Tension in three point loaded beam for Fracture calculation

[Supernovah]

A beam with dimensions 10x10x50mm is loaded in it's middle with a load F and it's supported by two wedges at either end

Given it's fracture toughness say 500MPa, what is the largest load that it can hold?

I am assuming that the underside of the beam will go into Tension and to calculate the largest F will be related to this but to choose a "underside" dimension accurately means to the level of the unit cell dimension and we don't know the material of the beam.

So to do this question, is it is simple as Force/Area = Fracture Stress, Solving for Force?

 

[Mapes]

No, it's not quite that simple. Do you know how to make a shear and moment diagram for the beam, and then to calculate the stress due to bending moment? That's how I'd solve the problem.