VM-WB-MECH-021

VM-WB-MECH-021
Buckling Analysis of Beams

Overview

Reference:	Young, W. C. Roark's Formulas for Stress and Strains (6th ed., Table 34, Case 3a, p. 675).
Solver(s):	Ansys Mechanical
Analysis Type(s):	Buckling Analysis
Element Type(s):	Beam

Test Case

A beam fixed at one end and is subjected to two compressive forces. One of the forces is applied on a portion of the beam of length 50 mm (L₁) from the fixed end and the other is applied on the free vertex, as shown below.

Find the load multiplier for the first buckling mode.

Figure 24: Schematic

Material Properties

Geometric Properties

E = 2e11 Pa

ν = 0.3

L₁ = 50 mm

Total length = 200 mm

Rectangular cross section = 10 mm x 10 mm

Force on L₁ = -1000 N (x direction)

Force on free vertex = -1000 N (x direction)

Results Comparison

Results	Target	Mechanical	Error (%)
Load Multiplier	10.2397	10.198	-0.407