
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
UBeam) and define from a surface sections (Beam from surface) are used. 

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

Specifications
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

Restraints:
Clamp on A 
Loads (Distributed force):
On B: P_{z} = 1N 


Results
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:
where:
 G: shearing coefficient (Pa)
For an isotropic material:
 J: Inertia/Constant of torsion (m^{4})
For a UBeam section (valid formula for t < B and H):
 M_{x}: moment of torsion (N.m)
 y_{c}: coordinates of point C on y (the origin of the axis
system is the center of gravity)
For a UBeam section:

For: J = 0.5376 x 10^{12 }m^{4}
y_{c} = 5.65046 x 10^{3} m x = LThe result of the analytic solution is:
= 1.33063 x 10^{2} rad
Computed results
Results 
Reference 
Case 1 "Thin Ubeam" 
Case 2 "Beam from surface" 
(rad) 
1.33063 x 10^{2} 
1.33063 x 10^{2} 
1.35608 x 10^{2} 
Normalized results 
1 
1 
1.019 


To Perform the Test:
The thin_u_beam.CATAnalysis document
presents a complete analysis of this case.
To compute the case, proceed as follow:

Open the CATAnalysis document.

Compute the case in the Generative Structural
Analysis workbench.

Create a local sensor
(Rotation vector).
