When a beam bends, fibres on one side are stretched and on the other compressed. The stress is zero at the neutral axis and largest at the outer fibre, a distance c away. Comparing the maximum bending stress with the allowable or yield stress of the material tells you if the beam is strong enough.
How to use the Bending Stress Calculator
- Cross-section
- Width b / flange width
- Height h
- Outer diameter
- Inner diameter
- Wall thickness / flange thickness
- Web thickness
- Bending moment
- Every result field is editable: type into Maximum bending stress and Bending moment plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Choose the cross-section, enter its dimensions and the bending moment. The calculator works out I, c and the section modulus S and the maximum stress. Type an allowable stress into the result to find the moment the section can carry.
Tips for an accurate estimate
- Keep units consistent – the calculator handles conversions, but check every field’s unit before reading a result.
- Use values from standards, data sheets or test pieces whenever you have them; typical values are only a starting point.
- Apply appropriate safety factors and have structural, electrical and pressure work checked by a qualified professional.
- Record the inputs you used so the calculation can be reviewed later.
Common mistakes to avoid
- Confusing diameter and radius, or nominal and actual sizes.
- Using allowable stresses and ultimate strengths interchangeably.
- Treating rule-of-thumb results as a substitute for code tables or an engineered design.
Inputs explained
| Field | What to enter |
|---|---|
| Cross-section | Choose one: Solid rectangle, Solid circle, Hollow circle (tube), Rectangular hollow section … |
| Width b / flange width | Units: mm, in, cm |
| Height h | Units: mm, in, cm |
| Outer diameter | Units: mm, in, cm |
| Inner diameter | Units: mm, in, cm |
| Wall thickness / flange thickness | Units: mm, in, cm |
| Web thickness | Units: mm, in, cm |
| Bending moment | Units: N·m, kN·m, lbf·ft, lbf·in |
What each result means
- Section modulus = [Moment of inertia]÷[Distance to outer fibre]
- Maximum bending stress = [Bending moment]×[Distance to outer fibre]÷[Moment of inertia]
Example values
How the main result changes when Bending moment changes and everything else stays at the example values above:
| Bending moment (N·m) | Maximum bending stress (MPa) |
|---|---|
| 1,000 | 12 |
| 1,500 | 18 |
| 2,000 | 24 |
| 2,500 | 30 |
| 3,000 | 36 |
| 4,000 | 48 |
Formula
σ = M × c ÷ I = M ÷ SRectangle: I = b h³ ÷ 12; circle: I = π d⁴ ÷ 64; tube: I = π (D⁴ − d⁴) ÷ 64Rectangular hollow: I = (B H³ − (B − 2t)(H − 2t)³) ÷ 12; I-beam: I = (b h³ − (b − t_w)(h − 2t_f)³) ÷ 12Worked example
Inputs — Cross-section: Solid rectangle; Width b / flange width: 50 mm; Height h: 100 mm; Outer diameter: 60 mm; Inner diameter: 50 mm; Wall thickness / flange thickness: 8 mm; Web thickness: 6 mm; Bending moment: 2,000 N·m.
Results — Moment of inertia = 416.67 cm⁴; Distance to outer fibre = 50 mm; Section modulus = 83.33 cm³; Maximum bending stress = 24 MPa.
Frequently asked questions
What is the bending stress formula?
σ = M·c/I, where M is the bending moment, c the distance to the outer fibre and I the moment of inertia.
What is the section modulus?
S = I/c; the bending stress is simply M/S.
How do I know if the stress is acceptable?
Compare with the allowable stress – for structural steel often about 0.6 × yield (≈ 150–165 MPa for S235/A36).
What formula does the Bending Stress Calculator use?
σ = M × c ÷ I = M ÷ S.