V. AISC LRFD - Non Compact Wide Flange 3

To determine the design bending strength of a non-compact American wide flange section bent about its strong axis.

References

AISC Load Factor Resistance Design, 3rd Edition, Example 5.2, case (b), page 5-16.

Details

W21x48 shape

Fy = 50 ksiLength = 40 ftLb = 160 in.

Calculations

Validation

The plastic limiting unbraced length is given by:

The inelastic limiting unbraced length is given by:

(F1-6)

where

FL
=
Fyf - Fr = 50 ksi - 10 ksi = 40 ksi
X1
=
X2
=

Lp < Lb < Lr ; thus, the section is inelastic.

The nominal flexural strength is:

(F1-2)
Mr = FLSx = 40 × 93.0 = 3,720 in·k
(F1-7)
Mp = FyZx = 50 × 107 = 5,350 in·k

Conservatively assume Cb = 1.0 (this is the default behavior in STAAD.Pro when the parameter is not directly specified).

The lateral-torsional buckling limit state capacity:

ϕbMn = 0.9×(4,071) = 3,664 in·k

Results

The reported STAAD.Pro value is based on the term MNZ in the STAAD.Pro output.

Table 1. Comparison of results
Result Type Reference STAAD.Pro Difference Comments
Design flexural strength, ϕbMn (in·kips) 3,664 3,658.52 negligible

Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Non Compact Wide Flange 3.STD is typically installed with the program.

STAAD

STAAD SPACE BENDING CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  EXAMPLE PROBLEM 5.2, CASE (B), PAGE 5-16, AISC LRFD 3RD ED.
*  CAPACITY (MNZ) SHOULD BE ABOUT 306 KIP-FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 40 0 0;
*
MEMBER INCIDENCES
1 1 2;
*
MEMBER PROPERTY AMERICAN
1 TABLE ST W21X48
*
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
*
SUPPORTS
1 PINNED
2 FIXED BUT MZ
*
LOAD 1
MEMBER LOAD
1 CON GY -10 13.333
1 CON GY -10 26.667
*
PERFORM ANALYSIS
*
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
UNT 13.333 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH

Output

                         STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
                         ***********************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
      1  ST   W21X48                   (AISC SECTIONS)
                           PASS     LRFD-H1-1B-C       0.437         1
                        0.00 C          0.00        -133.33       13.33
 +---------------------------------------------------------------------+
 | DESIGN STRENGTHS FOR MEMBER     1       UNITS - KIP IN              |
 | PNC=   35.84  PNT=  634.50  MNZ= 3658.52  MNY=  636.75  VN=  194.67 | 
 +---------------------------------------------------------------------+