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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. |
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Reference:
Modélisation des structures par éléments finis, BATOZ
J.L., DHATT G., Vol.2; Hermès
Edition, Paris 1990. |
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Specifications
Geometry Specifications
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L = 0.1 m
H = 0.01 m
B = 0.008 m
t = 0.0004 m |
Analysis Specifications
Young Modulus (material):
E = 200 GPa |
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Poisson's Ratio (material):
ν = 0.266 |
Mesh Specifications:
- One beam element on the whole length
- Mesh size: 100 mm
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Restraints:
Clamp on A |
Loads (Distributed force):
On B: Pz = 1N |
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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 (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:
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For: J = 0.5376 x 10-12 m4
yc = -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 U-beam" |
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 |
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To Perform the Test:
The thin_u_beam.CATAnalysis document
presents a complete analysis of this case.
To compute the case, proceed as follow:
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Open the CATAnalysis document.
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Compute the case in the Generative Structural
Analysis workbench.
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Create a local sensor
(Rotation vector).
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