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Elastic Section Modulus Calculator — result sheet
Calculate second moment of area, elastic section modulus, and simple elastic bending stress for common symmetric cross-sections.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Z = I/c and elastic bending stress = M/Z; rectangle I = b h³/12, solid circle I = pi d⁴/64, hollow circle I = pi(do⁴−di⁴)/64.
The elastic section modulus packages cross-section geometry into a bending-resistance quantity. This tool calculates common symmetric shapes and reports the simple extreme-fiber stress under a stated bending moment.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Cross-section shape — 3 choices
- Rectangle width — mm; minimum 1.0E-6; maximum 1000000
- Rectangle depth — mm; minimum 1.0E-6; maximum 1000000
- Outer diameter — mm; minimum 1.0E-6; maximum 1000000
- Inner diameter — mm; minimum 0; maximum 1000000
- Bending moment — N·m; minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Cross-section shape | rectangle |
| Rectangle width | 100 |
| Rectangle depth | 200 |
| Outer diameter | 100 |
| Inner diameter | 60 |
| Bending moment | 1000 |
Rectangle I = 66.67 million mm⁴; Z = 666,667 mm³; stress ≈ 1.50 MPa.
Assumptions and limits
- Dimensions use millimetres, the section is symmetric about the bending axis, and the moment is converted to N·mm for stress in MPa.
- The material is homogeneous and behaves linearly elastically within small-deflection beam theory.
- Shear deformation, local buckling, plastic behavior, torsion, stress concentrations, lateral restraint, and code compliance 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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