How to model a UDL over a plate for bending?

Question

If I have a square plate of height h supported along one side (an L-bracket, modeled as fixed support), and there is an evenly distributed force acting over the face of the plate. From load analysis I am able to determine the resulting force (acting in the centre of the plate) to be P, thus the distributed load over the plate is P/A = P/(L^2)

My question is if we are considering the bending of the plate, can we model this as a cantilever beam with UDL of P/L or will it be something else? I am leaning to the former, and my calculations with such an assumption seems to yeild a reasonable result, but I wanted to double check.

Cheers

Answer 1

A plate supported along one side, subject to a uniformly distributed load, will behave exactly the same as a cantilever beam. You are correct that the UDL will be P/L, as it will be P/A*w where w is the width.

With a non-uniform load, treating it as a beam would give you the average stress, but miss the fact that there will be regions of higher stress and regions of lower stress.