VM135

VM135
Bending of a Beam on an Elastic Foundation

Overview

Reference:S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 12, article 2.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):
3D 3-Node Beam Element (BEAM189)
3D Structural Surface Line Load Effect (SURF156)
Input Listing:vm135.dat

Test Case

A long (semi-infinite) rectangular beam on an elastic foundation is bent by a force F and a moment M applied at the end as shown. Determine the lateral end deflection of the beam δend.

Figure 188: Beam Problem Sketch

Beam Problem Sketch

Material PropertiesGeometric PropertiesLoading
k = 1515.15 lb/in3
E = 30 x 106 psi
h = 5 in
b = 4.224 in
F = 1000 lb
M = 10,000 in-lb

Analysis Assumptions and Modeling Notes

The beam length is arbitrarily selected to be 286 in.

Results Comparison

TargetMechanical APDLRatio
Deflectionend , in-0.03762-0.03767[1]1.001

  1. UY at Node 1.