# V. AISC 360-10 W Tens BM H3

Verify the interaction checks due to tension and bending moments in both axes of a W section 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 H.3, pp. H-8 - H-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

## Details

From reference (2):

Select an ASTM A992 W-shape with a 14-in. nominal depth to carry forces of 29.0 kips from dead load and 87.0 kips from live load in axial tension, as well as the following moments due to uniformly distributed loads:
• MxD = 32.0 kip-ft
• MxL = 96.0 kip-ft
• MyD = 11.3 kip-ft
• MyL = 33.8 kip-ft

The unbraced length is 30.0 ft and the ends are pinned. Assume the connections are made with no holes.

See example H.3 in reference (2) for calculations.

## Results

Interaction ratio per H1-1b [LRFD] 0.873 0.874 negligible
Interaction ratio per H1-1b [ASD] 0.874 0.876 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 W Tens BM H3.STD is typically installed with the program.

``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-May-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 30 0 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 W14X82
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
2 FIXED BUT FX MY MZ
1 PINNED
2 FX 174
1 FX -174
1 UNI GY -1.70668
1 UNI GZ 0.6009
UNIT INCHES KIP
1 FX 116
2 FX 116
1 UNI GY -0.0948
1 UNI GZ 0.0334
UNIT FEET KIP
1 1.0 2 1.0 3 1.0
4 1.0 5 1.0 6 1.0
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FYLD 50 ALL
FU 65 ALL
CB 1.41 ALL
TRACK 2 ALL
UNIT FEET KIP
CHECK CODE ALL
UNIT INCHES KIP
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FYLD 50 ALL
FU 65 ALL
CB 1.41 ALL
TRACK 2 ALL
UNIT FEET KIP
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   W14X82                   (AISC SECTIONS)
PASS   Eq. H1-1b            0.874         7
174.00 T        -67.60        -192.00       15.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    144.970  L/C  :     7                |
| Allowable Slenderness Ratio :    300.000  LOC  :    15.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      7    Ratio     :     0.874(PASS)                 |
|          Loc  :   15.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.740E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:  -6.760E+01     Mz:  -1.920E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.727E+01     Ayy:   7.293E+00     Cw:  6.688E+03              |
| Szz:   1.232E+02     Syy:   2.931E+01                                 |
| Izz:   8.810E+02     Iyy:   1.480E+02     Ix:  5.070E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        30.000                                   |
| 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     5.91     N/A     13.49    T.B4.1(a)-1  |
|                Non-Slender    22.35     N/A     35.88    T.B4.1(a)-5  |
| Flexure     :  Compact         5.91     9.15    24.08    T.B4.1(b)-10 |
|                Compact        22.35    90.55   137.27    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.    4
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       1.74E+02   1.08E+03   0.161      Eq. D2-1      7     0.00 |
| Rupture     1.74E+02   1.17E+03   0.149      Eq. D2-2      7     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   8.34E+02   0.000      Eq. E3-1      7     0.00 |
| Min Buck    0.00E+00   2.58E+02   0.000      Eq. E3-1      7     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   7.99E+02   0.000      Eq. E4-1      7     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.67E-01    59.42   5.56E+03   1.17E+04   9.27E+02        |
| Min Buck    1.67E-01   144.97   1.72E+03   1.96E+03   2.87E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.67E-01   5.32E+03   8.87E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     9.01E+00   4.66E+02   0.019      Eq. G2-1      7     0.00 |
| Local-Y     2.56E+01   2.19E+02   0.117      Eq. G2-1      7     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.20E-01     1.00     1.20     5.91   5.18E+02            |
| Local-Y     5.06E-02     1.00     0.00    22.35   2.19E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.92E+02   5.21E+02   0.368      Eq. F2-1      7    15.00 |
| Minor      -6.76E+01   1.68E+02   0.402      Eq. F6-1      7    15.00 |
| Intermediate   Mn        My                                           |
| Major       5.79E+02   0.00E+00                                       |
