V. AISC LRFD - Select Compression and Biaxial Bending

To select the lightest ASTM A992 W14 section capable of carrying an axial compression plus biaxial bending.

Reference

AISC Load Factor Resistance Design, 3rd Edition, Example 6.4, page 6-9.

Problem

F_y = 50 ksi

P_u = 400 kips

M_uy = 80 ft·kips, M_uz = 250 ft·kips

L_b = 14 ft

Reverse curvature bending with equal end moments for both axis.

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
Selection section	W14x99	W14x99	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Select 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 6.4, PAGE 6-9, AISC LRFD 3RD ED.
*  THE LIGHTEST SUITABLE SECTION SHOULD BE A W14X99
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 14 0 0;
*
MEMBER INCIDENCES
1 1 2;
*
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
*
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
*
SUPPORTS
1 FIXED
*
LOAD 1
JOINT LOAD
2 FX -400
2 MZ 250
2 MY 80
*
PERFORM ANALYSIS
*
PARAMETER 1
CODE LRFD
FYLD 7200 ALL
TRACK 2 ALL
SELECT ALL
*
FINISH

STAAD Output

      AXIAL COMPRESSION + BIAXIAL BENDING PER AISC LRFD 3RD ED -- PAGE NO.    3
                     STAAD.PRO MEMBER SELECTION - (LRFD 3RD EDITION)   v1.0
                     ***********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ===|===     ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |      |        AX=0.2910E+2 |
  |            *  | ST  W14X99                  |      |   --Z  AY=0.6887E+1 |
  |DESIGN CODE *  |                             |      |        AZ=0.1518E+2 |
  | LRFD 2001  *  ===============================   ===|===     PY=0.8360E+2 |
  |            *                                                PZ=0.1730E+3 |
  |            *  |&lt;---LENGTH (FT)=   14.00 --->|               RY=0.3717E+1 |
  |*************                                                RZ=0.6176E+1 |
  |                                                                          |
  |                250.0 (KIP-FEET)                                          |
  |PARAMETER        |                               L1  L1  L1  CAPACITIES   |
  |IN KIP  INCH     |                               L1  L1  L1  IN KIP  INCH |
  |---------------  +                               L1  L1  L1  -------------|
  | KL/R-Y=  45.20  |                               L1  L1  L1  PNC=0.1065E+4|
  | KL/R-Z=  27.20  +                               L1  L1  L1  pnc=0.4000E+3|
  | UNL   = 168.00  |L1 L1  L1  L1  L1  L1  L1  L1              PNT=0.1310E+4|
  | CB    =   1.00  +L1 L1  L1  L1  L1  L1  L1  L1              pnt=0.0000E+0|
  | PHIC  =   0.85  |L1 L1  L1  L1  L1  L1  L1  L1              MNZ=0.7717E+4|
  | PHIB  =   0.90  +L1 L1  L1  L1  L1  L1  L1  L1              mnz=0.3000E+4|
  | FYLD  =  50.00  |L1 L1  L1  L1  L1  L1  L1  L1              MNY=0.3698E+4|
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   mny=0.9600E+3|
  | DFF =     0.00 250.0                                        VN =0.1859E+3|
  | dff =     0.00               ABSOLUTE MZ ENVELOPE           vn =0.0000E+0|
  |                                 (WITH LOAD NO.)                          |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE     400.0         0.0        0.0        80.0       250.0      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         1           0          0           1           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        LRFD-H1-1A-C     0.951              1               |
  |        400.00 C        -80.00      -250.00             0.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
  |--------------------------------------------------------------------------|