V. Direct Analysis of a Column
Verify the maximum bending moment and deflection of a column using the direct analysis method.
Reference
American Institute of Steel Construction. 2005. Specifications for Structural Steel Buildings. Chicago, IL:AISC. p.16.1-435, Case 2
Details
A 25' tall cantilevered column (i.e., a flagpole) is subject to an axial load of 30 kips. The section is a W8x18 (Iz = 61.9 in4).
Validation
A notional load factor of 0.003 is used. Therefore, the horizontal notional load at the top (free end) of the column is H = 0.03 × 30 = 0.09 kips.
Maximum moment
The maximum moment occurs at the fixed base.
where= | ||
= | ||
= |
Therefore, the maximum moment is:
Maximum deflection
The maximum deflection occurs at the free end.
where= | ||
= |
Therefore, the maximum deflection is:
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\07 Nonlinear Analysis\Direct Analysis of a Column.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Jun-09
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 300 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-006
DAMP 0.03
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL ALL
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X18
SUPPORTS
1 FIXED
2 FIXED BUT FX FY MX MY MZ
DEFINE DIRECT ANALYSIS
FYLD 50 LIST 1
NOTIONAL LOAD FACTOR 0.002
END
LOAD 1 LOADTYPE None TITLE VERTICAL LOAD
JOINT LOAD
2 FY -30
perf analysi
change
LOAD 2 LOADTYPE Live REDUCIBLE TITLE VERT + NOTIONAL
REPEAT LOAD
1 1.0
NOTIONAL LOAD
1 X 0.003
PERFORM DIRECT ANALYSIS LRFD
load list 2
print joint disp list 2
print memb force list 1
FINISH
STAAD.Pro Output
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 2 2 1.14538 -0.05900 0.00000 0.00000 0.00000 -0.00586 ************** END OF LATEST ANALYSIS RESULT ************** 46. PRINT MEMB FORCE LIST 1 MEMB FORCE LIST 1 STAAD SPACE -- PAGE NO. 4 MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- KIP INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 2 1 30.00 0.09 0.00 0.00 0.00 61.36 2 -30.00 -0.09 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT **************