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V. AISC 360-05 Bending

To verify the flexural member strength in strong-axis bending of an I section for both LRFD and ASD methods per the AISC 360-05 code.

References

  1. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, page F-6. Example F.1-1a
  2. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005

Details

Verify the Flexural Member Strength in Strong- Axis Bending by both LRFD and ASD method with ASTM A992 W18X50 beam with a simple span of 35 feet. The nominal loads are a uniform dead load of 0.45 kip/ft and a uniform live load of 0.75 kip/ft. Assuming the beam is continuously braced.

Validation

ASTM A992: Fy = 50 ksi, Fu = 65 ksi

Calculate the required flexural strength:

LRFD

wu = 1.2(0.450 kip/ft) + 1.6(0.750 kip/ft) = 1.74 kip/ft

M u = 1.74 kip/ft ( 35.0 ft 2 ) 8 = 266 kip⋅ft

ASD

wa = 0.450 kip/ft + 0.750 kip/ft = 1.20 kip/ft

M a = 1.20 kip/ft ( 35.0 ft 2 ) 8 = 184 kip⋅ft

Per the User Note in section F-2 of ref 2 (p.16.1-47), the W18X50 section is compact. Since the beam is continuously braced and compact, only the yielding limit state applies.

Tip: Per Table 3-2 of ref. 2 (p.3-17), the W18X50 is not the most efficient shape for this individual beam. This example follows that given in ref 1. STAAD.Pro will select a lighter beam if the member selection command is used.

LRFD

ϕbMn = ϕbMpx = 0.9× (101 in3 × 50 ksi)(1 ft /12 in) = 379 ft·kip > 266 ft·kip

ASD

Mnb = Mpxb = (101 in3 × 50 ksi)(1 ft /12 in) / 1.67 = 252 ft·kip > 180 ft·kip

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
ϕbMn (kips) [LRFD] 379 379 none  
Mnb (kips) [ASD] 252 252 none  

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2005\AISC 360-05 Bending.STD is typically installed with the program.

STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 27-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 35 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
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W18X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MZ
LOAD 1 DEAD LOAD
MEMBER LOAD
1 UNI Y -0.45
LOAD 2 LIVE LOAD
MEMBER LOAD
1 UNI Y -0.75
LOAD COMB 3 SERVICE LOAD
1 1.0 2 1.0 
LOAD COMB 4 ULTIMATE LOAD
1 1.2 2 1.6 
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 7200 ALL
FU 9360 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 7200 ALL
FU 9360 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       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   W18X50                   (AISC SECTIONS)
                           FAIL   Eq. H1-1b            3.331         3
                        0.00            0.00        -183.75       17.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    254.294  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     3.331(FAIL)                 |
|          Loc  :   17.50   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:  -1.838E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.550E+00     Ayy:   6.390E+00     Cw:  3.046E+03              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   8.000E+02     Iyy:   4.010E+01     Ix:  1.240E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        35.000                                   |
| 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     6.58     N/A     13.49    T.B4.1-3     |
|                Slender        45.23     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         6.58     9.15    24.08    T.B4.1-1     |
|                Compact        45.23    90.55   137.27    T.B4.1-9     |
      STAAD PLANE                                              -- PAGE NO.    4
                       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   4.40E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   4.78E+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   3.39E+02   0.000      Sec. E1       3     0.00 |
| Min Buck    0.00E+00   3.42E+01   0.000      Eq. E7-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.73E+02   0.000      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    9.88E-02    56.93   5.54E+03   1.27E+04   5.65E+02        |
| Min Buck    1.02E-01   254.29   5.59E+02   6.37E+02   5.71E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.02E-01   2.82E+03   2.88E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.54E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     2.10E+01   1.28E+02   0.164      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.94E-02     1.00     1.20     6.58   2.56E+02            |
| Local-Y     4.44E-02     1.00     0.00    45.23   1.92E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.84E+02   2.52E+02   0.729      Eq. F2-1      3    17.50 |
| Minor       0.00E+00   4.14E+01   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.21E+02   0.00E+00                                       |
| Minor       6.92E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.84E+02   5.52E+01   3.331      Eq. F2-3      3    17.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       9.21E+01   0.00E+00    1.00     5.83    16.97    35.00    |
      STAAD PLANE                                              -- PAGE NO.    5
                       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          3.331      Eq. H1-1b     3    17.50             |
| Flexure Tens          3.331      Eq. H1-1b     3    17.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         5.52E+01   1.84E+02   3.42E+01                   |
|                      4.14E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         5.52E+01   1.84E+02   4.40E+02                   |
|                      4.14E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    45. LOAD LIST 4
    46. PARAMETER 2
    47. CODE AISC UNIFIED 2005
    48. METHOD LRFD
    49. FYLD 7200 ALL
    50. FU 9360 ALL
    51. TRACK 2 ALL
    52. CHECK CODE ALL
 STEEL DESIGN    
      STAAD PLANE                                              -- PAGE NO.    6
                       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   W18X50                   (AISC SECTIONS)
                           FAIL   Eq. H1-1b            3.213         4
                        0.00            0.00        -266.44       17.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    254.294  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     3.213(FAIL)                 |
|          Loc  :   17.50   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:  -2.664E+02               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   8.550E+00     Ayy:   6.390E+00     Cw:  3.046E+03              |
| Szz:   0.000E+00     Syy:   0.000E+00                                 |
| Izz:   8.000E+02     Iyy:   4.010E+01     Ix:  1.240E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        35.000                                   |
| 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     6.58     N/A     13.49    T.B4.1-3     |
|                Slender        45.23     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         6.58     9.15    24.08    T.B4.1-1     |
|                Compact        45.23    90.55   137.27    T.B4.1-9     |
      STAAD PLANE                                              -- 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   6.61E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   7.17E+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   5.09E+02   0.000      Sec. E1       4     0.00 |
| Min Buck    0.00E+00   5.14E+01   0.000      Eq. E7-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   2.59E+02   0.000      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    9.88E-02    56.93   5.54E+03   1.27E+04   5.65E+02        |
| Min Buck    1.02E-01   254.29   5.59E+02   6.37E+02   5.71E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.02E-01   2.82E+03   2.88E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.31E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     3.05E+01   1.92E+02   0.159      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.94E-02     1.00     1.20     6.58   2.56E+02            |
| Local-Y     4.44E-02     1.00     0.00    45.23   1.92E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.66E+02   3.79E+02   0.703      Eq. F2-1      4    17.50 |
| Minor       0.00E+00   6.23E+01   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.21E+02   0.00E+00                                       |
| Minor       6.92E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.66E+02   8.29E+01   3.213      Eq. F2-3      4    17.50 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       9.21E+01   0.00E+00    1.00     5.83    16.97    35.00    |
      STAAD PLANE                                              -- 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          3.213      Eq. H1-1b     4    17.50             |
| Flexure Tens          3.213      Eq. H1-1b     4    17.50             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         8.29E+01   2.66E+02   5.14E+01                   |
|                      6.23E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         8.29E+01   2.66E+02   6.61E+02                   |
|                      6.23E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|