VM14

VM14
Large Deflection Eccentric Compression of a Column

Overview

Reference:S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 263, problem 1.
Analysis Type(s):Static, Large Deflection Analysis (ANTYPE = 0)
Element Type(s):Elastic Tapered Unsymmetric Beam Elements (BEAM188)
Input Listing:vm14.dat

Test Case

Find the deflection Δ at the middle and the maximum tensile and compressive stresses in an eccentrically compressed steel strut of length L. The cross-section is a channel with the dimensions shown in the diagram. The ends are pinned at the point of load application. The distance between the centroid and the back of the channel is e, and the compressive force F acts in the plane of the back of the channel and in the symmetry plane of the channel.

Figure 17: Slender Column Problem Sketch

Slender Column Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
L = 10 ft
h = 8 in
s = 0.22 in
t = 0.39 in
e = 0.6465 in
b = 2.26 in
F = 4,000 lb

Analysis Assumptions and Modeling Notes

Only one-half of the structure is modeled because of symmetry. The boundary conditions for the equivalent half model become fixed-free. Large deflection is needed since the stiffness of the structure and the loading change significantly with deflection. The offset e is defined in the element coordinate system.

Results Comparison

Target[1]Mechanical APDLRatio
Deflection, in0.10860.1088[2]1.002
Stresstens , psi1803.61807.34481.002
Stresscomp , psi-2394.5-2396.00071.001

  1. Solution recalculated

  2. Corresponds to negative of X-deflection at node 5