# V. AISC 360-05 WT Shape F.10

## References

1. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
2. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, Example F.10, pp.F-37,38

## Details

From reference (2):

Select an ASTM A992 WT beam with a simple span of 6 ft. The toe of the stem of the WT is in tension. The nominal loads are a uniform dead load of 0.08 kip/ft and a uniform live load of 0.24 kip/ft. There is no deflection limit for this member. Assume full lateral support.

## Validation

Ultimate moment:

Service moment:

Try a WT5×6, which has a plastic section modulus, Zx = 2.20 in3 and a section modulus, Sx = 1.22 in3.

Flexural Yielding

 (F9-2)

Lateral-torsional buckling does not govern since the member is continuously braced.

Flange compactness: $λ=bf2tf=9.43$

Determine the compact and slender flange ratio limits from Table B4.1b:

$λpf=0.38EFy=0.3829,00046=9.15$
$λrf=1.0EFy=1.029,00046=24.1$

Thus, the section has a non-compact flange.

So use Mn = 97.6 in·k = 8.13 ft·k

The available flexural strength:

LRFD:

ASD:

ϕbMn (ft·k) [LRFD] 7.32 7.21 1.5%
Mnb (ft·k) [ASD] 4.87 4.80 1.5%

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 11-Jun-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 6 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
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 T W10X12
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
1 UNI GY -0.08
1 UNI GY -0.24
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2005
FU 9360 ALL
FYLD 7200 ALL
FLX 2 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
FU 9360 ALL
FYLD 7200 ALL
FLX 2 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 T    W10X12                   (AISC SECTIONS)
PASS   Eq. H2-1             0.300         3
0.00            0.00          -2.16        3.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     91.750  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     3.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.300(PASS)                 |
|          Loc  :    3.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -2.160E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.316E-01     Ayy:   9.376E-01     Cw:  2.546E-02              |
| Szz:   1.202E+00     Syy:   5.505E-01                                 |
| Izz:   4.303E+00     Iyy:   1.090E+00     Ix:  2.735E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| 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 :  Slender        25.97     N/A     18.06    T.B4.1-8     |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact     9.43     9.15    24.08    T.B4.1-7     |
|                Slender        25.97     9.15    24.08    T.B4.1-7     |
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   7.96E+01   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   8.63E+01   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   4.31E+01   0.000      Sec. E1       3     0.00 |
| Min Buck    0.00E+00   3.28E+01   0.000      Eq. E7-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   2.72E+01   0.000      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.23E-02    46.18   3.89E+03   1.93E+04   4.79E+01        |
| Min Buck    1.23E-02    91.75   2.96E+03   4.90E+03   3.64E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.23E-02   2.46E+03   3.02E+01                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.25E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y    -1.44E+00   2.53E+01   0.057      Eq. G2-1      3     6.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.78E-03     1.00     1.20     9.43   2.49E+01            |
| Local-Y     6.51E-03     1.00     1.20    25.97   2.81E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.16E+00   7.21E+00   0.300      Eq. F9-1      3     3.00 |
| Minor       0.00E+00   3.26E+00   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       8.01E+00   0.00E+00                                       |
| Minor       3.63E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.16E+00   2.45E+01   0.088      Eq. F9-4      3     3.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.72E+01   0.00E+00    1.00     0.00     0.00     6.00    |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.16E+00   1.18E+01   0.182      Eq. F9-6      3     3.00 |
| Minor       0.00E+00   3.23E+00   0.000      Eq. F6-2      3     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       1.32E+01   7.16E+03                                       |
| Minor       3.59E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.300      Eq. H2-1      3     3.00             |
| Flexure Tens          0.300      Eq. H2-1      3     3.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         1.17E+03   0.00E+00   0.00E+00                   |
|                      3.92E+03   1.01E+04   2.21E+03                   |
| Flexure Tens         3.11E+03   0.00E+00   0.00E+00                   |
|                      1.04E+04   1.01E+04   6.48E+03                   |
|-----------------------------------------------------------------------|
57. PARAMETER 2
58. CODE AISC UNIFIED 2005
59. FU 9360 ALL
60. FYLD 7200 ALL
61. FLX 2 ALL
62. METHOD ASD
63. TRACK 2 ALL
64. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 T    W10X12                   (AISC SECTIONS)
PASS   Eq. H2-1             0.300         4
0.00            0.00          -1.44        3.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     91.750  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     3.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.300(PASS)                 |
|          Loc  :    3.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -1.440E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.316E-01     Ayy:   9.376E-01     Cw:  2.546E-02              |
| Szz:   1.202E+00     Syy:   5.505E-01                                 |
| Izz:   4.303E+00     Iyy:   1.090E+00     Ix:  2.735E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| 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 :  Slender        25.97     N/A     18.06    T.B4.1-8     |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact     9.43     9.15    24.08    T.B4.1-7     |
|                Slender        25.97     9.15    24.08    T.B4.1-7     |
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   5.30E+01   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   5.75E+01   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   2.87E+01   0.000      Sec. E1       4     0.00 |
| Min Buck    0.00E+00   2.18E+01   0.000      Eq. E7-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.81E+01   0.000      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.23E-02    46.18   3.89E+03   1.93E+04   4.79E+01        |
| Min Buck    1.23E-02    91.75   2.96E+03   4.90E+03   3.64E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.23E-02   2.46E+03   3.02E+01                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.49E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y    -9.60E-01   1.68E+01   0.057      Eq. G2-1      4     6.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.78E-03     1.00     1.20     9.43   2.49E+01            |
| Local-Y     6.51E-03     1.00     1.20    25.97   2.81E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.44E+00   4.80E+00   0.300      Eq. F9-1      4     3.00 |
| Minor       0.00E+00   2.17E+00   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       8.01E+00   0.00E+00                                       |
| Minor       3.63E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.44E+00   1.63E+01   0.089      Eq. F9-4      4     3.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.72E+01   0.00E+00    1.00     0.00     0.00     6.00    |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.44E+00   7.88E+00   0.183      Eq. F9-6      4     3.00 |
| Minor       0.00E+00   2.15E+00   0.000      Eq. F6-2      4     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       1.32E+01   7.16E+03                                       |
| Minor       3.59E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.300      Eq. H2-1      4     3.00             |
| Flexure Tens          0.300      Eq. H2-1      4     3.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         7.83E+02   0.00E+00   0.00E+00                   |
|                      2.61E+03   6.74E+03   1.47E+03                   |
| Flexure Tens         2.07E+03   0.00E+00   0.00E+00                   |
|                      6.90E+03   6.74E+03   4.31E+03                   |
|-----------------------------------------------------------------------|