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V. AISC 360-05 Compression

Verify the axial compression capacity for a the y-y axis of an I section for both the LRFD and ASD methods per the AISC 360-05 code.

References

  1. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, page E-4. Example E.1a
  2. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005

Details

The column is 30 ft long, pinned top and bottom in both axis.

The section is an ASTM A992 (Fy = 50 ksi) W-shape column to carry an axial dead load of 140 kips and live load of 420 kips. The column is 30 feet long

Validation

Calculate the required strength.

LRFD:

Pu = 1.2(140 kips) + 1.6(420 kips) = 840 kips

ASD:

Pa = 140 kips + 420 kips = 560 kips

For a pinned-pinned condition, K = 1.0 (Table C-C2.2 of ref. 2). Because the unbraced length is equal about both x-x and y-y directions, y-y axis buckling governs.

Use Table 4-1 in ref 2 and select a W14x132 (KLy = 30 ft). From this table:

ϕcPn = 892 kips > 840 kips

Pnc = 594 kips > 560 kips

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
ϕcPn (kips) [LRFD] 892 893 negligible  
Pnc (kips) [ASD] 594 594 none  

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2005\AISC 360-05 Compression.STD is typically installed with the program.

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 29-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 30 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X132
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MZ
LOAD 1 DEAD LOAD
JOINT LOAD
2 FY -140
LOAD 2 LIVE LOAD
JOINT LOAD
2 FY -420
LOAD COMB 3 SERVICE LOAD
1 1.0 2 1.0 
LOAD COMB 4 ULTIMATE LOAD
1 1.2 2 1.6 
PERFORM ANALYSIS
UNIT INCHES KIP
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   W14X132                  (AISC SECTIONS)
                           PASS   Eq. H1-1a            0.943         3
                      560.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     95.792  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.943(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   5.600E+02(C ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   3.028E+01     Ayy:   9.481E+00     Cw:  2.560E+04              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   1.530E+03     Iyy:   5.480E+02     Ix:  1.230E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       360.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     7.14     N/A     13.49    T.B4.1-3     |
|                Non-Slender    17.74     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         7.14     9.15    24.08    T.B4.1-1     |
|                Compact        17.74    90.55   137.27    T.B4.1-9     |
      STAAD PLANE                                              -- PAGE NO.    4
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   1.16E+03   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   1.16E+03   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    5.60E+02   9.14E+02   0.613      Sec. E1       3     0.00 |
| Min Buck    5.60E+02   5.94E+02   0.943      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    5.60E+02   9.28E+02   0.603      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.88E+01    57.33   3.93E+01   8.71E+01   1.53E+03        |
| Min Buck    3.88E+01    95.79   2.56E+01   3.12E+01   9.92E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    3.88E+01   3.99E+01   1.55E+03                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   5.44E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.90E+02   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.03E+01     1.00     1.20     7.14   9.08E+02            |
| Local-Y     9.48E+00     1.00     0.00    17.74   2.84E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   7.01E+03   0.000      Eq. F2-1      3     0.00 |
| Minor       0.00E+00   3.38E+03   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.17E+04   0.00E+00                                       |
| Minor       5.65E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.97E+03   0.000      Eq. F2-2      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       9.98E+03   0.00E+00    1.00   159.29   673.75   360.00    |
      STAAD PLANE                                              -- PAGE NO.    5
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.943      Eq. H1-1a     3     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     3     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         5.97E+03   0.00E+00   5.94E+02                   |
|                      3.38E+03   0.00E+00   5.60E+02                   |
| Flexure Tens         5.97E+03   0.00E+00   1.16E+03                   |
|                      3.38E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    53. LOAD LIST 4
    54. PARAMETER 2
    55. CODE AISC UNIFIED 2005
    56. METHOD LRFD
    57. FYLD 50 ALL
    58. TRACK 2 ALL
    59. CHECK CODE ALL
 STEEL DESIGN    
      STAAD PLANE                                              -- PAGE NO.    6
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   W14X132                  (AISC SECTIONS)
                           PASS   Eq. H1-1a            0.941         4
                      840.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     95.792  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.941(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   8.400E+02(C ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   3.028E+01     Ayy:   9.481E+00     Cw:  2.560E+04              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   1.530E+03     Iyy:   5.480E+02     Ix:  1.230E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       360.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     7.14     N/A     13.49    T.B4.1-3     |
|                Non-Slender    17.74     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         7.14     9.15    24.08    T.B4.1-1     |
|                Compact        17.74    90.55   137.27    T.B4.1-9     |
      STAAD PLANE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   1.75E+03   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.75E+03   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    8.40E+02   1.37E+03   0.612      Sec. E1       4     0.00 |
| Min Buck    8.40E+02   8.93E+02   0.941      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    8.40E+02   1.39E+03   0.602      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.88E+01    57.33   3.93E+01   8.71E+01   1.53E+03        |
| Min Buck    3.88E+01    95.79   2.56E+01   3.12E+01   9.92E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    3.88E+01   3.99E+01   1.55E+03                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   8.18E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   2.84E+02   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.03E+01     1.00     1.20     7.14   9.08E+02            |
| Local-Y     9.48E+00     1.00     0.00    17.74   2.84E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.05E+04   0.000      Eq. F2-1      4     0.00 |
| Minor       0.00E+00   5.08E+03   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.17E+04   0.00E+00                                       |
| Minor       5.65E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   8.98E+03   0.000      Eq. F2-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       9.98E+03   0.00E+00    1.00   159.29   673.75   360.00    |
      STAAD PLANE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.941      Eq. H1-1a     4     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     4     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         8.98E+03   0.00E+00   8.93E+02                   |
|                      5.08E+03   0.00E+00   8.40E+02                   |
| Flexure Tens         8.98E+03   0.00E+00   1.75E+03                   |
|                      5.08E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|