V. AISC 360-10 C Weak Axis Shear G.7

Verify the available shear strength along the weak axis of a singly symmetric 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.7, pp. G-15 - G-16

Details

From reference (2):

Verify the available shear strength and adequacy of a C9×20 ASTM A36 channel with end shears of 5.00 kips from dead load and 15.0 kips from live load in the weak direction.

Validation

Ultimate load:

V_{u} = 1.2 (5.0 kips) + 1.6 (15.0 kips) = 30.0 kips

Service load:

V_{a} = 5.0 kips + 15.0 kips = 20.0 kips

Area of the flanges for shear:

A_w = 2b_ft_f = 2(2.65)(0.413) = 2.19 in²

Section G2.1 of Reference 1 gives k_v = 1.2.

\frac{b_{f}}{t_{f}} = \frac{2.65}{0.413} = 6.42 < 1.10 \sqrt{\frac{k_{v} E}{F_{y}}} = 1.10 \sqrt{\frac{1.2 (29, 000)}{36}} = 34.2

Therefore, C_v = 1.0.

Nominal Shear Strength

V_{n} = 0.6 F_{y} A_{w} C_{v} = 0.6 (36) (2.19) (1.0) = 47.3 kips

(Eq. G2-1)

The available shear strength:

LRFD: $ϕ_{v} V_{n} = 0.90 (47.3) = 42.6 kips$

ASD: $V_{n} / Ω_{v} = \frac{47.3}{1.67} = 28.3 kips$

Results

Result Type	Reference	STAAD.Pro	Difference	Comments
ϕ_vV_n (kips) [LRFD]	42.6	42.6	none
V_n/Ω_v (kips) [ASD]	28.3	28.3	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 C Weak Axis Shear 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 C9X20
CONSTANTS
BETA 90 ALL
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -10
LOAD 2 LOADTYPE Live  TITLE LOAD CASE 2
MEMBER LOAD
1 CON GY -30
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
FYLD 36 ALL
FU 58 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FYLD 36 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   C9X20                    (AISC SECTIONS)
                           FAIL   Eq. H1-1b           11.619         3
                        0.00         -720.00           0.00       24.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     74.912  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :    24.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :    11.619(FAIL)                 |
|          Loc  :   24.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:  -3.000E+01               |
| Mx:   0.000E+00     My:  -7.200E+02     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.189E+00     Ayy:   4.032E+00     Cw:  3.933E+01              |
| Szz:   1.353E+01     Syy:   1.195E+00                                 |
| Izz:   6.090E+01     Iyy:   2.410E+00     Ix:  4.270E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   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     6.42     N/A     15.89    T.B4.1(a)-1  |
|                Non-Slender    18.25     N/A     42.29    T.B4.1(a)-5  |
| Flexure     :  Compact         6.42    10.79    28.38    T.B4.1(b)-10 |
|                Compact        18.25   106.72   161.78    T.B4.1(b)-15 |
      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   1.90E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   2.55E+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   1.88E+02   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   1.42E+02   0.000      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.70E+02   0.000      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    5.87E+00    14.90   3.56E+01   1.29E+03   2.09E+02        |
| Min Buck    5.87E+00    74.91   2.68E+01   5.10E+01   1.57E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    5.87E+00   3.22E+01   1.89E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     3.00E+01   4.26E+01   0.705      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   7.84E+01   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.19E+00     1.00     1.20     6.42   4.73E+01            |
| Local-Y     4.03E+00     1.00     5.00    18.25   8.71E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.48E+02   0.000      Eq. F2-1      3     0.00 |
| Minor      -7.20E+02   6.20E+01  11.619      Eq. F6-1      3    24.00 |
| Intermediate   Mn        My                                           |
| Major       6.08E+02   0.00E+00                                       |
| Minor       6.89E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.21E+02   0.000      Eq. F2-2      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.78E+02   0.00E+00    1.00    32.01   174.62    48.00    |
      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         11.619      Eq. H1-1b     3    24.00             |
| Flexure Tens         11.619      Eq. H1-1b     3    24.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         5.21E+02   0.00E+00   1.42E+02                   |
|                      6.20E+01  -7.20E+02   0.00E+00                   |
| Flexure Tens         5.21E+02   0.00E+00   1.90E+02                   |
|                      6.20E+01  -7.20E+02   0.00E+00                   |
|-----------------------------------------------------------------------|
    49. LOAD LIST 4
    50. PARAMETER 2
    51. CODE AISC UNIFIED 2010
    52. METHOD ASD
    53. FYLD 36 ALL
    54. FU 58 ALL
    55. TRACK 2 ALL
    56. CHECK CODE ALL
 STEEL DESIGN    
      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   C9X20                    (AISC SECTIONS)
                           FAIL   Eq. H1-1b           11.642         4
                        0.00         -480.00           0.00       24.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     74.912  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :    24.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :    11.642(FAIL)                 |
|          Loc  :   24.00   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:  -2.000E+01               |
| Mx:   0.000E+00     My:  -4.800E+02     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.189E+00     Ayy:   4.032E+00     Cw:  3.933E+01              |
| Szz:   1.353E+01     Syy:   1.195E+00                                 |
| Izz:   6.090E+01     Iyy:   2.410E+00     Ix:  4.270E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   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     6.42     N/A     15.89    T.B4.1(a)-1  |
|                Non-Slender    18.25     N/A     42.29    T.B4.1(a)-5  |
| Flexure     :  Compact         6.42    10.79    28.38    T.B4.1(b)-10 |
|                Compact        18.25   106.72   161.78    T.B4.1(b)-15 |
      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   1.27E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.70E+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   1.25E+02   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   9.42E+01   0.000      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.13E+02   0.000      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    5.87E+00    14.90   3.56E+01   1.29E+03   2.09E+02        |
| Min Buck    5.87E+00    74.91   2.68E+01   5.10E+01   1.57E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    5.87E+00   3.22E+01   1.89E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     2.00E+01   2.83E+01   0.706      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   5.22E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.19E+00     1.00     1.20     6.42   4.73E+01            |
| Local-Y     4.03E+00     1.00     5.00    18.25   8.71E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.64E+02   0.000      Eq. F2-1      4     0.00 |
| Minor      -4.80E+02   4.12E+01  11.642      Eq. F6-1      4    24.00 |
| Intermediate   Mn        My                                           |
| Major       6.08E+02   0.00E+00                                       |
| Minor       6.89E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   3.46E+02   0.000      Eq. F2-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       5.78E+02   0.00E+00    1.00    32.01   174.62    48.00    |
      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         11.642      Eq. H1-1b     4    24.00             |
| Flexure Tens         11.642      Eq. H1-1b     4    24.00             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         3.46E+02   0.00E+00   9.42E+01                   |
|                      4.12E+01  -4.80E+02   0.00E+00                   |
| Flexure Tens         3.46E+02   0.00E+00   1.27E+02                   |
|                      4.12E+01  -4.80E+02   0.00E+00                   |
|-----------------------------------------------------------------------|