V. End Moments in a Non Uniform Beam
To find end moments due to a uniform load on a beam with nonuniform sections, fixed at both ends.
Reference
Hand calculation using the following reference:
McCormack, J.C., Structural Analysis, Intext Educational Publishers, 3rd Edition, 1975.
Problem
Find the moment at the supports. Assume for input a unit width for the beam. Depths are as shown.
E = 30×(10)6 psi |
w = 4 k/ft |
d1 = 10 in., d2 = 20 in. |
L1 = 12 ft, L2 = 8 ft |
Beam A) problem sketch and B) mathematical model
Comparison
Result | Theory | STAAD.Pro | Difference |
---|---|---|---|
Moment at Node 1 (in·lb) | -98.2 | -96.93 | 1.3% |
Moment at Node 2 (in·lb) | -217.2 | -220.42 | 1.5% |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\End Moments in a Non Uniform Beam.STD is typically installed with the program.
STAAD PLANE :A FIXED-FIXED BEAM OF UNIFORM AND TAPERED SECTIONS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: MCCORMAC, J.C., STRUCTURAL ANALYSIS, INTEXT
* EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975
*
INPUT WIDTH 72
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 144 0 0; 3 240 0 0;
MEMBER INCIDENCES
1 1 2; 2 3 2;
MEMBER PROPERTY AMERICAN
1 PRIS YD 10 ZD 1
2 TAPERED 20 1 10 1 1 1 1
PRINT MEMBER PROPERTIES
UNIT FEET KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.32e+06
POISSON 0.290909
END DEFINE MATERIAL
UNIT INCHES KIP
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 3 FIXED
LOAD 1 UNIFORM LOAD OVER ENTIRE BEAM
UNIT FEET KIP
MEMBER LOAD
1 2 UNI GY -4
PERFORM ANALYSIS
PRINT SUPPORT REACTION
FINISH