Stresses in the bending of a thin walled cylinder

[mechE235]

I am looking into the bending of a thin walled cylinder about it's neutral axis. Should be simple enough, it is just Mr/I. However, that is the maximum stress at the outer fibers of the cylinder and I want to find an approximate expression for the load per unit circumference on a small element at the outer fibers of the cylinder. Anyone have a solution for this? A member of a team where I used to work had a solution, but I forgot it.

Thanks in advance for your help!

 

[Baluncore]

Welcome to PF.
The force required will depend on the degree of bending, and on how you hold or apply the force to the thin walled tube. Do you want a temporary elastic bend, or will you make a permanent plastic bend?

 

[PhanthomJay]

For uniaxial bending, the stress at any point along the outside fibers of the circumference is My/I, where y is the perpendicular distance from the Neutral Axis to the point of interest. You’ll have to use a little geometry/ trig to solve
it in terms of a general point along the circumference, or the central angle from the center of the tube to that point.