Center of Torsion of a Thin U-Beam

The purpose of this test is to take into account the center of torsion.
The type of test is a 1D model, non symmetric section with center of torsion, different from the center of gravity. Both predefine sections (Thin U-Beam) and define from a surface sections (Beam from surface) are used.


Modélisation des structures par éléments finis, BATOZ J.L., DHATT G., Vol.2; Hermès Edition, Paris 1990.


Geometry Specifications

 L = 0.1 m
 H = 0.01 m
 B = 0.008 m
 t = 0.0004 m

Analysis Specifications

Young Modulus (material):
E = 200 GPa

Poisson's Ratio (material):
ν = 0.266

Mesh Specifications:

  • One beam element on the whole length
  • Mesh size: 100 mm
Clamp on A
Loads (Distributed force):
On B: Pz = 1N


Analytical Solution

  • g: center of gravity
  • C: center of torsion/shearing. C is the point of the section where shearing restraints due to a cutting effort generate a null moment of torsion.
    The rotation of the section on x is given by:

    • G: shearing coefficient (Pa)
      For an isotropic material:
    • J: Inertia/Constant of torsion (m4)
      For a U-Beam section (valid formula for t < B and H):
    • Mx: moment of torsion (N.m)
    • yc: coordinates of point C on y (the origin of the axis system is the center of gravity)
      For a U-Beam section:

J = 0.5376 x 10-12 m4
yc = -5.65046 x 10-3 m
x = L

The result of the analytic solution is:
= -1.33063 x 10-2 rad

Computed results



Case 1 "Thin U-beam"

Case 2 "Beam from surface"


-1.33063 x 10-2

-1.33063 x 10-2

-1.35608 x 10-2

Normalized results




To Perform the Test:

The thin_u_beam.CATAnalysis document presents a complete analysis of this case.

To compute the case, proceed as follow:

  1. Open the CATAnalysis document.

  2. Compute the case in the Generative Structural Analysis workbench.

  3. Create a local sensor (Rotation vector).