# V. AISC LRFD - Non Compact Wide Flange 2

To determine the design bending strength of a non-compact American wide flange section bent about its strong axis. The deflection at mid-span due to two 10 kip concentrated loads acting at the third points along the beam is also to be calculated.

## Reference

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

## Details

W21x48 shape

 Fy = 50 ksi

 Length = 40 ft

 Lb = 60 in.

## Validation

Evaluate section for lateral-torsional buckling:

The plastic limiting unbraced length is given by:

Lb < Lp; thus, the member is plastic.

Check flange slenderness:

$λ p = 0.38 E / F y = 0.38 29,000 50 = 9.152 < b 2 t f = 9.47$

FL = 50 ksi - 10 ksi = 40 ksi

$λ r = 0.83 E / F L = 0.83 29,000 40 = 22.35 > b 2 t f = 9.47$

 Mr = FLSx = 40 × 93.0 = 3,720 in·k (F1-7)

Flanges are non-compact. The nominal moment capacity for the limit state of flange local buckling is:

 $M n = M p - ( M p - M r ) ( λ - λ p λ r - λ p )$ (A-F1-3)

 Mp = FyZx = 50 × 107 = 5,350 in·k

The flange local buckling limit state capacity:

ϕbMn = 0.9×(5,311) = 4,780 in·k

The ultimate moment is:

The capacity ratio is: 1,600 / 4,780 = 0.335

The deflection at mid-span for a beam loaded at third points:

## Results

Table 1. Comparison of results
Design flexural strength, ϕbMn (in·kips) 4,780

4,780.24

negligible
Capacity ratio 0.335 0.335 none
Deflection (in) 1.42 1.4114 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 2.STD is typically installed with the program.

The UNT 5 parameter specifies an unbraced length of 5'.

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 (A), PAGE 5-16, AISC LRFD 3RD ED.
*  CAPACITY (MNZ) SHOULD BE ABOUT 398 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
*
SECTION 0.5 ALL
PRINT SECTION DISPL
*
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
UNT 5 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH


     MEMBER SECTION DISPLACEMENTS
----------------------------
UNITS ARE - INCH
MEMB  LOAD     GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
1     1       0.0000    0.0000    0.0000    0.0000   -0.3644    0.0000
0.0000   -0.7057    0.0000    0.0000   -1.0010    0.0000
0.0000   -1.2273    0.0000    0.0000   -1.3654    0.0000
0.0000   -1.4114    0.0000    0.0000   -1.3654    0.0000
0.0000   -1.2273    0.0000    0.0000   -1.0010    0.0000
0.0000   -0.7057    0.0000    0.0000   -0.3644    0.0000
0.0000    0.0000    0.0000
MAX LOCAL  DISP =    1.41141   AT     240.00  LOAD    1   L/DISP=    340
************ END OF SECT DISPL RESULTS ***********
40. *
41. PARAMETER 1
42. CODE LRFD
43. MAIN 1 ALL
44. FYLD 7200 ALL
45. UNT 5 ALL
46. TRACK 1 ALL
47. CHECK CODE ALL
STEEL DESIGN
BENDING CAPACITY PER AISC LRFD 3RD ED                    -- PAGE NO.    4
STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
***********************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)