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Mohr's Circle — Plane Stress

Principal stresses σ₁,₂ = (σₓ+σy)/2 ± R, R = √[((σₓ−σy)/2)² + τₓy²]; τ_max = R; von Mises = √(σ₁²−σ₁σ₂+σ₂²). Stresses in MPa.

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σₓ (MPa)

σy (MPa)

τₓy (MPa)

σ₁ (MPa)

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σ₂ (MPa)

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τ max, in-plane (MPa)

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von Mises (MPa)

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θp (°)

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τ max, absolute (MPa)

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Plane stress. The absolute τ max counts the out-of-plane stress σ₃ = 0, so it exceeds the in-plane value (the circle's radius) whenever σ₁ and σ₂ share a sign — it is the one to use for Tresca. A helper, not a substitute for engineering judgment.