V. AISC 360-05 HSST D.4

References

Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
Design Examples, Version 13.0, American Institute of Steel Construction, 2005, Example D.4, pp.D-8,9

Details

From reference (2):

Verify, by LRFD and ASD, the 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. Assume the end connection is fillet welded to a 1/2 in. thick single concentric gusset plate and has a length of 16 in.

Validation

Ultimate load:

P_{u} = 1.2 (35 kips) + 1.6 (105 kips) = 210 kips

Service load:

P_{a} = 35 kips + 105 = 140 kips

Tensile Yielding

LRFD: $ϕ_{t} P_{n} = ϕ_{t} A_{g} F_{y} = 0.9 (6.18) (46) = 256 kips$

ASD: $P_{n} / Ω_{c} = \frac{A_{g} F_{y}}{Ω_{c}} = \frac{(6.18) (46)}{1.67} = 170 kips$

Tensile Rupture

Determine the shear lag factor for the effective area:

A_{e} = A_{n} U

(Eq. D3-1)

where

A_n	=	the net area; in this case allows for a 1/16-in gap in fit-up between the HSS and the gusset plate, $= A_{g} - 2 (t_{p} + 1 / 16) t = 6.18 - 2 (0.5 + 1 / 16) 0.349 = 5.79 {in}^{2}$
$\bar{x}$	=	$\frac{B^{2} + 2 B H}{4 (B + H)} = \frac{{(4.0)}^{2} + 2 (4.0) (6.0)}{4 (4.0 + 6.0)} = 1.60 in$
U	=	$1 - \frac{\bar{x}}{l} = 1 - \frac{1.60}{16.0} = 0.90$

A_{e} = 5.79 (0.90) = 5.21 {in}^{2}

Nominal Tensile Rupture Strength

P_{n} = F_{u} A_{e} = 58 (5.21) = 302 kips

(Eq D2-2)

The available tensile strength:

LRFD: $ϕ_{t} P_{n} = 0.75 (302) = 227 kips$

ASD: $P_{n} / Ω_{t} = \frac{302}{2.00} = 151 kips$

Slenderness

\frac{L}{r} = \frac{30 \times 12}{1.55} = 232

Result Type	Reference	STAAD.Pro	Difference
Tensile yielding ϕ_tP_n (kips) [LRFD]	256	256	none
Tensile rupture ϕ_tP_n (kips) [LRFD]	227	226	negligible
Tensile yielding P_n/Ω_t (kips) [ASD]	170	170	none
Tensile rupture P_n/Ω_t (kips) [ASD]	151	151	none
Slenderness ratio	232	231.848	negligible

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 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
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
JOINT LOAD
2 FX 35
LOAD 2 LOADTYPE Live  TITLE LOAD CASE 2
JOINT LOAD
2 FX 105
LOAD COMB 3 LRFD
1 1.2 2 1.6 
LOAD COMB 4 ASD
1 1.0 2 1.0 
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
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
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
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 Output

                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          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.B4.1-12    |
| Flexure     :  Compact         8.46    28.12    35.15    T.B4.1-12    |
|                Compact        14.19    60.76   143.12    T.B4.1-13    |
      STAAD SPACE                                              -- PAGE NO.    7
                       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       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      Sec. E1       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-360-05-LRFD)   v3.3a
                       ********************************************
 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                   |
|-----------------------------------------------------------------------|
    50. LOAD LIST 4
    51. PARAMETER 2
    52. CODE AISC UNIFIED 2005
    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-360-05-ASD)   v3.3a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          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.B4.1-12    |
| Flexure     :  Compact         8.46    28.12    35.15    T.B4.1-12    |
|                Compact        14.19    60.76   143.12    T.B4.1-13    |
      STAAD SPACE                                              -- PAGE NO.   10
                       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       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      Sec. E1       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-360-05-ASD)   v3.3a
                       ********************************************
 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                   |
|-----------------------------------------------------------------------|