Stress Equation

At the stress component, the equations of normal stress (σ) and shear stress (τ) as following below:

Equation 1       → σ = (σ_x + σ_y)/2  +  ((σ_x - σ_y) cos 2θ)/2 + (τ_xy sin 2θ)

Equation 2       → τ = - ((σ_x - σ_y) sin 2θ)/2 + (τ_xy cos 2θ)

The equation 1 is derived to θ and make the result equal to zero will be obtained the following stress equation:

Equation 3       → σ₁, σ₂ = (σ_x + σ_y)/2  ±  √(((σ_x - σ_y)/2)² + τ_xy²)

Equation 4       → τ₁, τ₂ = ±  √(((σ_x - σ_y)/2)² + τ_xy²)

σ₁ shows maximum normal stress and σ₂ shows minimum normal stress. Meanwhile τ₁ shows maximum shear stress and τ₂ shows minimum shear stress. From stress equation 3 and stress equation 4, Mohr Circle can be made as shown in Figure 1 below. 

Figure 1: Mohr Circle