# V. AISC LRFD - Compression and Biaxial Bending

To check the adequacy of an ASTM A992 W14X176 beam subject to axial compression and biaxial bending.

## Reference

AISC Load Factor Resistance Design, 3rd Edition, Example 6.2, page 6-6.

## Problem

W14x176 section.

 Fy = 50 ksi

 Pu = 1,400 kips

 Muy = 70 ft·kips, Muz = 200 ft·kips

 Lb = 14 ft

Reverse curvature bending with equal end moments for both axis.

## Hand Calculations

According to page 16.1 - 97 of the LRFD 3rd ed. code,

Mp = Fy · Z ≤ 1.5Fy · S

For a W14x176,

0.9 (1.5Fy · S) = 0.9 [1.5 (50)(107)] = 7,222 kip-in = 601.8 kip-ft,

which is lower than (0.9 Fy . Z) = 611. Hence, STAAD.Pro uses this limit state.

## Comparison

The reported STAAD.Pro value is based on the terms PNC, MNY, and MNZ in the STAAD.Pro output.

Table 1. Comparison of results
Design compressive strength, ϕcPn (kips) 1,940 1,938 negligible
Design bending strength, ϕbMny (ft·kips) 611

600.5

(7,206 in·kips)

1.7%

Design bending strength, ϕbMnz (ft·kips) 1,200

1,200

(14,400 in·kips)

none
Utilization ratio 0.973 0.974 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Compression and Biaxial Bending.STD is typically installed with the program.

``````STAAD SPACE AXIAL COMPRESSION + BIAXIAL BENDING PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
*  EXAMPLE PROBLEM 6.2, PAGE 6-6, AISC LRFD 3RD ED.
*  INTERACTION RATIO SHOULD BE ABOUT 0.973
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 14 0 0;
*
MEMBER INCIDENCES
1 1 2;
*
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X176
*
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
*
SUPPORTS
1 FIXED BUT FX MX MY MZ
2 FIXED BUT MY MZ
*
1 FX 1400
*
1 MZ 200
2 MZ 200
*
1 MY 70
2 MY 70
*
1 1.0 2 1.0 3 1.0
*
PERFORM ANALYSIS
PRINT MEMBER FORCES
*
PARAMETER 1
CODE LRFD
FYLD 7200 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=0.5180E+2 |
|            *  | ST  W14X176                 |      |   --Z  AY=0.1262E+2 |
|DESIGN CODE *  |                             |      |        AZ=0.2742E+2 |
| LRFD 2001  *  ===============================   ===|===     PY=0.1630E+3 |
|            *                                                PZ=0.3200E+3 |
|            *  |&lt;---LENGTH (FT)=   14.00 --->|               RY=0.4022E+1 |
|*************                                                RZ=0.6427E+1 |
|                                                                          |
|                200.0 (KIP-FEET)                                          |
|PARAMETER        |L4                                     L4  CAPACITIES   |
|IN KIP  INCH     |                                   L4      IN KIP  INCH |
|---------------  +   L4                                      -------------|
| KL/R-Y=  41.77  |       L4                      L4          PNC=0.1938E+4|
| KL/R-Z=  26.14  +                                           pnc=0.1400E+4|
| UNL   = 168.00  |           L4              L4              PNT=0.2331E+4|
| CB    =   1.00  +               L4      L4                  pnt=0.0000E+0|
| PHIC  =   0.85  |                                           MNZ=0.1440E+5|
| PHIB  =   0.90  +                                           mnz=0.2400E+4|
| FYLD  =  50.00  |                   L0                      MNY=0.7206E+4|
| NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.8400E+3|
| DFF =     0.00 -11.1                                        VN =0.3406E+3|
| dff =     0.00               ABSOLUTE MZ ENVELOPE           vn =0.2857E+2|
|                                                                          |
|                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
|                      -------------------------                           |
|                                                                          |
|                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
|                                                                          |
|      VALUE    1400.0        28.6       10.0        70.0       200.0      |
|   LOCATION       0.0         0.0        0.0         0.0         0.0      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|