# V. AISC 360-10 HSST D.4

Verify the tensile strength 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 D.4, pp. D-11 - D-13

## Details

From reference (2):

Verify the tensile strength of an HSS6×4×3/8, ASTM A500 Grade B, with a length of 30 ft. The member is carrying a dead load of 35 kips and a live load of 105 kips in tension. The end connection is a fillet welded 1/2-in.- thick single concentric gusset plate with a weld length of 16 in. Assume that the gusset plate and weld are satisfactory.

## Validation

Tensile Yielding

LRFD:

ASD:

Tensile Rupture

Determine the shear lag factor for the effective area:

 $Ae=AnU$ (Eq. D3-1)
where
 An = the net area; in this case allows for a 1/16-in gap in fit-up between the HSS and the gusset plate, $x¯$ = U = $1−x¯l=1−1.6016.0=0.90$

Nominal Tensile Rupture Strength

 (Eq D2-2)

The available tensile strength:

LRFD:

ASD:

Slenderness

$Lr=30×121.55=232$

## Results

Tensile yielding ϕtPn (kips) [LRFD] 256 256 none
Tensile rupture ϕtPn (kips) [LRFD] 227 226 negligible
Tensile yielding Pnt (kips) [ASD] 170 170 none
Tensile rupture Pnt (kips) [ASD] 151 151 none
Slenderness ratio 232 231.848 negligible

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 21-Jan-20
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 HSST6X4X0.375
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FX 35
2 FX 105
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2010
FU 8352 ALL
FYLD 6624 ALL
METHOD LRFD
TMAIN 300 ALL
NSF 0.936 ALL
SLF 0.9 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FU 8352 ALL
FYLD 6624 ALL
METHOD ASD
TMAIN 300 ALL
NSF 0.936 ALL
SLF 0.9 ALL
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)
PASS   Eq. H1-1a            0.927         3
210.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    231.848  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.927(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   2.100E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| 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:        30.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.94 SLF:    0.90 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-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       2.10E+02   2.56E+02   0.821      Eq. D2-1      3     0.00 |
| Rupture     2.10E+02   2.26E+02   0.927      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   4.93E+01   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   2.60E+01   0.000      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.29E-02   168.23   1.28E+03   1.46E+03   5.48E+01        |
| Min Buck    4.29E-02   231.85   6.72E+02   7.67E+02   2.89E+01        |
|-----------------------------------------------------------------------|
| 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     0.00E+00   8.59E+01   0.000      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       0.00E+00   4.11E+01   0.000      Eq. F7-1      3     0.00 |
| 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.    8
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          0.000      Eq. H1-1b     3     0.00             |
| Flexure Tens          0.927      Eq. H1-1a     3     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.11E+01   0.00E+00   2.60E+01                   |
|                      3.08E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         4.11E+01   0.00E+00   2.26E+02                   |
|                      3.08E+01   0.00E+00   2.10E+02                   |
|-----------------------------------------------------------------------|
51. PARAMETER 2
52. CODE AISC UNIFIED 2010
53. FU 8352 ALL
54. FYLD 6624 ALL
55. METHOD ASD
56. TMAIN 300 ALL
57. NSF 0.936 ALL
58. SLF 0.9 ALL
59. TRACK 2 ALL
60. 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.    9
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)
PASS   Eq. H1-1a            0.927         4
140.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    231.848  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.927(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.400E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| 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:        30.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.94 SLF:    0.90 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.   10
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       1.40E+02   1.70E+02   0.822      Eq. D2-1      4     0.00 |
| Rupture     1.40E+02   1.51E+02   0.927      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   3.28E+01   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   1.73E+01   0.000      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.29E-02   168.23   1.28E+03   1.46E+03   5.48E+01        |
| Min Buck    4.29E-02   231.85   6.72E+02   7.67E+02   2.89E+01        |
|-----------------------------------------------------------------------|
| 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     0.00E+00   5.71E+01   0.000      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       0.00E+00   2.73E+01   0.000      Eq. F7-1      4     0.00 |
| 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.   11
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          0.000      Eq. H1-1b     4     0.00             |
| Flexure Tens          0.927      Eq. H1-1a     4     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.73E+01   0.00E+00   1.73E+01                   |
|                      2.05E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         2.73E+01   0.00E+00   1.51E+02                   |
|                      2.05E+01   0.00E+00   1.40E+02                   |
|-----------------------------------------------------------------------|