# ASD vs LRFD

Document Sample

```					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   =   dead load
L   =   live load
W   =   wind load
E   =   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   =   dead load
L   =   live load
W   =   wind load
E   =   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   =   dead load
L   =   live load
W   =   wind load
E   =   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 9 th 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 cross-
section‟s Gross Area
• Check Tensile Strength based on the cross-
section‟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                              (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

14
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
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              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

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 = 25374 / Fy
.
26
Compression Members
ASD    KL/r ≤ C′c                             (ASD E2-1 or A-B5-11)

  KL / r  2 
Q 1             Fy
      2Cc 
2
                                         2 2 E
Fa                                  Where    Cc 

5 3 KL / r   KL / r 
3
QFy
           
3      8Cc        8Cc
3

LRFD      c Q  15
.                                 (LRFD A-E3-2)

                F
Q c 2                             KL     Fy
Fcr  Q 0.658                        Where     c 
y                        r     E

27
Compression Members
ASD   KL/r > C′c                              (ASD E2-2)

12 2 E                           2 2 E
Fa                        Where     Cc 

23 KL / r 
2
QFy

LRFD c     Q  15
.                            (LRFD A-E3-3)

 0.877                             KL    Fy
Fcr   2  Fy             Where      c 
r
 c                                      E

28
Compression Members
LRFD
 0.877                                                Fy
Fcr   2  Fy                     Where         c 
KL
 c                                           r      E
                     
                     
                     
0.877
Fcr                        Fy
                  
2

  KL Fy           
  r E            
                  

0.877 2 E                         20171 2 E
.
Fcr                               Fcr 
 KL / r                          23 KL / r 
2                                    2

29
Compression Members
ASD                       LRFD
12 2 E                  20171 2 E
.
Fa                       Fcr 
23 KL / r                23 KL / r 
2                          2

Fcr / Fa = 1.681

LRFD Fcr = ASD Fa × 1.681

30
Compression Members
ASD              K y LY K z Lz  KL  
 r , r , r  
KL / r  
 y         z
     e

 KL          E               (ASD C-E2-2)
Where      
 r e         Fe

LRFD

λc = Maximum of ( λcy , λcz , λe )

31
Compression Members
LRFD
Where:
K y Ly   Fy
 cy 
ry     E

Kz Lz      Fy
 cz 
rz       E

Fy
e 
Fe
32
Compression Members
Flexural-Torsional Buckling

  2 EC             10  .
Fe            w
 GJ 
  K x Lx 

2
 I y  Iz


33
Qs Computation
ASD
When 95 / Fy / k c  b / t  195 / Fy / k c
Qs  1293  0.00309(b / t ) Fy / k c
.
4.05
kc                      if h / t  70, otherwise k c  10
.
h / t    0.46

LRFD
When 056 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 9536 / Fy  b / t  1754 / 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 
2

LRFD    When b / t  1754 / 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     E
be  191t
.     1              b
f  (b / t )   f 

325.26t     57.9 
Assume E  29000 ksi,       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              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

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
160.967   10.    .
10 0.941
Area for LRFD  14.4                           16.05
.     .
100.734 1681 085 0.944

LRFD          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
160.967   10.    .
10
LRFD Ratio computed from ASD  0845 
.                         0.944
.      .
100806 1681 085 .

LRFD          W10x54        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  376 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
Flexural Members
-15.00
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                    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

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
2165.777   0.9   0.982

LRFD          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
3462.933 0.66 68.4
LRFD Ratio computed from ASD  0.959                      0.981
2165.777 0.9 78.4

LRFD          W18x40         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   Fy

d t w  640   Fy          h t w  760   Fb

LRFD
0.38 E Fy  b / t  083 E FL
.

376 E Fy  h t w  57 E Fy
.                  .
