# V. AISC 360-10 - E-2

## Reference

Design Examples, Version 14.0, American Institute of Steel Construction, 2011, page E-11.

Note: This reference is freely available for download from the AISC website at https://www.aisc.org/globalassets/aisc/university-programs/teaching-aids/first-semester-design-examples.pdf

## Problem

From the reference:

Verify that a built-up, ASTM A572 Grade 50 column with PL 1 in. × 8 in. flanges and a PL 4 in. × 15 in. web is sufficient to carry a dead load of 70 kips and live load of 210 kips in axial compression. The column length is 15 ft and the ends are pinned in both axes.

Refer to the reference for calculations.

## Comparison

Table 1. Comparison of results
ϕcPn (kips) [LRFD] 508 513 1.0%
Pnc (kips) [ASD] 338 341 0.9%

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2010\AISC 360-10 - E-2.STD is typically installed with the program.

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.
``````STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 31-Oct-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 15 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
*TABLE 1
*UNIT INCHES KIP
*ISECTION
*I1
*17 0.25 17 8 1 8 1 0 0 0
TABLE 2
UNIT INCHES KIP
WIDE FLANGE
I
19.75 17 0.25 8 1 1095.65 85.3529 5.41146 4.25 10.6667 8 1
END
UNIT inch KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 65 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT INCHES KIP
CONSTANTS
MATERIAL STEEL ALL
MEMBER PROPERTY AMERICAN
1 UPTABLE 2 I
UNIT FEET KIP
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MY MZ
2 FY -70
2 FY -210
UNIT INCHES KIP
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH
``````

```                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   I                        (UPT)
PASS   Eq. H1-1a            0.819         3
420.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     86.586  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.819(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   4.200E+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:   1.067E+01     Ayy:   4.250E+00     Cw:  5.461E+03              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   1.096E+03     Iyy:   8.535E+01     Ix:  5.411E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          65.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       180.000                                   |
| 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     4.00     N/A     13.66    T.B4.1(a)-1  |
|                Slender        60.00     N/A     36.33    T.B4.1(a)-5  |
| Flexure     :  Compact         4.00     9.27    24.39    T.B4.1(b)-10 |
|                Compact        60.00    91.69   139.00    T.B4.1(b)-15 |
STAAD PLANE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   8.89E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   9.63E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    4.20E+02   8.03E+02   0.523      Eq. E7-1      3     0.00 |
| Min Buck    4.20E+02   5.13E+02   0.819      Eq. E7-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    4.20E+02   6.84E+02   0.614      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.86E+01    24.17   4.52E+01   5.02E+02   8.93E+02        |
| Min Buck    1.91E+01    86.59   2.89E+01   3.91E+01   5.70E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.88E+01   3.85E+01   7.60E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.88E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.15E+02   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.07E+01     1.00     1.20     4.00   3.20E+02            |
| Local-Y     4.25E+00     1.00     5.00    60.00   1.27E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   6.39E+03   0.000      Eq. F2-1      3     0.00 |
| Minor       0.00E+00   1.45E+03   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.10E+03   0.00E+00                                       |
| Minor       1.61E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.44E+03   0.000      Eq. F2-2      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       6.04E+03   0.00E+00    1.00    89.22   311.02   180.00    |
STAAD PLANE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.819      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         5.44E+03   0.00E+00   5.13E+02                   |
|                      1.45E+03   0.00E+00   4.20E+02                   |
| Flexure Tens         5.44E+03   0.00E+00   8.89E+02                   |
|                      1.45E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
64. PARAMETER 2
65. CODE AISC UNIFIED 2010
66. FU 65 ALL
67. FYLD 50 ALL
68. METHOD ASD
69. TRACK 2 ALL
70. CHECK CODE ALL
STEEL DESIGN
STAAD PLANE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   I                        (UPT)
PASS   Eq. H1-1a            0.820         4
280.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     86.586  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.820(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   2.800E+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:   1.067E+01     Ayy:   4.250E+00     Cw:  5.461E+03              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   1.096E+03     Iyy:   8.535E+01     Ix:  5.411E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          65.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       180.000                                   |
| 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     4.00     N/A     13.66    T.B4.1(a)-1  |
|                Slender        60.00     N/A     36.33    T.B4.1(a)-5  |
| Flexure     :  Compact         4.00     9.27    24.39    T.B4.1(b)-10 |
|                Compact        60.00    91.69   139.00    T.B4.1(b)-15 |
STAAD PLANE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   5.91E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   6.42E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    2.80E+02   5.35E+02   0.524      Eq. E7-1      4     0.00 |
| Min Buck    2.80E+02   3.41E+02   0.820      Eq. E7-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    2.80E+02   4.55E+02   0.615      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.86E+01    24.17   4.52E+01   5.02E+02   8.93E+02        |
| Min Buck    1.91E+01    86.59   2.89E+01   3.91E+01   5.70E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.88E+01   3.85E+01   7.60E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.92E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   7.63E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.07E+01     1.00     1.20     4.00   3.20E+02            |
| Local-Y     4.25E+00     1.00     5.00    60.00   1.27E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   4.25E+03   0.000      Eq. F2-1      4     0.00 |
| Minor       0.00E+00   9.65E+02   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.10E+03   0.00E+00                                       |
| Minor       1.61E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.62E+03   0.000      Eq. F2-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       6.04E+03   0.00E+00    1.00    89.22   311.02   180.00    |
STAAD PLANE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.820      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         3.62E+03   0.00E+00   3.41E+02                   |
|                      9.65E+02   0.00E+00   2.80E+02                   |
| Flexure Tens         3.62E+03   0.00E+00   5.91E+02                   |
|                      9.65E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
```