Solvers/structural/mohrs-circle

Mohr's Circle 2D Stress Transformation Calculator

Transform 2D biaxial stress states to determine principal stresses, maximum shear planes, and equivalent Von Mises stress with a dynamic graphical Mohr's circle.

2D State of Stress (In-Plane)

Normal Stress σ_x [MPa]

Normal Stress σ_y [MPa]

Shear Stress τ_xy [MPa]

Principal Stresses (σ₁, σ₂)

89.5 / -49.5 MPa

Max Shear Stress (τ_max)

69.5 MPa

Von Mises Stress (σ_vM)

122.0 MPa

Interactive Mohr's Circle Graphical Transformation

Radius R = 69.46 MPa

Transformation Formulas

1. Center & Radius of Mohr's Circle

Center coordinate (σ_avg, 0) and radius in 2D stress state.

2. Principal Normal Stresses (σ₁, σ₂)

Maximum and minimum normal stresses acting on planes of zero shear stress.

3. Maximum In-Plane Shear & Principal Orientation

Plane orientation to align with principal stress axes.

4. Von Mises Equivalent Stress

Ductile failure criterion for multiaxial stress states.

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Recommended Reference Handbooks & Standards

Handpicked essential literature for Mohr's Circle 2D Stress Transformation Calculator

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Recommended

Mechanics of Materials

by Ferdinand Beer & E. Russell Johnston

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Governing Equation

Analytical equations compliant with standard university curricula and professional engineering practice codes.