V. AISC 360-10 HSSP Shear Capacity G.5

Verify the available shear strength along the strong axis of a round HSS section per the LRFD and ASD methods of the AISD 360-10 code.

References

American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example G.5, pp. G-11 - G-12

Details

From reference (2):

Verify the available shear strength and adequacy of a round HSS16.000×0.375 ASTM A500 Grade B member spanning 32 ft with end shears of 30.0 kips from dead load and 90.0 kips from live load.

Validation

Ultimate load:

V_{u} = 1.2 (30.0 kips) + 1.6 (90.0 kips) = 180 kips

Service load:

V_{a} = 30.0 kips + 90.0 kips = 120 kips

Shear Buckling Stress

F_{c r} = {}_{\max}{| \begin{array}{l} \frac{\begin{matrix} 1.60 E \end{matrix}}{\sqrt{\frac{L_{v}}{D}} {(\frac{D}{t})}^{5 / 4}} = \frac{\begin{matrix} 1.60 (29, 000) \end{matrix}}{\sqrt{\frac{192}{16.0}} {(\frac{16.0}{0.349})}^{5 / 4}} = 112 ksi \\ \frac{0.78 E}{{(\frac{D}{t})}^{3 / 2}} = \frac{0.78 (29, 000)}{{(\frac{16.0}{0.349})}^{3 / 2}} = 72.9 ksi \end{array}}

The maximum permitted value is $F_{c r} \leq 0.6 F_{y} = 0.6 (42) = 25.2 ksi$ (governs).

Nominal Shear Strength

V_{n} = F_{c r} A_{g} / 2 = (25.2) (17.2) / 2 = 217 kips

(Eq. G2-1)

The available shear strength:

LRFD: $ϕ_{v} V_{n} = 0.90 (217) = 195 kips$

ASD: $V_{n} / Ω_{v} = \frac{217}{1.67} = 130 kips$

Results

Result Type	Reference	STAAD.Pro	Difference	Comments
ϕ_vV_n (kips) [LRFD]	195	195	none
V_n/Ω_v (kips) [ASD]	130	130	none

STAAD.Pro Input

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 20-May-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 32 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 HSSP16X0.375
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
MEMBER LOAD
UNIT INCHES KIP
1 UNI GY -0.15625
UNIT FEET KIP
LOAD 2 LOADTYPE Live  TITLE LOAD CASE 2
MEMBER LOAD
UNIT INCHES KIP
1 UNI GY -0.46875
UNIT FEET KIP
LOAD COMB 3 LRFD LOAD
1 1.2 2 1.6 
LOAD COMB 4 ASD LOAD
1 1.0 2 1.0 
PERFORM ANALYSIS
UNIT INCHES KIP
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FYLD 42 ALL
FU 58 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FYLD 42 ALL
FU 58 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
 *     1 ST   HSSP16X0.375             (AISC SECTIONS)
                           FAIL   Eq. H1-1b            5.347         3
                        0.00            0.00      -17280.00      192.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     69.439  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :   192.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     5.347(FAIL)                 |
|          Loc  :  192.00   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:  -1.728E+04               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.728E+00     Ayy:   8.728E+00     Cw:  0.000E+00              |
| Szz:   6.575E+01     Syy:   6.575E+01                                 |
| Izz:   5.260E+02     Iyy:   5.260E+02     Ix:  1.052E+03              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          42.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       384.000                                   |
| 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    45.85     N/A     75.95    T.B4.1(a)-9  |
|                Non-Slender    45.85     N/A     75.95    T.B4.1(a)-9  |
| Flexure     :  Compact        45.85    48.33   214.05    T.B4.1(b)-20 |
|                Compact        45.85    48.33   214.05    T.B4.1(b)-20 |
      STAAD SPACE                                              -- PAGE NO.    4
                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   6.50E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   7.48E+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   4.84E+02   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   4.84E+02   0.000      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.72E+01    69.44   3.12E+01   5.94E+01   5.37E+02        |
| Min Buck    1.72E+01    69.44   3.12E+01   5.94E+01   5.37E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.95E+02   0.000      Eq. G6-1      3     0.00 |
| Local-Y     1.80E+02   1.95E+02   0.923      Eq. G6-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.72E+01     0.00     0.00     0.00   2.17E+02            |
| Local-Y     1.72E+01     0.00     0.00     0.00   2.17E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   2.97E+03   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.52E+01   3.30E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.73E+04   3.23E+03   5.347      Eq. F8-1      3   192.00 |
| Minor       0.00E+00   3.23E+03   0.000      Eq. F8-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.59E+03   0.00E+00                                       |
| Minor       3.59E+03   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    5
                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          5.347      Eq. H1-1b     3   192.00             |
| Flexure Tens          5.347      Eq. H1-1b     3   192.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         3.23E+03   1.73E+04   4.84E+02                   |
|                      3.23E+03   0.00E+00   0.00E+00                   |
| Flexure Tens         3.23E+03   1.73E+04   6.50E+02                   |
|                      3.23E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    52. LOAD LIST 4
    53. PARAMETER 2
    54. CODE AISC UNIFIED 2010
    55. METHOD ASD
    56. FYLD 42 ALL
    57. FU 58 ALL
    58. TRACK 2 ALL
    59. 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  INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
 *     1 ST   HSSP16X0.375             (AISC SECTIONS)
                           FAIL   Eq. H1-1b            5.357         4
                        0.00            0.00      -11520.00      192.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     69.439  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :   192.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     5.357(FAIL)                 |
|          Loc  :  192.00   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:  -1.152E+04               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.728E+00     Ayy:   8.728E+00     Cw:  0.000E+00              |
| Szz:   6.575E+01     Syy:   6.575E+01                                 |
| Izz:   5.260E+02     Iyy:   5.260E+02     Ix:  1.052E+03              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          42.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       384.000                                   |
| 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    45.85     N/A     75.95    T.B4.1(a)-9  |
|                Non-Slender    45.85     N/A     75.95    T.B4.1(a)-9  |
| Flexure     :  Compact        45.85    48.33   214.05    T.B4.1(b)-20 |
|                Compact        45.85    48.33   214.05    T.B4.1(b)-20 |
      STAAD SPACE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   4.33E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   4.99E+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   3.22E+02   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   3.22E+02   0.000      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.72E+01    69.44   3.12E+01   5.94E+01   5.37E+02        |
| Min Buck    1.72E+01    69.44   3.12E+01   5.94E+01   5.37E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.30E+02   0.000      Eq. G6-1      4     0.00 |
| Local-Y     1.20E+02   1.30E+02   0.925      Eq. G6-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.72E+01     0.00     0.00     0.00   2.17E+02            |
| Local-Y     1.72E+01     0.00     0.00     0.00   2.17E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.98E+03   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.52E+01   3.30E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.15E+04   2.15E+03   5.357      Eq. F8-1      4   192.00 |
| Minor       0.00E+00   2.15E+03   0.000      Eq. F8-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.59E+03   0.00E+00                                       |
| Minor       3.59E+03   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          5.357      Eq. H1-1b     4   192.00             |
| Flexure Tens          5.357      Eq. H1-1b     4   192.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.15E+03   1.15E+04   3.22E+02                   |
|                      2.15E+03   0.00E+00   0.00E+00                   |
| Flexure Tens         2.15E+03   1.15E+04   4.33E+02                   |
|                      2.15E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|