59
Limiting Width-Thickness Ratios
for Compression Elements
Assume E = 29000 ksi
ASD
65   Fy  b t  95   Fy

d t w  640   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            Fy          (ASD F1-3)

             2t f          


 76b f             20000 
If   Lb  Lc  minimum         or                
 F
    y                   
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
102  10 3 Cb    l   510  10 3 Cb
When                      
Fy         rT        Fy

2   Fy l / rT  
2

Fb                    Fy  0.6Fy Qs   (ASD F1-6)
 3 1530  10 Cb 
3
                  

62
Flexural Members
Noncompact Section
ASD

l   510  10 3 Cb
When      
rT        Fy

170  10 3 Cb
Fb                       0.6Fy Qs   (ASD F1-7)
l / rT    2

63
Flexural Members
Noncompact Section
ASD

For any value of l/rT

12  10 3 Cb
Fb                0.6Fy Qs   (ASD F1-8)
ld / A f

64
Flexural Members
Noncompact Section
LRFD

1.   LTB, Lateral-Torsional Buckling
2.   FLB, Flange Local Buckling
3.   WLB, Web Local Buckling

65
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

66
Flexural Members
Noncompact Section
LRFD      LTB                                          (Table A-F1.1)

For λp < λ ≤ λr
                    p 
         
      Mp
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

λp = 176 E Fyf
.

67
Flexural Members
Noncompact Section
LRFD         LTB                   (Table A-F1.1)

Where:

X1
λr   =    1  1  X 2 FL
2
FL

    EGJA
X1 =
Sz    2
2
C S 
X2 = 4 w  z 
I y  GJ 
68
Flexural Members
Noncompact Section
LRFD        FLB                                               (Table A-F1.1)

For   λp < λ ≤ λr
                   p 

Mn   M p  M p  Mr       
    
 r


                        p                 (LRFD A-F1-3)
Where:
Mp   =   Fy Zz ≤ 1.5Fy Sz
Mr   =   FLSz                   FL = Smaller of (Fyf − Fr) or Fyw
λ    =   b/t
λp   =   0.38 E Fy
λr   =   0.83 E FL

69
Flexural Members
Noncompact Section
LRFD      WLB                                      (Table A-F1.1)

For λp < λ ≤ λr
                   p 

Mn   M p  M p  Mr     
    
 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                  (Table A-F1.1)

λ   = h/tw

λp = 376 E Fy
.

λr = 57 E Fy
.

71
Flexural Members
Noncompact Section
ASD
Cb  175  105 M 1 M 2   0.3 M1 M 2   2.3
2
.     .
M1  M 2
If M max between M1 and M 2 , Cb  10
.

LRFD
12.5 M max
Cb 
2.5 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
Flexural Members
-12.00
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 / t w  380   Fy

fv = FY/Aw ≤ Fv = 0.4Fy              (ASD F4-1)

LRFD     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              (ASD F4-1)

LRFD      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
Fy
fv = FY/Ay ≤ Fv            Cv     0.4 Fy          (ASD F4-2)
2.89

LRFD       2.45 E / Fyw  h / t w  307 E / Fyw
.

 2.45 E / Fyw 
Vu = FY ≤ ϕvVn = ϕv 0.6Fyw Aw                       (LRFD F2-2)
     h / tw   
              
Where ϕv = 0.9

79
Design for Shear
LRFD   307 E / Fyw  h / t w  260
.

 4.52 E 
Vu = FY ≤ ϕvVn = ϕv Aw                        (LRFD F2-3)
 h / t w  

2


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       (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

83
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

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

.
144.289 0.4 10
LRFD Ratio computed from ASD  08 
.                    0.948
90.241 0.6 0.9

LRFD         W18x40         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

fa      Cmy f by       Cmz f bz
                              10
.   (ASD H1-1)
Fa       fa             fa 
1       Fby  1        
                  Fez 
    Fey 
fa   f by   f
       bz  10
.                    (ASD H1-2)
0.6Fy Fby Fbz

LRFD     Pu /ϕPn ≥ 0.2

Pu  8  M uy   M uz                    (LRFD H1-1a)
   M   M   10
 .
Pn 9  b ny    b   nz 

87
Combined Forces
ASD    fa /Fa ≤ 0.15

fa   f by   f bz
             10
.       (ASD H1-1)
Fa Fby Fbz

LRFD      Pu /ϕPn < 0.2

Pu   M uy   M uz 
  M   M   10
                .
(LRFD H1-1a)
2Pn  b ny   b   nz 

88
Combined Forces

Y

Z       X
89
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

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   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

97
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
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.    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
103
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
104
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

105
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

106
General Comparison between AISC
LRFD and ASD

Questions

107

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