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

Comparison

Table 1. Comparison of results
Moment at Node 1 (in·lb) -98.2 -96.93 1.3%
Moment at Node 2 (in·lb) -217.2 -220.42 1.5%

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
UNIT FEET KIP
1 2 UNI GY -4
PERFORM ANALYSIS
PRINT SUPPORT REACTION
FINISH
``````

```   SUPPORT REACTIONS -UNIT KIP  FEET    STRUCTURE TYPE = PLANE