
b n y
u z
b n z
φ φ φ
+ +







 ≤
8
9
1 0
.

88. 88
Combined Forces
ASD fa /Fa ≤ 0.15
(ASD H1-1)
LRFD Pu /ϕPn < 0.2
(LRFD H1-1a)
f
F
f
F
f
F
a
a
b y
b y
b z
b z
+ + ≤ 1 0
.
P
P
M
M
M
M
u
n
u y
b n y
u z
b n z
2
1 0
φ φ φ
+ +







 ≤ .

89. 89
Combined Forces
X
Y
Z

90. 90
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

91. 91
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 >
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

92. 92
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 >
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

93. 93
Combined Forces
ASD
WEIGHT = 46.566 kips
LRFD
WEIGHT = 33.874 kips

94. 94
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 >
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

95. 95
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 >
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

96. 96
Deflection Design
ASD
WEIGHT = 46.933 kips
LRFD
WEIGHT = 38.345 kips

97. 97
Compare Design without and with
Deflection Design
ASD
Without Deflection Design WEIGHT = 46.566 kips
With Deflection Design WEIGHT = 46.933 kips
LRFD
Without Deflection Design WEIGHT = 33.874 kips
With Deflection Design WEIGHT = 38.345 kips

98. 98
Design same example based on
Cb = 1.0
Code and deflection design with Cb = 1.0
ASD
Compute Cb WEIGHT = 46.933 kips
Specify Cb = 1.0 WEIGHT = 51.752 kips
LRFD
Compute Cb WEIGHT = 38.345 kips
Specify Cb = 1.0 WEIGHT = 48.421 kips

99. 99
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

100. 100
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

101. 101
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.

102. 102
Nonlinear Analysis
Commands
• NONLINEAR EFFECT
• TENSION ONLY
• COMPRESSION ONLY
• GEOMETRY AXIAL
• MAXIMUM NUMBER OF CYCLES
• CONVERGENCE TOLERANCE
• NONLINEAR ANALYSIS

103. 103
Design using Nonlinear Analysis
Input File # 1
1. Geometry, Material Type, Properties,
2. Loading ‘SW’, ‘LL’, and ‘WL’
3. FORM LOAD ‘A’ FROM ‘SW’ 1.4
4. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6
5. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5
6. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6
7. DEFINE PHYSICAL MEMBERS
8. PARAMETERS
9. MEMBER CONSTRAINTS
10. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’ $ Activate only the FORM loads
11. STIFFNESS ANALYSIS
12. SAVE

104. 104
Design using Nonlinear Analysis
Input File # 2
1. RESTORE
2. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’
3. SELECT MEMBERS
4. SMOOTH PHYSICAL MEMBERS
5. DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’
6. SELF WEIGHT LOADING RECOMPUTE
7. FORM LOAD ‘A’ FROM ‘SW’ 1.4
8. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6
9. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5
10. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6
11. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’
12. STIFFNESS ANALYSIS
13. CHECK MEMBERS
14. STEEL TAKE OFF
15. SAVE

105. 105
Design using Nonlinear Analysis
Input File # 3
1. RESTORE
2. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’
3. SELECT MEMBERS
4. SMOOTH PHYSICAL MEMBERS
5. DELETE LOADINGS ‘A’ ‘B’ ‘C’ ‘D’
6. SELF WEIGHT LOADING RECOMPUTE
7. FORM LOAD ‘A’ FROM ‘SW’ 1.4
8. FORM LOAD ‘B’ FROM ‘SW’ 1.2 ‘LL’ 1.6
9. FORM LOAD ‘C’ FROM ‘SW’ 1.2 ‘WL’ 1.6 ‘LL’ 0.5
10. FORM LOAD ‘D’ FROM ‘SW’ 0.9 ‘WL’ 1.6

106. 106
Design using Nonlinear Analysis
Input File # 3 (continue)
1. NONLINEAR EFFECT
2. GEOMETRY ALL MEMBERS
3. MAXIMUM NUMBER OF CYCLES
4. CONVERGENCE TOLERANCE DISPLACEMENT
5. LOAD LIST ‘A’ ‘B’ ‘C’ ‘D’
6. NONLINEAR ANALYSIS
7. CHECK MEMBERS
8. STEEL TAKE OFF
9. SAVE

107. 107
General Comparison between AISC
LRFD and ASD
Questions