For the two-dimensional plane stress case (see Exercise 3.5), show that the relationship between the maximum shear stress and von Mises stress is given by τ ² _max = 1/3 (σ²_e—I²₁/4).

Data from exercise 3.5

A two-dimensional state of plane stress in the x, y-plane is defined by σ_z =  τ _yz =  τ _zx = 0. Using general principal value theory, show that for this case the in-plane principal stresses and maximum shear stress are given by:

Transcribed Image Text:

2 ax+ay 012=",+8+(";2) + + - ay - V(22)++ Ox - Oy Tmax =