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.
Reverse curvature bending with equal end moments for both axis.
Hand Calculations
According to page 16.1 - 97 of the LRFD 3rd ed. code,
For a W14x176,
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.
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 2024\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 |
|* *|
|**************************************************************************|
| |
|--------------------------------------------------------------------------|