Bending Stress Calculator
Bending stress is greatest at the outer fibre, σ = My/I: a 100 × 200 mm rectangle under 20 kN·m has σ = 30 MPa.
30 MPa
- Second moment of area I
- 66666700 mm⁴
- Extreme fibre distance y
- 100 mm
- Section modulus Z = I/y
- 666667 mm³
Step-by-step solution
- σ = M y / I = M / Z
- I = bh³/12 = 100 × 200³ ÷ 12 = 66666700 mm⁴
- σ = 20000000 N·mm × 100 mm ÷ 66666700 mm⁴ = 30 MPa
Bending Stress Formula
σ = M y / I = M / Z
M bending moment, y distance from the neutral axis, I second moment of area, Z = I/y
Worked Example
A 100 × 200 mm rectangular beam carrying a 20 kN·m bending moment:
- σ = M y / I = M / Z
- I = bh³/12 = 100 × 200³ ÷ 12 = 66666700 mm⁴
- σ = 20000000 N·mm × 100 mm ÷ 66666700 mm⁴ = 30 MPa
Extreme fibre distance y: 100 mm · Section modulus Z = I/y: 666667 mm³
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Frequently asked questions
What is the section modulus of a rectangle?
Z = I/y = bh²/6. For a solid circle it is πd³/32, so σ = 32M/πd³.
Where is bending stress zero?
At the neutral axis, which passes through the centroid of the section; stress grows linearly to its maximum at the outer fibres.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Bending Stress Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/bending-stress-calculator/
IEEE
Scientific Converters, "Bending Stress Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/bending-stress-calculator/