Curved (twisted) Catilever beam

[hello1581]

How you can calculate max stress on curved or twisted cantilever beam with point load on end.

How you can calculate the torsion for that as well?

 

[ishvaaag]

Assuming small deformations, and since an isostatic problem, you make a cut normal to the directrix, and then project the integrated effect of both force and moment on the moment and force components respect such normal cut; just what we learnt to do when dealing with solicitations in arches.

It is easier when you have only the point load at end because otherwise you have to find for every point you want the solicitations the resultant of distributed loads beyond the cut, something feasible approximately if non analytical, and when analytical (hopefully) by integration.

 

[BAretired]

Curved or twisted? Sketch please.

BA

 

[csd72]

First principles.

If not a first year statics problem then definately a second year.

 

[BAretired]

csd72 is right. No matter how the beam curves or twists, M = P.x where M is the moment at a point located x from load P. As M is a vector quantity, it can be resolved into components which produce bending about each principal axis and torsion about the longitudinal axis. No sketch required.

BA

 

[JStephen]

However, the question didn't ask how to find moments and torsion, it asked how to find stresses, which is a bit more involved and not well addressed in most of the normal references.

 

[BAretired]

The shape and size of the cross section have not been provided. If Vx, Vy, Mx, My and Mt are known, stresses can be found for a given cross section.

BA