From the way you described it, it sounds like the bar will fail due to bending stress. If the beam we are talking about is fixed at either end with cantilever supports, then the analysis goes something like this:...
Moment of inertia for the beam: ##\frac{1}{12}base*height^3##. Calculate that, being mindful of your units.
Calculate the reaction forces and moments at the beam supports: Symmetry makes the vertical reactions pretty easy, 50N up at both supports. However, when we do the sum of the moments, notice that we have two moments which we can't solve for using a simple sum of moments equation, we have to move use...
This equation: ##EI\frac{d^2}{dx^2} = M(x)##. Where "v" in that equation is the vertical deflection, this is where things get weird... We know that 1/4th of the way across the beam, ##\frac{d^2}{dx^2} = 0##, right? Because we that ##\frac{dv}{dx} = 0## at both the base (because cantilever) and at the midpoint (because of symmetry), so it makes sense that the inflection point is equal to zero half way in between those two points, like sines and cosines. Armed with that knowledge, we can make an imaginary "cut" at that point (1/4th of the way across) and find the necessary reactionary moment at A to ensure that there is no moment at this point. E.i, the internal moment at A and the vertical reaction force times distance must equal zero...
The moment is at A must be ##\frac{reaction- at- A * Length}{4}## or ##{Force*L}{8}## ... that is the moment reaction at the base. Only this reaction will ensure that there is no internal moment 1/4th of the way across the beam. The base is where the beam will snap, if you calculate the internal moment at the beam center, it's less, I will leave that for you if you want to compare the two.
So yes, once you have the moment of inertia, max moment and Y, (5mm/2), you can calculate stress.
reference:
http://www.engineersedge.com/beam_bending/beam_bending18.htm
If you were actually talking about simply supported beams (not cantilever) everything is a lot easier.