V. AISC ASD - Compression and Biaxial Bending

Determine the suitability of a W14x109 shape to resist axial compression and biaxial bending.

Reference

AISC Allowable Stress Design, 9th Edition,Example 4, page 3-11.

Problem

P =200 kips

M_z = 120 ft·kips (strong axis)

M_y = 40 ft·kips (weak axis)

KL = 14 ft

C_m= 0.85

Maximum unbraced length of compression flange is 15 ft.

Comparison

Table 1. Comparison of results
Result Type		Theory	STAAD.Pro	Difference
Selected section		OK	OK (stress ratio = 0.93)	none

STAAD Input

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

STAAD SPACE AISC VERIFICATION PROBLEM FOR COMBINED AXIAL + BENDING.
START JOB INFORMATION
ENGINEER DATE 22-Sep-18
END JOB INFORMATION
* PAGE 3-11 OF 9TH ED. AISC-ASD. EXAMPLE 4.
* RATIO SHOULD BE APPROXIMATELY 1.0
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 14 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X109
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL_50_KSI
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 62 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 FIXED
LOAD 1
JOINT LOAD
2 FY -200
2 MZ 120
2 MX 40
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC
FYLD 36 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC
FYLD 36 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (AISC 9TH EDITION)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ===|===     ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |      |        AX =  32.00  |
  |            *  | ST  W14X109                 |      |   --Z  AY =   6.87  |
  |DESIGN CODE *  |                             |      |        AZ =  16.80  |
  | AISC-1989  *  ===============================   ===|===     SY =  61.23  |
  |            *                                                SZ = 173.43  |
  |            *  |&lt;---LENGTH (FT)=   14.00 --->|               RY =   3.74  |
  |*************                                                RZ =   6.22  |
  |                                                                          |
  |                120.0 (KIP-FEET)                                          |
  |PARAMETER        |                               L1  L1  L1  STRESSES     |
  |IN KIP  INCH     |                               L1  L1  L1  IN KIP  INCH |
  |---------------  +                               L1  L1  L1  -------------|
  | KL/R-Y=  44.95  |                               L1  L1  L1  FA  =  18.78 |
  | KL/R-Z=  26.99  +                               L1  L1  L1  fa  =   6.25 |
  | UNL   = 168.00  |L1 L1  L1  L1  L1  L1  L1  L1              FCZ =  23.76 |
  | CB    =   1.00  +L1 L1  L1  L1  L1  L1  L1  L1              FTZ =  23.76 |
  | CMY   =   0.85  |L1 L1  L1  L1  L1  L1  L1  L1              FCY =  27.00 |
  | CMZ   =   0.85  +L1 L1  L1  L1  L1  L1  L1  L1              FTY =  27.00 |
  | FYLD  =  36.00  |L1 L1  L1  L1  L1  L1  L1  L1              fbz =   8.30 |
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   fby =   7.84 |
  | DFF   =   0.00 120.0                                        Fey =  73.91 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez = 205.02 |
  | (KL/R)max =  44.95              (WITH LOAD NO.)             FV  =  14.40 |
  |                                                             fv  =   0.00 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE     200.0         0.0        0.0        40.0       120.0      |
  |   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        AISC- H1-2       0.929              1               |
  |        200.00 C         40.00      -120.00             0.00              |
  |*                                                                        *|
  |                                                                          |
  |--------------------------------------------------------------------------|
      AISC VERIFICATION PROBLEM FOR COMBINED AXIAL + BENDING.  -- PAGE NO.    6
    47. FINISH