Beam Failure Analysis: Calculate Stress & Compare to Ultimate Strength

[grapfinest]

When determining if a beam will fail under a given load, is it correct to first calculate the stress in the beam caused by the load. Then compare that stress to the ultimate tensile strength of the material and this will render a answer of if the beam will fail (break or yeild)

 

[timthereaper]

Well, that's a simple way to do it. However, there are a lot of failure theories out there, like maximum-shear-stress or distortional (or maximum strain) energy. It all depends on the loadings and your definition of failure. Depending on the situation, failure can mean plastic yielding or can mean fracture. You would have to be more specific about your failure criteria, choose a failure theory, analyze the loads and then determine if the failure criteria are met.

 

[Studiot]

When determining if a beam will fail under a given load, is it correct to first calculate the stress in the beam caused by the load. Then compare that stress to the ultimate tensile strength of the material and this will render a answer of if the beam will fail

Hello grapfinest and welcome,

Is this coursework, and if so what is the course?



The first part of your proposal is a question using of the mechanics and geometry of the arrangement to calculate the imposed internal loading (bending moment). Note I do not say stress since the stress you calculate depends upon the model as TTR has said.

You will no doubt be aware that in normal working we choose a beam with a moment of resistance greater than that calculated above so it does not break.

If we are looking for a collapse moment a different technique is in order, since the beam cannot break, just because the extreme fibres have reached yield.
We have to undertake a plastic analysis where a plastic hinge (or hinges depending upon the support conditions) is fully developed.