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Mohr’s Circle Plane-Stress Calculator — result sheet
Calculate the center, radius, principal stresses, and maximum in-plane shear stress for a plane-stress state.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Center=(σx+σy)/2; radius=√[((σx−σy)/2)²+τxy²]; principal stresses=center±radius.
Mohr’s circle converts a plane-stress state into its average stress, principal extremes, and maximum in-plane shear magnitude.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Normal stress σx — Pa; minimum -1.0E+15; maximum 1.0E+15
- Normal stress σy — Pa; minimum -1.0E+15; maximum 1.0E+15
- Shear stress τxy — Pa; minimum -1.0E+15; maximum 1.0E+15
Worked example
| Input | Value |
|---|---|
| Normal stress σx | 80000000 |
| Normal stress σy | 20000000 |
| Shear stress τxy | 10000000 |
Center =50 MPa; principal stresses ≈81.62 MPa and 18.38 MPa; max shear ≈31.62 MPa.
Assumptions and limits
- The input describes a two-dimensional plane-stress state with a consistent sign convention.
- The principal-stress results are mathematical transformations of the entered components.
- Three-dimensional stress, material failure criteria, stress concentrations, and design codes are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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