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V. AISC 360-05 C Weak Axis Shear G.7

References

  1. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
  2. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, Example G.7, p.G-12

Details

From reference (2):

Verify the strength of a C9×20 ASTM A36 channel with end shears of 5 kips from dead load and 15 kips from live load in the weak direction.

Validation

Ultimate load:

Vu=1.2(5.0 kips)+1.6(15.0 kips)=30.0 kips

Service load:

Va=5.0 kips+15.0 kips=20.0 kips

Area of the flanges for shear:

Aw = 2bftf = 2(2.65)(0.413) = 2.19 in2

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

bftf=2.650.413=6.42<1.10kvEFy=1.101.2(29,000)36=34.2

Therefore, Cv = 1.0.

Nominal Shear Strength

Vn=0.6FyAwCv=0.6(36)(2.19)(1.0)=47.3 kips(Eq. G2-1)

The available shear strength:

LRFD: ϕvVn=0.90(47.3)=42.6 kips

ASD: Vn/Ωv=47.31.67=28.3 kips

Result Type Reference STAAD.Pro Difference Comments
ϕvVn (kips) [LRFD] 42.6 42.6 none  
Vnv (kips) [ASD] 28.3 28.3 none  

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 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 2005
FYLD 36 ALL
FU 58 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 36 ALL
FU 58 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  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.B4.1-3     |
|                Non-Slender    18.25     N/A     42.29    T.B4.1-10    |
| Flexure     :  Compact         6.42    10.79    28.38    T.B4.1-1     |
|                Compact        18.25   106.72   161.78    T.B4.1-9     |
      STAAD SPACE                                              -- PAGE NO.    4
                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
                       ********************************************
 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      Sec. E1       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-360-05-LRFD)   v3.3a
                       ********************************************
 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 2005
    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-360-05-ASD)   v3.3a
                       ********************************************
 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.B4.1-3     |
|                Non-Slender    18.25     N/A     42.29    T.B4.1-10    |
| Flexure     :  Compact         6.42    10.79    28.38    T.B4.1-1     |
|                Compact        18.25   106.72   161.78    T.B4.1-9     |
      STAAD SPACE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
                       ********************************************
 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      Sec. E1       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-360-05-ASD)   v3.3a
                       ********************************************
 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                   |
|-----------------------------------------------------------------------|