VM127

VM127
Buckling of a Bar with Hinged Ends (Line Elements)

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. 148, article 29.
Analysis Type(s):
Linear Perturbed Buckling Analysis (ANTYPE = 1)
Element Type(s):

3D 2 Node Beam (BEAM188)

Input Listing: vm127.dat

Test Case

Determine the critical buckling load of an axially loaded long slender bar of length  with hinged ends. The bar has a square cross-section with width and height set to 0.5 inches.

Figure 179: Buckling Bar Problem Sketch

Buckling Bar Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
= 200 in
l= 0.5 in
F = 1 lb

Analysis Assumptions and Modeling Notes

Only the upper half of the bar is modeled because of symmetry. The boundary conditions become free-fixed for the half symmetry model. The linear buckling analysis is solved using PSTRES command and using Linear Perturbation method.

Results Comparison

TargetMechanical APDLRatio
Using PSTRES command
Fcr, lb38.55338.553[1]1.000
Using Linear Perturbation Method
Fcr, lb38.55338.553[1]1.000

  1. Fcr = Load Factor (1st mode).