In three dimensions, the elements of primary stress can be described in Figure 1 where the three normal stresses are shown in σx, σy, and σz and six shear stresses are shown in τxy, τyx, τyz, τzy, τzx, and τxz in positive direction. The condition of biaxial stress or plane stress is shown in Figure 2 which all of them are shown in positive direction. The stress is depicted in xy plane.
 |
| Figure 1: Primary Stress Elements |
 |
| Figure 2: (a) Biaxial Stress (b) Stress on Inclined Cut |
If figure 2 (a) is cut by inclined plane with angle θ to x axis as shown in Figure 2 (b), so by adding all of forces which caused by all of stresses is equal with zero and the equation can be written as follow:
σ = (σx + σy)/2 + ((σx - σy) cos 2θ)/2 + (τxy sin 2θ)
τ = - ((σx - σy) sin 2θ)/2 + (τxy cos 2θ)