V. AISC LRFD - Compression and Biaxial Bending
To check the adequacy of an ASTM A992 W14X176 beam subject to axial compression and biaxial bending.
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.
Comparison
The reported STAAD.Pro value is based on the terms PNC, MNY, and MNZ in the STAAD.Pro output.
| Result Type | Theory | STAAD.Pro | Difference |
|---|---|---|---|
| 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 |
STAAD Input
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
*
LOAD 1
JOINT LOAD
1 FX 1400
*
LOAD 2
JOINT LOAD
1 MZ 200
2 MZ 200
*
LOAD 3
JOINT LOAD
1 MY 70
2 MY 70
*
LOAD COMBINATION 4
1 1.0 2 1.0 3 1.0
*
PERFORM ANALYSIS
LOAD LIST 4
PRINT MEMBER FORCES
*
PARAMETER 1
CODE LRFD
FYLD 7200 ALL
TRACK 2 ALL
CHECK CODE ALL
*
FINISH
STAAD Output
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 | | * |<---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| | (WITH LOAD NO.) | | | | 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 | | LOADING 4 4 4 4 4 | | | |**************************************************************************| |* *| |* DESIGN SUMMARY (KIP-FEET) *| |* -------------- *| |* *| |* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *| | FX MY MZ LOCATION | | ====================================================== | | PASS LRFD-H1-1A-C 0.974 4 | | 1400.00 C 70.00 200.00 0.00 | |* *| |**************************************************************************| | | |--------------------------------------------------------------------------|