V. AISC 360-05 HSST NonCompact Flange F.7

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.7, pp.F-28 - F-31

Details

From reference (2):

Select a rectangular ASTM A500 Gr. B HSS beam with a span of 21 ft. The nominal loads include a uniform dead load of 0.15 kip/ft and a uniform live load of 0.40 kip/ft. Limit the live load deflection to L/240. Assume the beam is braced at the end points only.

Validation

Ultimate moment:

Service moment:

Try a HSS 10×6×3/16, which has a plastic section modulus, Zx = 18.0 in3 and a section modulus, Sx = 14.9 in3.

Flange compactness: λ = b/t = 31.5

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

$λ p = 1.12 E F y = 1.12 29,000 46 = 28.1$
$λ r = 1.40 E F y = 1.40 29,000 46 = 35.2$

Thus, the section has a non-compact flange.

Web compactness: λ = h/t = 54.5

$λ p = 2.42 E F y = 2.42 29,000 46 = 60.8 > λ$

Thus, the section has a compact web.

 $M n = M p − ( M p − F y S ) ( 3.57 b t F y E - 4.0 )$ (F7-2)

The available flexural strength:

LRFD:

ASD:

ϕbMn (ft·k) [LRFD] 57.0 57.0 none
Mnb (ft·k) [ASD] 37.9 37.9 none

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 19-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 21 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
CONSTANTS
MATERIAL STEEL ALL
MEMBER PROPERTY AMERICAN
1 TABLE ST HSST10X6X0.188
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
1 UNI GY -0.15
1 UNI GY -0.4
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2005
FU 8352 ALL
FYLD 6624 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
FU 8352 ALL
FYLD 6624 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 ST   HSST10X6X0.188           (AISC SECTIONS)
PASS   Eq. H1-1b            0.792         3
0.00            0.00         -45.20       10.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    100.002  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :    10.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.792(PASS)                 |
|          Loc  :   10.50   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -4.520E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.906E+00     Ayy:   3.298E+00     Cw:  0.000E+00              |
| Szz:   1.492E+01     Syy:   1.137E+01                                 |
| Izz:   7.460E+01     Iyy:   3.410E+01     Ix:  7.380E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        21.000                                   |
| 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     0.00     N/A      0.00      N/A        |
|                Slender        54.47     N/A     35.15    T.B4.1-12    |
| Flexure     :  Non-Compact    31.48    28.12    35.15    T.B4.1-12    |
|                Compact        54.47    60.76   143.12    T.B4.1-13    |
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   2.22E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   2.34E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.43E+02   0.000      Sec. E1       3     0.00 |
| Min Buck    0.00E+00   1.06E+02   0.000      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.11E-02    67.61   4.28E+03   9.02E+03   1.59E+02        |
| Min Buck    3.11E-02   100.00   3.15E+03   4.12E+03   1.18E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   4.74E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     8.61E+00   8.19E+01   0.105      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.32E-02     1.00     5.00    31.48   5.26E+01            |
| Local-Y     2.29E-02     1.00     5.00    54.47   9.10E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   4.12E+01   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   4.58E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       4.52E+01   6.21E+01   0.728      Eq. F7-1      3    10.50 |
| Minor       0.00E+00   4.38E+01   0.000      Eq. F7-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.90E+01   0.00E+00                                       |
| Minor       4.87E+01   0.00E+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       4.52E+01   5.70E+01   0.792      Eq. F7-2      3    10.50 |
| Minor       0.00E+00   3.05E+01   0.000      Eq. F7-3      3     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       6.34E+01   0.00E+00                                       |
| Minor       3.39E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.792      Eq. H1-1b     3    10.50             |
| Flexure Tens          0.792      Eq. H1-1b     3    10.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         5.70E+01   4.52E+01   1.06E+02                   |
|                      3.05E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         5.70E+01   4.52E+01   2.22E+02                   |
|                      3.05E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
48. PARAMETER 2
49. CODE AISC UNIFIED 2005
50. FU 8352 ALL
51. FYLD 6624 ALL
52. METHOD ASD
53. TRACK 2 ALL
54. CHECK CODE ALL
STEEL DESIGN
WARNING: For member#      1 the profile has been selected from HSS Rect/Round (non A1085)/Pipe
tables of AISC database. Weld type is considered to be Elect-resist-weld.
Thickness is already reduced from the table. Further reductions will not be done.
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 ST   HSST10X6X0.188           (AISC SECTIONS)
PASS   Eq. H1-1b            0.799         4
0.00            0.00         -30.32       10.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    100.002  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :    10.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.799(PASS)                 |
|          Loc  :   10.50   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -3.032E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.906E+00     Ayy:   3.298E+00     Cw:  0.000E+00              |
| Szz:   1.492E+01     Syy:   1.137E+01                                 |
| Izz:   7.460E+01     Iyy:   3.410E+01     Ix:  7.380E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        21.000                                   |
| 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     0.00     N/A      0.00      N/A        |
|                Slender        54.47     N/A     35.15    T.B4.1-12    |
| Flexure     :  Non-Compact    31.48    28.12    35.15    T.B4.1-12    |
|                Compact        54.47    60.76   143.12    T.B4.1-13    |
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   1.48E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.56E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   9.55E+01   0.000      Sec. E1       4     0.00 |
| Min Buck    0.00E+00   7.04E+01   0.000      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.11E-02    67.61   4.28E+03   9.02E+03   1.59E+02        |
| Min Buck    3.11E-02   100.00   3.15E+03   4.12E+03   1.18E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   3.15E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     5.78E+00   5.45E+01   0.106      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.32E-02     1.00     5.00    31.48   5.26E+01            |
| Local-Y     2.29E-02     1.00     5.00    54.47   9.10E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   2.74E+01   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   4.58E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       3.03E+01   4.13E+01   0.734      Eq. F7-1      4    10.50 |
| Minor       0.00E+00   2.92E+01   0.000      Eq. F7-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.90E+01   0.00E+00                                       |
| Minor       4.87E+01   0.00E+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       3.03E+01   3.79E+01   0.799      Eq. F7-2      4    10.50 |
| Minor       0.00E+00   2.03E+01   0.000      Eq. F7-3      4     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       6.34E+01   0.00E+00                                       |
| Minor       3.39E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.799      Eq. H1-1b     4    10.50             |
| Flexure Tens          0.799      Eq. H1-1b     4    10.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         3.79E+01   3.03E+01   7.04E+01                   |
|                      2.03E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         3.79E+01   3.03E+01   1.48E+02                   |
|                      2.03E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|