Bending Stress Calculator
Use this bending stress calculator to estimate section properties and maximum bending stress for the same cross-sections listed on Omni.
Result
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Quick Answer: Maximum bending stress is sigma_max = M / S, where M is the applied bending moment and S is the elastic section modulus of the chosen cross-section.
How to Calculate
- Choose the cross-section: Select the beam shape you want to analyze.
- Enter the section dimensions: Provide the depth, width, thicknesses, or radii required by that shape.
- Enter the bending moment: Use a moment value consistent with the same unit system as the dimensions.
- Review I, c, S, and stress: The calculator reports the section properties and the maximum elastic bending stress.
Formula
sigma_max = M / S = M y_c / I
| Variable | Meaning | Unit |
|---|---|---|
| sigma_max | Maximum bending stress | pressure |
| M | Applied bending moment | force x length |
| S | Section modulus | length^3 |
| I | Area moment of inertia | length^4 |
Worked Examples
Rectangular section - Basic stress check
- Width: 100 mm
- Depth: 200 mm
- Moment: 2,000,000 N mm
Result: sigma_max = 3 N/mm^2
A deeper section increases I and S, which reduces bending stress.
Interpretation Table
| Range | Meaning | Action |
|---|---|---|
| Low stress | Stress is well below allowable or yield values | Continue with other checks such as deflection, shear, and connections. |
| Moderate stress | Stress is meaningful but may still be acceptable | Compare with the design strength required by your code and material. |
| High stress | Section may be undersized or the moment may be too high | Increase section modulus or reduce the applied moment. |
Frequently Asked Questions
Bending stress is the normal stress that develops in a member because of an applied bending moment.
Section modulus measures how efficiently a cross-section resists bending. Larger section modulus means lower stress for the same moment.
Yes. It reports stress from the elastic relation sigma = M y / I or sigma = M / S.
Note: This calculator estimates elastic bending stress only. Design checks should also consider shear, lateral stability, local buckling, stress concentrations, and applicable code factors.
References
Last reviewed: March 14, 2026