Mohr's Circle — Stress & Strain

Analysis — Stress & Strain

Mohr’s Circle

2D Stress State 2D Strain State Principal stresses Stress transformation

Stress State

σx

σy

τxy

Units: (optional label, does not affect calculation)

Mohr’s Circle

Principal Values & Key Results

MPa

Parameter	Formula	Value

Stress Transformation — Rotate Element by θ

θ (degrees) 0°

Or type: °

σ_x′

—

σ_y′

—

τ_x′y′

—

Sign Convention & Notes

Normal stress σ: positive = tension, negative = compression.
Shear stress τ_xy: positive = acts in +y direction on the +x face (counterclockwise tendency on element).
Principal stresses σ₁ ≥ σ₂ (algebraically). Principal planes have zero shear stress.
θ_p: angle from the x-axis to the σ₁ principal axis, measured counterclockwise positive.
Maximum shear stress τ_max occurs on planes at ±45° to the principal planes (θ_s = θ_p + 45°).
Strain mode: inputs are ε_x, ε_y, γ_xy (engineering shear strain). Mohr’s circle for strain uses γ/2 on the vertical axis. Output γ_max = 2R.
Transformation: σ_x′ = σ_c + (σ_x−σ_y)/2 · cos 2θ + τ_xy · sin 2θ. Positive θ = CCW rotation of element.

Disclaimer: For educational and preliminary analysis only. Verify all results before use in design. Not a substitute for professional engineering advice.