Computing the maximum force a rod can bear Suppose I had a rod of diameter $d$ composed of some material with tensile strength $T$.  If I then exterted a pulling force $F$ on the ends of the bar, how do I compute the force $F$ for which the rod will break apart?  Is there some general equation that I can use to compute this?
 A: Breaking stress is the maximum force that can be applied on a cross sectional area of a material in such a way that the material is unable to withstand any additional amount of stress before breaking.
Breaking stress is calculated with the formula:
Breaking Stress = Force / Area (in your case Area= pi*d^2/4)
Breaking stress may also be known as ultimate tensile stress or breaking strength.

This is a picture from wikipedia which explains this for more info you can visit them
https://en.wikipedia.org/wiki/Stress%E2%80%93strain_curve
A: If you know ultimate tensile strength $T$ of material, then knowing breaking force of rod is trivial,
$$ F_{~br} = T \cdot A $$
,where $A$ is rod cross-section area.
However there is no way to compute ultimate tensile strength of materials, it can only be known from Tensile testing of materials, with some exceptions. For example if metal is heated in the process of annealing, then metals changes it's properties due to structural changes in recrystallization. Then if you'll draw some metals Ultimate tensile strength Vs Young's modulus chart,- you may see correlation :

So in this case one can predict annealed metals ultimate tensile strength from it's Young's modulus by linear equation :
$$ T[\text{MPa}] = 1.3~E[\text{GPa}] + 34.1$$
Thus if you know that some materials shares common properties, you may try to extrapolate ultimate tensile strength based on some other key variables, such as Young's modulus, density, etc. However in general no common method exist to predict material ultimate strength and this can only be measured by destructive testing.
