# V. AISC 360-10 W E.1D

Verify the compressive strength of a column torsionally braced at the midpoint in the weak axis per the LRFD and ASD methods of the AISC 360-10 code.

## References

1. American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
2. American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example E.1D, p E-6, pp.E-9 - E-10

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

## Details

From the reference example E.1C

Calculate the available strength of a W14×90 with a strong axis unbraced length of 30.0 ft and weak axis and torsional unbraced lengths of 15.0 ft.

From the reference example E.1A:

… 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 ft long and is pinned top and bottom in both axes.

See example E.1D in reference (2) for calculations.

## Results

ϕcPn (kips) [LRFD] 927 927 none
Pnc (kips) [ASD] 617 617 none
Slenderness ratio 58.6 58.63 negligible

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

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Jan-19
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
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
2 FY -140
2 FY -420
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FYLD 7200 ALL
FU 9360 ALL
KX 0.5 ALL
KY 0.5 ALL
METHOD LRFD
PROFILE W14 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FYLD 7200 ALL
FU 9360 ALL
KX 0.5 ALL
KY 0.5 ALL
METHOD ASD
PROFILE W14 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
``````

```                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   W14X90                   (AISC SECTIONS)
PASS   Eq. H1-1a            0.906         3
840.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     58.633  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.906(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:   2.059E+01     Ayy:   6.160E+00     Cw:  1.598E+04              |
| Szz:   1.427E+02     Syy:   4.993E+01                                 |
| Izz:   9.990E+02     Iyy:   3.620E+02     Ix:  4.060E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        30.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    0.50 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender    10.21     N/A     13.49    T.B4.1(a)-1  |
|                Non-Slender    25.86     N/A     35.88    T.B4.1(a)-5  |
| Flexure     :  Non-Compact    10.21     9.15    24.08    T.B4.1(b)-10 |
|                Compact        25.86    90.55   137.27    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   1.19E+03   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   1.29E+03   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    8.40E+02   9.27E+02   0.906      Eq. E3-1      3     0.00 |
| Min Buck    8.40E+02   1.00E+03   0.838      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    8.40E+02   1.02E+03   0.821      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.84E-01    58.63   5.60E+03   1.20E+04   1.03E+03        |
| Min Buck    1.84E-01    48.70   6.05E+03   1.74E+04   1.11E+03        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.84E-01   6.18E+03   1.14E+03                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   5.56E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.85E+02   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.43E-01     1.00     1.20    10.21   6.18E+02            |
| Local-Y     4.28E-02     1.00     0.00    25.86   1.85E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.89E+02   0.000      Eq. F2-1      3     0.00 |
| Minor       0.00E+00   2.84E+02   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.54E+02   0.00E+00                                       |
| Minor       3.15E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   4.66E+02   0.000      Eq. F2-2      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.18E+02   0.00E+00    1.00    13.05    42.60    30.00    |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.74E+02   0.000      Eq. F3-1      3     0.00 |
| Minor       0.00E+00   2.73E+02   0.000      Eq. F6-2      3     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       6.37E+02   0.00E+00                                       |
| Minor       3.03E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.906      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         4.66E+02   0.00E+00   9.27E+02                   |
|                      2.73E+02   0.00E+00   8.40E+02                   |
| Flexure Tens         4.66E+02   0.00E+00   1.19E+03                   |
|                      2.73E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
53. PARAMETER 2
54. CODE AISC UNIFIED 2010
55. FYLD 7200 ALL
56. FU 9360 ALL
57. KX 0.5 ALL
58. KY 0.5 ALL
59. METHOD ASD
60. PROFILE W14 ALL
61. TRACK 2 ALL
62. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    9
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   W14X90                   (AISC SECTIONS)
PASS   Eq. H1-1a            0.908         4
560.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     58.633  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.908(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:   2.059E+01     Ayy:   6.160E+00     Cw:  1.598E+04              |
| Szz:   1.427E+02     Syy:   4.993E+01                                 |
| Izz:   9.990E+02     Iyy:   3.620E+02     Ix:  4.060E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        30.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    0.50 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender    10.21     N/A     13.49    T.B4.1(a)-1  |
|                Non-Slender    25.86     N/A     35.88    T.B4.1(a)-5  |
| Flexure     :  Non-Compact    10.21     9.15    24.08    T.B4.1(b)-10 |
|                Compact        25.86    90.55   137.27    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.   10
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   7.93E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   8.61E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    5.60E+02   6.17E+02   0.908      Eq. E3-1      4     0.00 |
| Min Buck    5.60E+02   6.67E+02   0.839      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    5.60E+02   6.81E+02   0.822      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.84E-01    58.63   5.60E+03   1.20E+04   1.03E+03        |
| Min Buck    1.84E-01    48.70   6.05E+03   1.74E+04   1.11E+03        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.84E-01   6.18E+03   1.14E+03                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   3.70E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   1.23E+02   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.43E-01     1.00     1.20    10.21   6.18E+02            |
| Local-Y     4.28E-02     1.00     0.00    25.86   1.85E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.92E+02   0.000      Eq. F2-1      4     0.00 |
| Minor       0.00E+00   1.89E+02   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.54E+02   0.00E+00                                       |
| Minor       3.15E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.10E+02   0.000      Eq. F2-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.18E+02   0.00E+00    1.00    13.05    42.60    30.00    |
STAAD SPACE                                              -- PAGE NO.   11
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.82E+02   0.000      Eq. F3-1      4     0.00 |
| Minor       0.00E+00   1.81E+02   0.000      Eq. F6-2      4     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       6.37E+02   0.00E+00                                       |
| Minor       3.03E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.908      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         3.10E+02   0.00E+00   6.17E+02                   |
|                      1.81E+02   0.00E+00   5.60E+02                   |
| Flexure Tens         3.10E+02   0.00E+00   7.93E+02                   |
|                      1.81E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
```