Bending Stress Calculator
Find bending stress from moment and section, and check it against yield.
Please note: These are idealised textbook models using representative material data. They are for study, sizing and sanity-checking only — never for final design. Real engineering requires code-compliant analysis, verified material certificates and a qualified engineer’s sign-off.
What the Bending Stress Calculator does
Bending stress is the moment divided by the section modulus — a single number describing how efficiently a shape resists bending. Because the section modulus already folds in both the shape’s stiffness and how far its outer fibres sit from the neutral axis, comparing sections is just comparing that one figure.
Formula
σ = M ÷ SS = I ÷ cM capacity = σ_allowable × SSafety factor = Yield strength ÷ σ
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Solve for | one of 2 options | Yes | — |
| Bending moment | kN·m | In some modes | Accepts more than 0. Shown in 5 of the 10 modes. |
| Allowable stress | MPa | In some modes | Accepts more than 0. Shown in 5 of the 10 modes. |
| Material | one of 13 options | Yes | — |
| Cross-section | one of 5 options | Yes | — |
| Width | number | In some modes | Shown in 6 of the 10 modes. |
| Width unit | one of 9 options | In some modes | Shown in 6 of the 10 modes. |
| Height / depth | number | In some modes | Shown in 6 of the 10 modes. |
| Height / depth unit | one of 9 options | In some modes | Shown in 6 of the 10 modes. |
| Outer diameter | number | In some modes | Shown in 4 of the 10 modes. |
| Outer diameter unit | one of 9 options | In some modes | Shown in 4 of the 10 modes. |
| Inner diameter | number | In some modes | Shown Solve for is Stress from a known moment and Cross-section is Round tube (hollow circle), or Solve for is Moment the section can carry and Cross-section is Round tube (hollow circle). |
| Inner diameter unit | one of 9 options | In some modes | Shown Solve for is Stress from a known moment and Cross-section is Round tube (hollow circle), or Solve for is Moment the section can carry and Cross-section is Round tube (hollow circle). |
| Wall thickness | number | In some modes | Shown Solve for is Stress from a known moment and Cross-section is Rectangular hollow section, or Solve for is Moment the section can carry and Cross-section is Rectangular hollow section. |
| Wall thickness unit | one of 9 options | In some modes | Shown Solve for is Stress from a known moment and Cross-section is Rectangular hollow section, or Solve for is Moment the section can carry and Cross-section is Rectangular hollow section. |
| Flange thickness | number | In some modes | Shown Solve for is Stress from a known moment and Cross-section is I-beam / wide flange, or Solve for is Moment the section can carry and Cross-section is I-beam / wide flange. |
| Flange thickness unit | one of 9 options | In some modes | Shown Solve for is Stress from a known moment and Cross-section is I-beam / wide flange, or Solve for is Moment the section can carry and Cross-section is I-beam / wide flange. |
| Web thickness | number | In some modes | Shown Solve for is Stress from a known moment and Cross-section is I-beam / wide flange, or Solve for is Moment the section can carry and Cross-section is I-beam / wide flange. |
| Web thickness unit | one of 9 options | In some modes | Shown Solve for is Stress from a known moment and Cross-section is I-beam / wide flange, or Solve for is Moment the section can carry and Cross-section is I-beam / wide flange. |
| Required safety factor | number | Optional | Accepts 0.1 or more. |
How to use it
- Choose Solve for and Material.
- Fill in the remaining inputs the form shows for your choice.
- Optionally add Required safety factor.
- Select Calculate.
Worked example
A 5.625 kN·m moment on a 100 × 200 mm steel rectangle.
- Moment
- 5.625 kN·m
- Section
- 100 × 200 mm
- Material
- Structural steel
S = 666,667 mm³, so σ = 5,625 ÷ 0.000667 = 8.44 MPa. Against 250 MPa yield that is a safety factor of 29.6.
Frequently asked questions
What is section modulus?
Second moment of area divided by the distance to the extreme fibre. It captures a shape’s bending resistance in one number, so stress is simply moment divided by it.
Why are I-beams shaped that way?
Bending stress is proportional to distance from the neutral axis, so material at the centre does almost nothing. Moving it into flanges far from the axis buys stiffness for very little weight.
Method and sources
Method. Bending stress as moment over section modulus, σ = M ÷ S, with the section modulus derived from the geometry entered.
Assumptions
- Plane sections remain plane, the material is linear-elastic, and bending is about a principal axis.
Limitations
- Valid below the elastic limit only; beyond yield the linear distribution this assumes no longer holds.
- Stress concentrations at holes, notches and section changes are not modelled and can multiply local stress several times.
- Combined loading — bending with torsion or axial force — needs the stresses combined, which this does not do.
Sources
- The design code governing the component, and classical beam bending theory — Varies by jurisdiction and material. The permissible stress and safety factors. The stress relationship itself is standard mechanics of materials.