Mohr's Circle Stress Transformation

Civil Engineering

How It Works

Mohr's circle is a geometric representation of 2D plane stress transformation equations. As a structural element rotates through an arbitrary angle θ, the resulting normal stress σ and shear stress τ trace a circle in the stress plane. The circle's center corresponds to the average normal stress, while intersections with the horizontal axis denote the principal stresses where shear stress vanishes.

Governing Equation
(σ - σ_avg)² + τ² = R²  |  σ₁,₂ = (σ_x + σ_y)/2 ± √[((σ_x - σ_y)/2)² + τ_xy²]