 # V. AISC LRFD - Wide Flange Flexural Strength 2

To determine the design flexural strength of an ASTM A992 W18X40 bent about its strong axis on a 35-ft span with a uniformly distributed load.

## Reference

Hand calculation using the following reference:

AISC Load Factor Resistance Design, 3rd Edition, Example 5.1, Case (b), page 5-12.

## Details

The beam is braced at the ends and at third points such that Lb = 140 in.

 Fy = 50 ksi

 Length = 35 ft

## 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 = $π S x E G J A 2 = π 68.4 29,000 ( 11,200 ) ( 0.810 ) ( 11.85 ) 2 = 1,813$ X2 = $4 C w I y ( S x G J ) 2 = 4 ( 1,440 19.1 ) [ 68.4 11,200 ( 0.810 ) ] 2 = 0.0171$

 Mr = FLSx = 40 × 68.4 = 2,736 in·k (F1-7)

Lp = 53.8 in.

Lr = 144.9 in.

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)

Mp = FyZx = 50 × 78.4 = 3,920 in·k

Conservatively assume Cb = 1.0.

The lateral-torsional buckling limit state capacity:

ϕbMn = 0.9×(2,800) = 2,520 in·k

## Results

Table 1. Comparison of results
Design flexural strength, ϕbMn (in·kips) 2,520 2,514 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Wide Flange Flexural Strength 2.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 5.1, CASE (B), PAGE 5-12, AISC LRFD 3RD ED.
*  CAPACITY (MNZ) SHOULD BE ABOUT 211 KIP-FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 35 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W18X40
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 UNI GY -1.3
PERFORM ANALYSIS
PARAMETER 1
CODE LRFD
MAIN 1 ALL
CB 1 ALL
FYLD 7200 ALL
UNT 11.7 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=0.1180E+2 |
|            *  | ST  W18X40                  |      |   --Z  AY=0.5638E+1 |
|DESIGN CODE *  |                             |      |        AZ=0.4214E+1 |
| LRFD 2001  *  ===============================   ===|===     PY=0.1000E+2 |
|            *                                                PZ=0.7840E+2 |
|            *  |&lt;---LENGTH (FT)=   35.00 --->|               RY=0.1272E+1 |
|*************                                                RZ=0.7202E+1 |
|                                                                          |
|                199.1 (KIP-FEET)                                          |
|PARAMETER        |               L1  L1  L1                  CAPACITIES   |
|IN KIP  INCH     |                                           IN KIP  INCH |
|---------------  +           L1              L1              -------------|
| KL/R-Y= 330.12  |                                           PNC=0.2310E+2|
| KL/R-Z=  58.32  +       L1                      L1          pnc=0.0000E+0|
| UNL   = 140.40  |                                           PNT=0.5310E+3|
| CB    =   1.00  +   L1                              L1      pnt=0.0000E+0|
| PHIC  =   0.85  |                                           MNZ=0.2514E+4|
| PHIB  =   0.90  +                                           mnz=0.2389E+4|
| FYLD  =  50.00  |L0                                     L0  MNY=0.4283E+3|
| NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.0000E+0|
| DFF =     0.00 -11.1                                        VN =0.1522E+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        22.7        0.0         0.0       199.1      |
|   LOCATION       0.0         0.0        0.0         0.0        17.5      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|