Lateral Buckling of Narrow Rectangular Beam

This test lets you check analysis results for rectangular beams, in the context of a buckling case.
You will use 1D meshes.

Reference:

  • W. FLIGE, MC GRAW-HILL, Handbook of Engineering Mechanics, New York, 1962

  • J.H. ARGYRIS, Finite Element Method - The Natural Approach, 1979
 

Specifications

Geometry Specifications

Length:
L1 = 240 mm  

Height:
b = 30 mm

Thickness:
t = 0.6 mm


Analysis Specifications

Young Modulus (material):
E = 71240 GPa

Poisson's Ratio (material):
ν = 0.31

Inertia:
Ix = 2.16 mm4 (torsionnal)
Iy = 0.54 mm4 (minor)
Iz = 1350 mm4 (major)

Mesh Specifications:

21 nodes, 20 beam elements.

Restraints (User-defined):

  • Test 1:
    At End 1, all degrees of freedom for nodes are fixed 

  • Test 2:
    At End 1,
    Tx = Ty = Tz = Rx = Ry = 0

    At End 2,
    Ty = Tz = Rx = Ry = 0

Loads:

  • Test 1:
    At End 2,
    distributed force Fx = 1 N

  • Test 2:
    At End 1,
    moment Mz = -1 N x mm

    At End 2,
    moment Mz = 1 N x mm
 

Results

The following table presents the results for buckling eigen values.

 

Argyris theory

CATIA beam

Test 1

1.088

1.088

Test 2

624.77

624.77

To Perform the Test:

The Lateral_buckling_rectangular_beam.CATAnalysis document presents the complete lateral buckling case, and includes the tests 1 and 2.

To compute the case, proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the analysis and generate an image called Deformed Mesh.