I beam torsion modeling

German

Hi,
I'm comparing 3 models of a I beam under torsion, one with just 1D beam elements, the second with 2D shell elements and the last one with solid elements.
The model with beam elements gives a maximum rotation angle of 14º, but the other models give maximum rotation angle of 9º.
Manual calculations give me almost 14º, but I'm not sure if I did it wright (I'm just a chemist, not mechanic engineer).

I couldn't find errors in loads and restrictions so I can't explain the difference.



I'm attaching the models file.

PS: There is no difference in the behavior of the 3 models when bending.

Victor

I've only had a brief look at it but I'm guessing it might be the fixed supports on the solid and shell models that constrain warping at the base.

The torsion constants for beams assume they're free to warp regardless of the constraints, which is perhaps misleading.

German

I've changed the fixed supports for x, y and z zero displacement, and the results are the same as before.

I´ve also seen that there are several formulas for the torsion constant for this profile, so manual calculations may be between 9 and 14 degrees depending of the formula used.

Victor

Zero displacement will have the same effect as fixed support for solids.

I put something like a fixed diaphragm constraint (Y and Z constraints on the whole surface, and X constraint on one node for rigid body motion) on the shells and solids and now all 3 agree:
14.9 degree solids
14.9 degree shells
14.5 degree beams

Mecway shows the torsion constant that it uses for beams in the material properties box. It's using a formula from Roark's Formulas For Stress And Strain.

German

Thank you very much.

Victor

Thank you for bringing this effect to my attention! It might look like I already knew what I was talking about but I spent a while identifying the problem after trying to refine the mesh, change the Poisson's ratio and stiffen the free end before realizing the torsion constant was independent of the constraints. It looks like there may be no way to add a warping restraint to beams.

disla

Hi,

Roark's formula is an aproximate value.
It for this I section (r=0) is It=47.963 cm4

Introducing that value on a general beam section produces the exact result of 14.56º which agree with the analytical solution