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V. AISC 360-05 HSST Torsional Strength H.5A

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 H.5a, pp.H-12,13

Details

From reference (2):

Determine the available torsional strength of an ASTM A500 Gr. B HSS6×4×1/4.

Validation

h/t > b/t, so h/t governs.

ht=22.8<2.45EFy=2.4529,00046=61.5
Fcr=0.6Fy=0.6(46)=27.6 ksi(Eq. H3-3)

Nominal Torsional Strength

Tn=FcrC=27.6(10.1)=279 in⋅k(Eq. G2-1)

The available shear strength:

LRFD: ϕTTn=0.90(279)=251 in⋅k

ASD: Tn/ΩT=2791.67=167 in⋅k

Result Type Reference STAAD.Pro Difference Comments
ϕGTn (in·k) [LRFD] 251 251 none  
GnT (in·k) [ASD] 167 167 none  

STAAD.Pro Input File

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 29-Jun-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 4 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 HSST6X4X0.25
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
UNIT INCHES KIP
MEMBER LOAD
1 UMOM GX -1.5
UNIT FEET KIP
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 46 ALL
FU 58 ALL
TORSION 1 ALL
TND 3 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 46 ALL
FU 58 ALL
TORSION 1 ALL
TND 3 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   HSST6X4X0.25             (AISC SECTIONS)
                           PASS   Eq. H3-1             0.287         1
                        0.00            0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     29.875  L/C  :     1                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      1    Ratio     :     0.287(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H3-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   7.200E+01     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.538E+00     Ayy:   2.470E+00     Cw:  0.000E+00              |
| Szz:   6.967E+00     Syy:   5.550E+00                                 |
| Izz:   2.090E+01     Iyy:   1.110E+01     Ix:  2.360E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          46.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        48.000                                   |
| 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        |
|                Non-Slender    22.75     N/A     35.15    T.B4.1-12    |
| Flexure     :  Compact        14.17    28.12    35.15    T.B4.1-12    |
|                Compact        22.75    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  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   1.78E+02   0.000      Eq. D2-1      1     0.00 |
| Rupture     0.00E+00   1.87E+02   0.000      Eq. D2-2      1     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.72E+02   0.000      Sec. E1       1     0.00 |
| Min Buck    0.00E+00   1.68E+02   0.000      Eq. E3-1      1     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.30E+00    21.77   4.46E+01   6.04E+02   1.92E+02        |
| Min Buck    4.30E+00    29.88   4.33E+01   3.21E+02   1.86E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   3.82E+01   0.000      Eq. G2-1      1     0.00 |
| Local-Y     0.00E+00   6.14E+01   0.000      Eq. G2-1      1     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.54E+00     1.00     5.00    14.17   4.25E+01            |
| Local-Y     2.47E+00     1.00     5.00    22.75   6.82E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             7.20E+01   2.51E+02   0.287      Eq. H3-1      1     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.76E+01   2.79E+02                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.53E+02   0.000      Eq. F7-1      1     0.00 |
| Minor       0.00E+00   2.67E+02   0.000      Eq. F7-1      1     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.92E+02   0.00E+00                                       |
| Minor       2.97E+02   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    5
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H1-1b     1     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     1     0.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         3.53E+02   0.00E+00   1.68E+02                   |
|                      2.67E+02   0.00E+00   0.00E+00                   |
| Flexure Tens         3.53E+02   0.00E+00   1.78E+02                   |
|                      2.67E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP TORSION SHEAR INTERACTION                 |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flx Tor Comp Shr      0.082      Eq. H3-6      1     0.00             |
| Flx Tor Tens Shr      0.082      Eq. H3-6      1     0.00             |
| Intermediate         Mcx /      Mcy /      Mrx /      Mry /           |
|                      Vcx /      Vcy /      Vrx /      Vry /           |
|                      Tc         Tr         Pc         Pr              |
| Flx Tor Comp Shr     3.53E+02   2.67E+02   0.00E+00   0.00E+00        |
|                      3.82E+01   6.14E+01   0.00E+00   0.00E+00        |
|                      2.51E+02   7.20E+01   1.68E+02   0.00E+00        |
| Flx Tor Tens Shr     3.53E+02   2.67E+02   0.00E+00   0.00E+00        |
|                      3.82E+01   6.14E+01   0.00E+00   0.00E+00        |
|                      2.51E+02   7.20E+01   1.78E+02   0.00E+00        |
|-----------------------------------------------------------------------|
|---------------------------------------------------------------------------------|
| AISC DESIGN GUIDE-9                                                             |
|---------------------------------------------------------------------------------|
| Member:     1 Section:       HSST6X4X0.25             AISC                      |
| End Condition:  Fix-Free                                                        |
| Shear Capacity :  2.4840E+01  Shear Criteria : DG9 Eq. 4.13                     |
| Normal Capacity:  4.1400E+01  Normal Criteria: DG9 Eq. 4.12                     |
|---------------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    6
| Stress Point   Shear     Ratio     LC/ | Stress Point   Normal    Ratio     LC/ |
|                                   Sect |                                   Sect |
| Mid Flange:   0.00000E+00 0.0000     1 | Flange Edge:  0.00000E+00 0.0000     1 |
|                                  0.000 |                                  0.000 |
| FL/WB Junc:   6.43777E+00 0.2592     1 |                                        |
|                                  0.000 |                                        |
| Mid-Web:      6.43777E+00 0.2592     1 |                                        |
|                                  0.000 |                                        |
|---------------------------------------------------------------------------------|
| Pure Torsion Shear Stress     Criteria: DG9 T4.1                                |
| Flange Edge:  6.43777E+00     Web Edge:     6.43777E+00                         |
|---------------------------------------------------------------------------------|
