How to Calculate Bending Stress
What is Bending Stress?
Bending stress is normal stress from moment loading, the primary stress in beams. It varies linearly across the section, maximum at outer fibers.
Formula
Calculate: σ = M×c/I where M is moment, c is distance from neutral axis, I is moment of inertia
- M
- I/c) — I/c)
- I
- I value — Variable used in the calculation
Step-by-Step Guide
- 1Calculate: σ = M×c/I where M is moment, c is distance from neutral axis, I is moment of inertia
- 2Or: σ = M/S where S is section modulus (S = I/c)
- 3Results show stress distribution
Worked Examples
Input
M = 50 kN·m, I = 1×10⁹ mm⁴, c = 200 mm
Result
σ = 10 MPa at extreme fiber
Safe stress level
Common Mistakes to Avoid
- ✕Using average stress instead of maximum stress
- ✕Forgetting compression and tension can develop simultaneously
Frequently Asked Questions
Why does stress vary across the beam?
Outer fibers experience maximum stretch/compression; inner material near neutral axis experiences less.
How is section modulus useful?
S directly gives maximum stress: σ_max = M/S, simpler than calculating I and c separately.
Ready to calculate? Try the free Bending Stress Calculator
Try it yourself →