# V. AISC 360-10 HSST Shear Capacity G.4

Verify the available shear strength along the strong axis of a rectangular HSS section per the LRFD and ASD methods of the AISD 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 G.4, pp. G-9 - G-10

## Details

From reference (2):

Determine the available shear strength and adequacy of an HSS6×4×3/8 ASTM A500 Grade B member with end shears of 11.0 kips from dead load and 33.0 kips from live load. The beam is oriented with the shear parallel to the 6 in. dimension.

## Validation

Area of the web for shear:

Note: The corner radius is taken as 1.5× the design wall thickness per Section B4.1b of Reference 1.

h = H - 3t = 6.0 - 3× 0.349 = 4.95 in

Section G5 of Reference 1 gives kv = 5.

Aw = 2ht = 2(4.95)(0.349) = 3.46 in2

$htw=4.950.349=14.2<1.10kvEFy=1.105(29,000)46=61.8$

Therefore, Cv = 1.0.

Nominal Shear Strength

 (Eq. G2-1)

The available shear strength:

LRFD:

ASD:

## Results

ϕvVn (kips) [LRFD] 86.0 85.9 negligible
Vnv (kips) [ASD] 57.2 57.1 negligible

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-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 HSST6X4X0.375
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
1 CON GY -22
1 CON GY -66
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
FYLD 6624 ALL
FU 8352 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FYLD 6624 ALL
FU 8352 ALL
METHOD ASD
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   HSST6X4X0.375            (AISC SECTIONS)
FAIL   Eq. H1-1b            3.215         3
0.00            0.00        -132.00        2.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     30.913  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     2.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     3.215(FAIL)                 |
|          Loc  :    2.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   6.600E+01     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -1.320E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.061E+00     Ayy:   3.457E+00     Cw:  0.000E+00              |
| Szz:   9.433E+00     Syy:   7.450E+00                                 |
| Izz:   2.830E+01     Iyy:   1.490E+01     Ix:  3.280E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         4.000                                   |
| 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    14.19     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact         8.46    28.12    35.15    T.B4.1(b)-17 |
|                Compact        14.19    60.76   143.12    T.B4.1(b)-19 |
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       0.00E+00   2.56E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   2.69E+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   2.47E+02   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   2.40E+02   0.000      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.29E-02    22.43   6.40E+03   8.19E+04   2.75E+02        |
| Min Buck    4.29E-02    30.91   6.21E+03   4.31E+04   2.67E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   5.12E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     6.60E+01   8.59E+01   0.769      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.43E-02     1.00     5.00     8.46   5.69E+01            |
| Local-Y     2.40E-02     1.00     5.00    14.19   9.54E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   2.94E+01   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   3.27E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.32E+02   4.11E+01   3.215      Eq. F7-1      3     2.00 |
| Minor       0.00E+00   3.08E+01   0.000      Eq. F7-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.56E+01   0.00E+00                                       |
| Minor       3.43E+01   0.00E+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          3.215      Eq. H1-1b     3     2.00             |
| Flexure Tens          3.215      Eq. H1-1b     3     2.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.11E+01   1.32E+02   2.40E+02                   |
|                      3.08E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         4.11E+01   1.32E+02   2.56E+02                   |
|                      3.08E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
48. PARAMETER 2
49. CODE AISC UNIFIED 2010
50. FYLD 6624 ALL
51. FU 8352 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-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
*     1 ST   HSST6X4X0.375            (AISC SECTIONS)
FAIL   Eq. H1-1b            3.222         4
0.00            0.00         -88.00        2.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     30.913  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     2.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     3.222(FAIL)                 |
|          Loc  :    2.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   4.400E+01     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -8.800E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.061E+00     Ayy:   3.457E+00     Cw:  0.000E+00              |
| Szz:   9.433E+00     Syy:   7.450E+00                                 |
| Izz:   2.830E+01     Iyy:   1.490E+01     Ix:  3.280E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         4.000                                   |
| 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    14.19     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact         8.46    28.12    35.15    T.B4.1(b)-17 |
|                Compact        14.19    60.76   143.12    T.B4.1(b)-19 |
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       0.00E+00   1.70E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.79E+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   1.65E+02   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   1.60E+02   0.000      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.29E-02    22.43   6.40E+03   8.19E+04   2.75E+02        |
| Min Buck    4.29E-02    30.91   6.21E+03   4.31E+04   2.67E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   3.41E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     4.40E+01   5.71E+01   0.770      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.43E-02     1.00     5.00     8.46   5.69E+01            |
| Local-Y     2.40E-02     1.00     5.00    14.19   9.54E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.96E+01   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   3.27E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       8.80E+01   2.73E+01   3.222      Eq. F7-1      4     2.00 |
| Minor       0.00E+00   2.05E+01   0.000      Eq. F7-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.56E+01   0.00E+00                                       |
| Minor       3.43E+01   0.00E+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          3.222      Eq. H1-1b     4     2.00             |
| Flexure Tens          3.222      Eq. H1-1b     4     2.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.73E+01   8.80E+01   1.60E+02                   |
|                      2.05E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         2.73E+01   8.80E+01   1.70E+02                   |
|                      2.05E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|