# 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
ϕcPn (kips) [LRFD] 892 893 negligible
Pnc (kips) [ASD] 594 594 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\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
2 FY -140
2 FY -420
1 1.0 2 1.0
1 1.2 2 1.6
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
``````

```                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
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:   2.082E+02     Syy:   7.456E+01                                 |
| 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                   |
|-----------------------------------------------------------------------|
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)
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:   2.082E+02     Syy:   7.456E+01                                 |
| 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                   |
|-----------------------------------------------------------------------|
```