VM128

VM128
Buckling of a Bar with Hinged Ends (Area 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): 2D 4-Node Structural Solid Elements (PLANE182)
Input Listing: vm128.dat

Test Case

Determine the critical buckling load of an axially loaded long slender bar of length  with hinged ends. The bar has a cross-sectional height h, and area A.

Figure 180: Buckling Bar Problem Sketch

Buckling Bar Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
= 200 in
A = 0.25 in 2
h = 0.5 in
F = 1 lb

Analysis Assumptions and Modeling Notes

Only the upper half of the bar is modeled because of symmetry. The model is meshed using PLANE182 elements with enhanced strain formulation. The boundary conditions become free-fixed for the half symmetry model. The bar is assumed to have a rectangular cross-section (thickness = A/h = 0.5 in).

Results Comparison

TargetMechanical APDLRatio
Fcr, lb Subspace38.55338.755 [1]1.005

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