Principal Stress Formula
At any point in a loaded material, stress can be resolved into principal stresses — the maximum and minimum normal stresses, occurring on planes where shear stress is zero. For a 2D stress state, they’re given by σ1,2 = (σx + σy)/2 ± √(((σx−σy)/2)2 + τxy2).
The difference between the two principal stresses, divided by two, equals the maximum in-plane shear stress. Engineers use principal stresses to check against material strength limits, since failure theories typically compare the largest normal or shear stress against allowable values.
Last reviewed August 2026