# V. AISC LRFD - Non Compact Wide Flange 1

To check the adequacy of a non-compact fully braced W shape to carry a uniformly distributed load of 5.5 kips/ft.

## Reference

AISC Load Factor Resistance Design, 3rd Edition, Table 5.4, , page 5-65.

## Details

W14x90 shape. Beam is bent about its strong axis.

 Fy = 50 ksi

 Length = 30 ft

## Validation

Check flange slenderness:

$λ p = 0.38 E / F y = 0.38 29,000 50 = 9.152 < b 2 t f = 10.2$

FL = 50 ksi - 10 ksi = 40 ksi

$λ r = 0.83 E / F L = 0.83 29,000 40 = 22.35 > b 2 t f = 10.2$

 Mr = FLSx = 40 × 143 = 5,720 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 × 157 = 7,850 in·k

Note: As the flanges are fully braced, lateral-torsional buckling does not govern the capacity.

The flange local buckling limit state capacity:

ϕbMn = 0.9×(7,681) = 6,913 in·k

The ultimate moment is:

The capacity ratio is: 7,425 / 6,913 = 1.074

## Results

Table 1. Comparison of results
Design flexural strength, ϕbMn (in·kips) 6,913 6,910 negligible
Capacity ratio 1.074 1.074 none

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 1.STD is typically installed with the program.

Note: The UNT parameter is set to 1.0 in. in order to approximate a fully-braced condition.
STAAD SPACE BENDING CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  TABLE 5-4, PAGE 5-65, AISC LRFD 3RD ED.
*  OBJECTIVE : TO CHECK THE ADEQUACY OF A NON-COMPACT W SHAPE.
*
*  BEAM IS FULLY BRACED. ACCORDING TO ABOVE REFERENCE,
*  CAPACITY OF A 30 FT LONG W14X90 IS 154/30=5.133 KIP/FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 30 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 PINNED
2 FIXED BUT MZ
1 UNI GY -5.5
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE LRFD
MAIN 1 ALL
* FULLY BRACED CONDITION IS ACHIEVED WITH A UNT OF 1.0 INCH
UNT 1 ALL
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (LRFD 3RD EDITION)   v1.0
********************************************
|--------------------------------------------------------------------------|
|                                                    Y        PROPERTIES   |
|*************                                       |        IN INCH UNIT |
|            *  |=============================|   ===|===     ------------ |
|MEMBER   1  *  |  AISC SECTIONS              |      |        AX=0.2650E+2 |
|            *  | ST  W14X90                  |      |   --Z  AY=0.6160E+1 |
|DESIGN CODE *  |                             |      |        AZ=0.1373E+2 |
| LRFD 2001  *  ===============================   ===|===     PY=0.7560E+2 |
|            *                                                PZ=0.1570E+3 |
|            *  |&lt;---LENGTH (FT)=   30.00 --->|               RY=0.3696E+1 |
|*************                                                RZ=0.6140E+1 |
|                                                                          |
|                618.7 (KIP-FEET)                                          |
|PARAMETER        |               L1  L1  L1                  CAPACITIES   |
|IN KIP  INCH     |                                           IN KIP  INCH |
|---------------  +           L1              L1              -------------|
| KL/R-Y=  97.40  |                                           PNC=0.5628E+3|
| KL/R-Z=  58.63  +       L1                      L1          pnc=0.0000E+0|
| UNL   =   1.00  |                                           PNT=0.1192E+4|
| CB    =   1.00  +   L1                              L1      pnt=0.0000E+0|
| PHIC  =   0.85  |                                           MNZ=0.6910E+4|
| PHIB  =   0.90  +                                           mnz=0.7425E+4|
| FYLD  =  50.00  |L0                                     L0  MNY=0.3280E+4|
| NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.0000E+0|
| DFF =     0.00 -34.4                                        VN =0.1663E+3|
| dff =     0.00               ABSOLUTE MZ ENVELOPE           vn =0.0000E+0|
|                                                                          |
|                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
|                      -------------------------                           |
|                                                                          |
|                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
|                                                                          |
|      VALUE       0.0        82.5        0.0         0.0       618.8      |
|   LOCATION       0.0         0.0        0.0         0.0        15.0      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|