Simply-supported Thick Beam

This test is used to validate the following attributes:

  • Repeated eigen values

  • Transverse shear effects

  • Rotary inertia effects.

You will use a 1D mesh.

Reference:
NAFEMS-Glasgow, Benchmark newsletter, p.16, April 1989.
 

Specifications

Geometry Specifications

Length:
L = 10 m

Area:
a = 2 m x 2 m 


Analysis Specifications

Young Modulus (material):
E = 200 MPa

Poisson's Ratio (material):
ν = 0.3

Density:
ρ = 8000 kg/m3

Mesh Specifications:
5 beam elements (exact 3D beam elements) 

Restraints (User-defined):
Point A: Tx = Ty = Tz =Rx = 0
Point B: Ty = Tz = 0
 

Results

The results are based on the 9 lowest normal modes of the structure.
The percentages of errors are listed in the table below:

Mode

Exact [Hz]

Beam [Hz]

Error [%]

 1 and 2 (bending modes)

 42.568 

42.531

0.09

 3 (torsional mode)

71.5

71.554

0.08

 4 (longitudinal mode)

125.51

 125.515 

0.00

 5 and 6 (bending modes)

145.46

145.064

0.27

 7 (torsional mode)

213.24

221.756

3.99

 8 and 9 (bending modes)

267.01

265.79

0.46

To Perform the Test:

The simplysupported_thick_beam.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of beam elements.

To compute the case, proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the case and generate an image called Deformed mesh.