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.

 

[petro_man]

The context here is that we have a structure on the sea floor and while working at the surface something can be dropped by accident and hit the structure. Our client specifies 5 kJ impact energy which is typical. The dropped object protection is provided to prevent the dropped object from hitting sensitive components like pipes, valves, tubing etc in the structure. The protective structure is allowed to be permanently deformed, absorbing the impact energy, as long as the structure doesn't get pushed into the sensitive components. This is the design philosophy.

 

[HTURKAK]

Given the impact energy, I have need to calculate the deflection and plastic strain in a plastic hinge on a beam.

This wording means the loading is impact loading but apparently you have performed inverse calculation and Pu is the static load corresponding to Mp plastic moment of the section .


The relations between strain ε and curvature ρ are ,
ε = y/ρ ε 1=h1/ ρ and ε2 = −h2/ ρ

If you know the plastic hinge length Lh , and rotation angle θ ,( assuming ur calculation is correct and the last two line items at ur post )
The outer strain would be,
ε 1= (h1* θ )/(Lh)

P.S.: The figure in my post from the book Formulas for Mechanical-and-Structural Shock and impact.

 

[SWComposites]

Seems like the formulas should include section properties for the beam, and the stress-strain curve for the material