| Minor       1.87E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.92E+02   4.91E+02   0.391      Eq. F2-2      7    15.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.45E+02   0.00E+00    1.41     8.77    33.01    30.00    |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.794      Eq. H1-1b     7    15.00             |
| Flexure Tens          0.874      Eq. H1-1b     7    15.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.91E+02   1.92E+02   2.58E+02                   |
|                      1.68E+02  -6.76E+01   0.00E+00                   |
| Flexure Tens         4.91E+02   1.92E+02   1.08E+03                   |
|                      1.68E+02  -6.76E+01   1.74E+02                   |
|-----------------------------------------------------------------------|
66. UNIT INCHES KIP
68. PARAMETER 2
69. CODE AISC UNIFIED 2010
70. METHOD ASD
71. FYLD 50 ALL
72. FU 65 ALL
73. CB 1.41 ALL
74. TRACK 2 ALL
75. UNIT FEET KIP
76. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   W14X82                   (AISC SECTIONS)
PASS   Eq. H1-1b            0.876         8
116.00 T        -45.09        -127.98       15.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    144.970  L/C  :     8                |
| Allowable Slenderness Ratio :    300.000  LOC  :    15.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      8    Ratio     :     0.876(PASS)                 |
|          Loc  :   15.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.160E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:  -4.509E+01     Mz:  -1.280E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.727E+01     Ayy:   7.293E+00     Cw:  6.688E+03              |
| Szz:   1.232E+02     Syy:   2.931E+01                                 |
| Izz:   8.810E+02     Iyy:   1.480E+02     Ix:  5.070E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        30.000                                   |
| 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     5.91     N/A     13.49    T.B4.1(a)-1  |
|                Non-Slender    22.35     N/A     35.88    T.B4.1(a)-5  |
| Flexure     :  Compact         5.91     9.15    24.08    T.B4.1(b)-10 |
|                Compact        22.35    90.55   137.27    T.B4.1(b)-15 |
STAAD SPACE                                              -- PAGE NO.    7
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       1.16E+02   7.19E+02   0.161      Eq. D2-1      8     0.00 |
| Rupture     1.16E+02   7.80E+02   0.149      Eq. D2-2      8     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   5.55E+02   0.000      Eq. E3-1      8     0.00 |
| Min Buck    0.00E+00   1.72E+02   0.000      Eq. E3-1      8     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   5.31E+02   0.000      Eq. E4-1      8     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.67E-01    59.42   5.56E+03   1.17E+04   9.27E+02        |
| Min Buck    1.67E-01   144.97   1.72E+03   1.96E+03   2.87E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.67E-01   5.32E+03   8.87E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     6.01E+00   3.10E+02   0.019      Eq. G2-1      8     0.00 |
| Local-Y     1.71E+01   1.46E+02   0.117      Eq. G2-1      8     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.20E-01     1.00     1.20     5.91   5.18E+02            |
| Local-Y     5.06E-02     1.00     0.00    22.35   2.19E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.28E+02   3.47E+02   0.369      Eq. F2-1      8    15.00 |
| Minor      -4.51E+01   1.12E+02   0.403      Eq. F6-1      8    15.00 |
| Intermediate   Mn        My                                           |
| Major       5.79E+02   0.00E+00                                       |
| Minor       1.87E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.28E+02   3.26E+02   0.392      Eq. F2-2      8    15.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.45E+02   0.00E+00    1.41     8.77    33.01    30.00    |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.795      Eq. H1-1b     8    15.00             |
| Flexure Tens          0.876      Eq. H1-1b     8    15.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         3.26E+02   1.28E+02   1.72E+02                   |
|                      1.12E+02  -4.51E+01   0.00E+00                   |
| Flexure Tens         3.26E+02   1.28E+02   7.19E+02                   |
|                      1.12E+02  -4.51E+01   1.16E+02                   |
|-----------------------------------------------------------------------|
```