Mohr's Circle for Plane Stress

Mechanical Engineering

How It Works

Mohr's circle is a two-dimensional graphical representation of stress tensor transformations under arbitrary planar coordinate rotations. For a given state of plane stress (σ_x, σ_y, τ_xy), the circle's center lies at average normal stress σ_avg, and its radius represents maximum in-plane shear stress τ_max. The principal stresses (σ₁ and σ₂) occur at zero shear stress where the circle intersects the horizontal normal stress axis.

Governing Equation
σ_avg = (σ_x + σ_y) / 2 , R = √(((σ_x - σ_y) / 2)² + τ_xy²) , σ₁,₂ = σ_avg ± R