Mohr circle explorer calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Circle below Mohr–Coulomb envelope — 0.90

Method, formulas and assumptions

• σn = (σx+σy)/2 + (σx−σy)/2·cos2θ + τxy sin2θ
• τ = −(σx−σy)/2·sin2θ + τxy cos2θ
• Mobilised ratio = R/(c′cosφ′ + s sinφ′); ≥ 1 means failure

Related analysis & loading calculators

• Section properties: arbitrary polygon — Area, centroid, second moments, product of inertia, principal axes and section moduli for any polygon given…
• Euler buckling (end conditions) — Critical buckling load and stress for the four classic end conditions.
• Torsion of thin-walled closed sections (Bredt) — Shear flow q = T/(2Ao), wall shear stresses and torsion constant J = 4Ao²/∮ds/t for a rectangular box.
• Strain rosette (0/45/90) — Principal strains, direction and principal stresses (plane stress) from a 0°/45°/90° rosette.
• Thick-walled cylinder (Lamé) — Hoop and radial stresses at the bore and outside surface under internal and external pressure, with von…
• Continuous beam (stiffness method) — Any number of spans with UDLs; exact BMD, SFD, reactions and deflected shape. End fixity selectable.