C10. Specific behavior in shear and torsion

C10. Specific behavior in shear and torsion

In general, it should be noted that beam element models do not systematically consider shear stress deformations, nor do they adequately account for torsional deformations.

However, in the case of modeling a structure that is sensitive to shear and torsion, one must activate the option to consider shear and torsional deformations and to clearly define the reduced cross-sections and torsional inertias.

It can also be noted that the phenomena with blocked torsion are impossible to model in beam-element structures because the beam elements of Strength of Materials are built on the assumption of conservation of straight sections (without distortion or buckling) and yet, their consideration leads to stress distributions different from those calculated in "classical" Strength of Materials.

Considering the blocked torsion will generally require the separate modeling of all the plates constituting the thin profile of the section.

Here are some examples of structures sensitive to these phenomena:

 


Comparing calculations of the angle of rotation of a cantilever I-beam

 

Data - cantilever beam:

Plate element model: 

Loading: 

Reaction: 

Displacement θ(L)=0.042 rad

Beam-element model 

Loading:

Reaction: 

Displacement θ(L)=0.1198 rad

Analytical calculation

The differential equation for the angle of rotation is given by:

With the boundary conditions given in the previous paragraph, the solution of this equation is:

With:

Application:

The analytical calculation and the surface element model give the same rotation result θ(L)=0.042 rad.

The beam element model calculation gives a result 2.85 times higher.

In the beam element model, the stiffness due to the buckling inertia is not taken into account for the calculation of the rotation angle:

Conclusion

In general, for beam element models, the stiffnesses due to the torsion of an open section beam are not considered properly in the calculations.

In case of any doubt, a shell-type element approach on a simplified, global, or local model can help identifying the effects.

 


Révision #1
Créé 21 September 2023 09:14:22 par Paul Terrasson Duvernon
Mis à jour 21 September 2023 13:36:16 par Paul Terrasson Duvernon