Calculating Failure Load for Beams: What is the Equation?

[serfinos]

Homework Statement

Hi , I got a MI problem for a given application. I need the failure load of a beam in order
to derive the Merit Index.

Does anybody knows the equation of the failure load of a beam ?

 

[pongo38]

Beams have many failure modes, but usually flexure. Could be shear, deflection, vibration, local failure, out-of-plane buckling etc. I have no idea what a merit index is. Do you?