Maximum stress example
Given: M = 5 kN·m, c = 50 mm, I = 8×10⁶ mm⁴
Working: σ = (5,000,000 N·mm × 50 mm) / 8,000,000 mm⁴
σ = 31.25 MPa.
Structural & Mechanical Engineering
Bending Stress Formula
Learn the bending stress formula σ = My/I, its variables, units and assumptions, with worked examples and a live maximum bending-stress calculator.
Governing equation
σ = M × y / I
The elastic flexure formula relates normal bending stress to bending moment, distance from the neutral axis and the section's second moment of area.
For maximum elastic bending stress, y is usually the distance c from the neutral axis to the extreme fibre. The relationship assumes classical linear-elastic beam behaviour within its applicable range.
Live calculator
Maximum bending stress calculator
Uses σ = Mc/I with moment in kN·m and section properties in mm units.
Result
31.25MPa
Elastic maximum flexural stress
Formula variables and units
| Symbol | Meaning | Typical SI unit |
|---|---|---|
| σ | Bending stress | MPa or Pa |
| M | Bending moment at the section | N·m or N·mm |
| y | Distance from neutral axis | m or mm |
| I | Second moment of area | m⁴ or mm⁴ |
How to calculate it
- 1Determine the bending moment at the section of interest.
- 2Locate the neutral axis and extreme-fibre distance.
- 3Calculate the second moment of area about the same bending axis.
- 4Use a consistent unit system.
- 5Apply σ = My/I and compare with the appropriate material/design limit.
Common mistakes
- Mixing N·m with mm-based section properties.
- Using the wrong section axis for I.
- Using total section depth instead of neutral-axis-to-fibre distance.
- Using elastic flexure theory outside its assumptions without further checks.
Worked examples
Section stiffness effect
Given: Same M and c, but I doubles
Working: Stress is inversely proportional to I
Bending stress is reduced by half.
Go deeper
Use the dedicated OneCalcApp tool
The quick calculator above demonstrates the governing equation. Open the related engineering tool for broader inputs, outputs and calculation context where available.
Frequently asked questions
What is the bending stress formula?
For classical elastic beam bending, σ = My/I. Maximum stress uses the extreme-fibre distance c.
What unit is bending stress normally reported in?
In SI engineering work it is commonly reported in pascals or megapascals (MPa).
What is section modulus in the bending formula?
Section modulus Z = I/c, so maximum bending stress can also be written σmax = M/Z.
Does the bending stress formula check beam deflection?
No. Stress and deflection are separate checks even though both depend on section geometry.
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