In materials science the Tresca criterion, named after French mechanical engineer Henri Tresca, is used to predict whether a structure (a beam, a strut, a pressure vessel, anything subject to mechanical force) will fail under a given load.
Tresca is one of two commonly used failure criteria; the other is the von Mises criterion. The math is trivially simple (once you get past calculating the principal stresses).
To use the Tresca criterion, find the principal stresses. Call the largest one σ1 and the smallest one σ3. (In two dimensions, there will only be two; in three dimensions, ignore the one in the middle.) As long as the yield point of the material σyp is greater than the difference between these two stresses, the structure will not yield.
In short: to avoid mechanical failure, σyp ≥ σ1 - σ3.
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