V. Direct Analysis of a Beam
Verify the maximum bending moment and deflection of a beam 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 1
Details
A 40' long, simply-supported beam is subject to a uniformly distributed load of 100 lbs/ft and axial compression of 100 kips. The section is a W10x60 (Iz = 341 in4).
Validation
The maximum moment and deflection both occur at mid-span.
Maximum moment
Therefore, the maximum moment is:
Maximum deflection
Therefore, the maximum deflection is:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
MMAX (ft·k) | 26.36 | 26.308 | negligible | |
δMAX (in) | 0.763 | 0.757 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\07 Nonlinear Analysis\Direct Analysis of a Beam.std is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 17-Apr-08
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 40 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W10X60
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MX MY MZ
DEFINE DIRECT ANALYSIS
FYLD 7200 ALL
END
LOAD 1 LOADTYPE None TITLE APPLIED LOADS
MEMBER LOAD
1 UNI GY -0.1
JOINT LOAD
1 FX 100
2 FX -100
PERFORM DIRECT ANALYSIS LRFD PDITER 15 REDUCEDEI 1
SECTION 0.5 ALL
PRINT MEMBER SECTION FORCES ALL
PRINT SECTION DISPL ALL
FINISH
STAAD.Pro Output
MEMBER FORCES AT INTERMEDIATE SECTIONS
--------------------------------------
ALL UNITS ARE -- KIP FEET
MEMB LOAD SEC AXIAL SHEAR-Y SHEAR-Z MOM-X MOM-Y MOM-Z
1 1 0.50 100.00 -0.00 0.00 0.00 0.00 -20.00
************** END OF LATEST ANALYSIS RESULT **************
38. PRINT SECTION DISPL ALL
SECTION DISPL ALL
STAAD PLANE -- PAGE NO. 4
MEMBER SECTION DISPLACEMENTS
----------------------------
UNITS ARE - INCH
MEMB LOAD GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS
1 1 0.0000 0.0000 0.0000 -0.0078 -0.1984 0.0000
-0.0156 -0.3822 0.0000 -0.0234 -0.5386 0.0000
-0.0312 -0.6577 0.0000 -0.0390 -0.7321 0.0000
-0.0468 -0.7574 0.0000 -0.0545 -0.7321 0.0000
-0.0623 -0.6577 0.0000 -0.0701 -0.5386 0.0000
-0.0779 -0.3822 0.0000 -0.0857 -0.1984 0.0000
-0.0935 0.0000 0.0000
MAX LOCAL DISP = 0.75736 AT 240.00 LOAD 1 L/DISP= 633
************ END OF SECT DISPL RESULTS ***********
39. FINISH