1. The problem statement, all variables and given/known data My textbook says that the state of plane stress at a point is uniquely represented by two normal stress components and one shear stress component acting on an element that has a specific orientation at the point. Also, the complementary property of shear says that all four shear stresses must have equal magnitude and be directed either toward or away from each other at opposite edges of the element. Under pure shear, I can prove the complementary property of shear using force and moment balances. When normal and shear stress components are present, I am having difficulty understanding why shear stress and normal stress are unique, and why the complementary property of shear is still valid. 2. Relevant equations Force and moment balances 3. The attempt at a solution I have tried to construct a proof for this (see attached pdf), but I have not been able to complete it. I intentionally set up the directions of the shear stress components to violate the complementary property of shear, since I would like to show what the directions must be mathematically. I am a third-year mechanical engineering student and I have already taken solid mechanics. This has just always bothered me, and I would like to see a proof for this.