| Pure Flexure Shear Stress     Criteria: DG9 Eq. 4.6                             |
| Flange Edge:  0.00000E+00  FL/WB Junc:   0.00000E+00  Mid-Web:      0.00000E+00 |
|---------------------------------------------------------------------------------|
| Direct Axial Bending Stress   Criteria: DG9 Eq. 4.5                             |
| Flange Edge:  0.00000E+00                                                       |
|---------------------------------------------------------------------------------|
    43. PARAMETER 2
    44. CODE AISC UNIFIED 2005
    45. METHOD ASD
    46. FYLD 46 ALL
    47. FU 58 ALL
    48. TORSION 1 ALL
    49. TND 3 ALL
    50. TRACK 2 ALL
    51. 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.    7
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   HSST6X4X0.25             (AISC SECTIONS)
                           PASS   Eq. H3-1             0.431         1
                        0.00            0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     29.875  L/C  :     1                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      1    Ratio     :     0.431(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H3-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   7.200E+01     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.538E+00     Ayy:   2.470E+00     Cw:  0.000E+00              |
| Szz:   6.967E+00     Syy:   5.550E+00                                 |
| Izz:   2.090E+01     Iyy:   1.110E+01     Ix:  2.360E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          46.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        48.000                                   |
| 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        |
|                Non-Slender    22.75     N/A     35.15    T.B4.1-12    |
| Flexure     :  Compact        14.17    28.12    35.15    T.B4.1-12    |
|                Compact        22.75    60.76   143.12    T.B4.1-13    |
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   1.18E+02   0.000      Eq. D2-1      1     0.00 |
| Rupture     0.00E+00   1.25E+02   0.000      Eq. D2-2      1     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.15E+02   0.000      Sec. E1       1     0.00 |
| Min Buck    0.00E+00   1.12E+02   0.000      Eq. E3-1      1     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.30E+00    21.77   4.46E+01   6.04E+02   1.92E+02        |
| Min Buck    4.30E+00    29.88   4.33E+01   3.21E+02   1.86E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.54E+01   0.000      Eq. G2-1      1     0.00 |
| Local-Y     0.00E+00   4.08E+01   0.000      Eq. G2-1      1     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.54E+00     1.00     5.00    14.17   4.25E+01            |
| Local-Y     2.47E+00     1.00     5.00    22.75   6.82E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             7.20E+01   1.67E+02   0.431      Eq. H3-1      1     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.76E+01   2.79E+02                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   2.35E+02   0.000      Eq. F7-1      1     0.00 |
| Minor       0.00E+00   1.78E+02   0.000      Eq. F7-1      1     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.92E+02   0.00E+00                                       |
| Minor       2.97E+02   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H1-1b     1     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     1     0.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.35E+02   0.00E+00   1.12E+02                   |
|                      1.78E+02   0.00E+00   0.00E+00                   |
| Flexure Tens         2.35E+02   0.00E+00   1.18E+02                   |
|                      1.78E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP TORSION SHEAR INTERACTION                 |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flx Tor Comp Shr      0.186      Eq. H3-6      1     0.00             |
| Flx Tor Tens Shr      0.186      Eq. H3-6      1     0.00             |
| Intermediate         Mcx /      Mcy /      Mrx /      Mry /           |
|                      Vcx /      Vcy /      Vrx /      Vry /           |
|                      Tc         Tr         Pc         Pr              |
| Flx Tor Comp Shr     2.35E+02   1.78E+02   0.00E+00   0.00E+00        |
|                      2.54E+01   4.08E+01   0.00E+00   0.00E+00        |
|                      1.67E+02   7.20E+01   1.12E+02   0.00E+00        |
| Flx Tor Tens Shr     2.35E+02   1.78E+02   0.00E+00   0.00E+00        |
|                      2.54E+01   4.08E+01   0.00E+00   0.00E+00        |
|                      1.67E+02   7.20E+01   1.18E+02   0.00E+00        |
|-----------------------------------------------------------------------|
|---------------------------------------------------------------------------------|
| AISC DESIGN GUIDE-9                                                             |
|---------------------------------------------------------------------------------|
| Member:     1 Section:       HSST6X4X0.25             AISC                      |
| End Condition:  Fix-Free                                                        |
| Shear Capacity :  1.6527E+01  Shear Criteria : DG9 Eq. 4.18                     |
| Normal Capacity:  2.7545E+01  Normal Criteria: DG9 Eq. 4.17                     |
|---------------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   10
| Stress Point   Shear     Ratio     LC/ | Stress Point   Normal    Ratio     LC/ |
|                                   Sect |                                   Sect |
| Mid Flange:   0.00000E+00 0.0000     1 | Flange Edge:  0.00000E+00 0.0000     1 |
|                                  0.000 |                                  0.000 |
| FL/WB Junc:   6.43777E+00 0.3895     1 |                                        |
|                                  0.000 |                                        |
| Mid-Web:      6.43777E+00 0.3895     1 |                                        |
|                                  0.000 |                                        |
|---------------------------------------------------------------------------------|
| Pure Torsion Shear Stress     Criteria: DG9 T4.1                                |
| Flange Edge:  6.43777E+00     Web Edge:     6.43777E+00                         |
|---------------------------------------------------------------------------------|
| Pure Flexure Shear Stress     Criteria: DG9 Eq. 4.6                             |
| Flange Edge:  0.00000E+00  FL/WB Junc:   0.00000E+00  Mid-Web:      0.00000E+00 |
|---------------------------------------------------------------------------------|
| Direct Axial Bending Stress   Criteria: DG9 Eq. 4.5                             |
| Flange Edge:  0.00000E+00                                                       |
|---------------------------------------------------------------------------------|