Mohr’s circle calculator
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Result
σ188.31 MPa
σ2−28.31 MPa
τmax58.31 MPa
θp15.48 °
σθ80.98 MPa
τθ−28.3 MPa
Step-by-step solution
Centre and radius
C = (σx + σy)/2 = 30 MPa
R = √(((σx − σy)/2)² + τxy²) = 58.31 MPa
Principal stresses
σ1,2 = C ± R = 88.31, −28.31 MPa
tan 2θp = 2τxy/(σx − σy) → θp = 15.48°
Stress on the plane at θ
σθ = C + (σx − σy)/2·cos 2θ + τxy·sin 2θ = 80.98 MPa
τθ = −(σx − σy)/2·sin 2θ + τxy·cos 2θ = −28.3 MPa
Key formulas
- Centre
- C = (σx + σy)/2
- Radius
- R = √(((σx − σy)/2)² + τxy²)
- Principal stresses
- σ1,2 = C ± R
- Principal direction
- tan 2θp = 2τxy/(σx − σy)
- Inclined plane
- σθ = C + (σx − σy)/2·cos 2θ + τxy·sin 2θ
Practise Mohr’s circle & stress transformation
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