strain in plastic hinge 1

[petro_man]

Given the impact energy, I have need to calculate the deflection and plastic strain in a plastic hinge on a beam. It is a simply supported beam with the impact happening in the center.
I have calculated the deflection but I'm stumped on calculating the plastic strain. Can't seem to find a formula anywhere.

I have attached my calculation so far. Any ideas on calculating the plastic strain in the hinge?

The method so far is from Advanced Mechanics of Materials. Cook, Young.

I know how to do it in FEA, but I want a fast method without all the headaches of making an FEA model.

 

[phamENG]

If you have a plastic hinge in the middle of a simply supported beam, you have a collapse mechanism. By the simplified models we use for design of structures, this implies infinite strain. Realistically, you're into some very non-linear stress/strain behavior that is likely not going to be easy to get with any accuracy. It's beyond what is really needed in most practical structural engineering (we tend to avoid collapse mechanisms, so modeling their behavior isn't too important), so I haven't tried to do anything like it in quite a while. Curious if anyone else has anything to say on it.