STAAD.Pro Help

V. AISC 360-05 C Flex Mem F.2-1

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 F.2-1a, p.F-15

Details

From reference (2):

Select an ASTM A36 channel to serve as a roof edge beam with a simple span of 25 ft. Limit the live load deflection to L/360. The nominal loads are a uniform dead load of 0.23 kip/ft and a uniform live load of 0.69 kip/ft. The beam is continuously braced.

Validation

Ultimate moment:

w u = 1.2 ( 0.23  k/ft ) + 1.6 ( 0.69  k/ft ) = 1.38  k/ft
M u = 1.38 ( 25 ) 2 8 = 108  ft-k

Service moment:

w a = 0.23  k/ft + 0.69  k/ft = 0.92  k/ft
M a = 0.92 ( 25 ) 2 8 = 71.9  ft-k

Try a C15×33.9, which has a plastic section modulus, Zx = 50.8 in3.

All ASTM A36 grade C-shapes are compact. The member is continuously braced, so therefore the yielding limit state governs.

M n = M p = F y × Z x = 36 × 50.8 = 1,830  in-k = 152  ft-k

The available flexural strength:

LRFD: ϕ b M n = 0.90 ( 152 ) = 137  ft-k

ASD: M n / Ω b = 152 1.67 = 91.0  ft-k

Result Type Reference STAAD.Pro Difference Comments
ϕbMn (ft·k) [LRFD] 137 137 none  
Mnb (ft·k) [ASD] 91 91.3 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 C Flex Mem F.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 07-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 25 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 C15X33
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -0.23
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GY -0.69
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6 
LOAD COMB 4 COMBINATION LOAD CASE 4
1 1.0 2 1.0 
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
FLX 2 ALL
FYLD 5184 ALL
FU 8352 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
FLX 2 ALL
FYLD 5184 ALL
FU 8352 ALL
METHOD ASD
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   C15X33                   (AISC SECTIONS)
                           FAIL   Eq. H1-1b            2.548         3
                        0.00            0.00        -107.81       12.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    333.952  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :    12.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     2.548(FAIL)                 |
|          Loc  :   12.50   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:  -1.078E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.420E+00     Ayy:   6.000E+00     Cw:  3.555E+02              |
| Szz:   4.200E+01     Syy:   3.178E+00                                 |
| Izz:   3.150E+02     Iyy:   8.070E+00     Ix:  1.010E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| 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     5.23     N/A     15.89    T.B4.1-3     |
|                Non-Slender    34.25     N/A     42.29    T.B4.1-10    |
| Flexure     :  Compact         5.23    10.79    28.38    T.B4.1-1     |
|                Compact        34.25   106.72   161.78    T.B4.1-9     |
      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       0.00E+00   3.24E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   4.35E+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   2.79E+02   0.000      Sec. E1       3     0.00 |
| Min Buck    0.00E+00   2.03E+01   0.000      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   2.07E+02   0.000      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    6.94E-02    53.45   4.46E+03   1.44E+04   3.10E+02        |
| Min Buck    6.94E-02   333.95   3.24E+02   3.70E+02   2.25E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    6.94E-02   3.31E+03   2.30E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   8.59E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     1.72E+01   1.17E+02   0.148      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.07E-02     1.00     1.20     5.23   9.55E+01            |
| Local-Y     4.17E-02     1.00     5.00    34.25   1.30E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.08E+02   1.37E+02   0.786      Eq. F2-1      3    12.50 |
| Minor       0.00E+00   1.37E+01   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.52E+02   0.00E+00                                       |
| Minor       1.53E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.08E+02   4.23E+01   2.548      Eq. F2-3      3    12.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       4.70E+01   0.00E+00    1.00     3.74    14.49    25.00    |
      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          2.548      Eq. H1-1b     3    12.50             |
| Flexure Tens          2.548      Eq. H1-1b     3    12.50             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.23E+01   1.08E+02   2.03E+01                   |
|                      1.37E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         4.23E+01   1.08E+02   3.24E+02                   |
|                      1.37E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    49. LOAD LIST 4
    50. PARAMETER 2
    51. CODE AISC UNIFIED 2005
    52. FLX 2 ALL
    53. FYLD 5184 ALL
    54. FU 8352 ALL
    55. METHOD ASD
    56. TRACK 2 ALL
    57. CHECK CODE ALL
 STEEL DESIGN    
      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   C15X33                   (AISC SECTIONS)
                           FAIL   Eq. H1-1b            2.553         4
                        0.00            0.00         -71.88       12.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    333.952  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :    12.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     2.553(FAIL)                 |
|          Loc  :   12.50   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:  -7.188E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.420E+00     Ayy:   6.000E+00     Cw:  3.555E+02              |
| Szz:   4.200E+01     Syy:   3.178E+00                                 |
| Izz:   3.150E+02     Iyy:   8.070E+00     Ix:  1.010E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| 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     5.23     N/A     15.89    T.B4.1-3     |
|                Non-Slender    34.25     N/A     42.29    T.B4.1-10    |
| Flexure     :  Compact         5.23    10.79    28.38    T.B4.1-1     |
|                Compact        34.25   106.72   161.78    T.B4.1-9     |
      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       0.00E+00   2.16E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   2.90E+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   1.85E+02   0.000      Sec. E1       4     0.00 |
| Min Buck    0.00E+00   1.35E+01   0.000      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.38E+02   0.000      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    6.94E-02    53.45   4.46E+03   1.44E+04   3.10E+02        |
| Min Buck    6.94E-02   333.95   3.24E+02   3.70E+02   2.25E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    6.94E-02   3.31E+03   2.30E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   5.72E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     1.15E+01   7.76E+01   0.148      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     3.07E-02     1.00     1.20     5.23   9.55E+01            |
| Local-Y     4.17E-02     1.00     5.00    34.25   1.30E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       7.19E+01   9.13E+01   0.788      Eq. F2-1      4    12.50 |
| Minor       0.00E+00   9.14E+00   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.52E+02   0.00E+00                                       |
| Minor       1.53E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       7.19E+01   2.82E+01   2.553      Eq. F2-3      4    12.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       4.70E+01   0.00E+00    1.00     3.74    14.49    25.00    |
      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          2.553      Eq. H1-1b     4    12.50             |
| Flexure Tens          2.553      Eq. H1-1b     4    12.50             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.82E+01   7.19E+01   1.35E+01                   |
|                      9.14E+00   0.00E+00   0.00E+00                   |
| Flexure Tens         2.82E+01   7.19E+01   2.16E+02                   |
|                      9.14E+00   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|