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ASD vs LRFD

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					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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