 # 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.

## Reference

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

## Problem

W21x48 shape

 Fy = 50 ksi

 Length = 40 ft

 Lb = 160 in.

## Validation

The plastic limiting unbraced length is given by:

The inelastic limiting unbraced length is given by:

 $L r = r y X 1 F L 1 + 1 + X 2 F L 2$ (F1-6)
where
 FL = Fyf - Fr = 50 ksi - 10 ksi = 40 ksi X1 = $π S x E G J A 2 = π 93.0 29,000 ( 11,200 ) ( 0.803 ) ( 14.1 ) 2 = 1,449$ X2 = $4 C w I y ( S x G J ) 2 = 4 ( 3,950 38.7 ) [ 93.0 11,200 ( 0.803 ) ] 2 = 0.0437$

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

The nominal flexural strength is:

 $M n = C b [ M p - ( M p - M r ) ( L b - L p L r - L p ) ] < M p$ (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

## Comparison

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

Table 1. Comparison of results
Design flexural strength, ϕbMn (in·kips) 3,664 3,658.52 negligible

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

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
*
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


                         STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
***********************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)