I read there are multiple models for it, Plate theory, euler-bernoulli, timoshenko beam theory etc

Which is the most accurate for modelling the bending of a stressed cantilever beam?


1 Answer 1


Your question is quite broad. Accuracy depends a lot on the context, so I'll caveat my response by noting that the below is valid only for completely linear-elastic materials (no plastic behaviour whatsoever).

For the most part, Euler-Bernoulli is less accurate than timoshenko since it doesn't account for shear deformations. However, with timoshenko formulations most implementations will approximate the shear factor (which is a complicated thing to solve for on it's own). A finely meshed plate model using standard FE formulations (Kirchoff-Love, etc) which is not susceptible to shear locking will probably be more accurate than timoshenko beam results ... but even here, the difference will be negligible for long memebers.

So for the most part and assuming my conditions noted above apply,

Euler-Bernoulli < Timoshenko < Plate Model

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    $\begingroup$ Thanks. Is there any context of beam bending where the plate model is not the most accurate $\endgroup$
    – Hisham
    Commented Oct 5, 2022 at 20:37
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    $\begingroup$ @Maalik off the top of my head, orthotropic materials comes to mind. Plate models are good for modelling behaviour where the material is isotropic. With orthotropic materials, you need to model using solids to properly account for out-of-plane stresses. $\endgroup$
    – Andorrax
    Commented Oct 6, 2022 at 22:59

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