What is formula for maximum load due to bending of a simply supported beam?

The strength, S, of the beam is Mc/I where M = max moment to fail = PL/4 for load concentrated in the middle of the beam or WL/8 for uniformly distributed load.

Here P is the concentrated load, W = distributed load, c = distance to outer fiber from neutral axis and I the area moment of inertia of the beam. L = length

Solving for load maximum,

P = 4IS/Lc for concentrated center load

W = 8IS/Lc for distributed load