Bending Stress Calculator
Use this bending stress calculator to help you find the bending stress on a beam of any typical cross-section and dimensions, given the bending moment it experiences.
Bending stress416.67 psi2.873 MPa
Section modulus (S)12 in³I ÷ c
Second moment of area (I)36 in⁴b d³ ÷ 12
Distance to the extreme fibre (c)3 in
Bending moment5,000 lb·in416.67 lb·ft · 564.93 N·m
Moment this section could take at 1,200 psi14,400 lb·intypical allowable for construction-grade timber
Moment at 24,000 psi288,000 lb·intypical allowable for structural steel
Stress in the compression face416.67 psiequal and opposite to the tension face on a symmetric section
The formula
σ = M ÷ S, where S = b d² ÷ 6 for a rectangle
Only the outer fibres work hard
Bending stress is zero at the neutral axis and greatest at the surface, growing linearly with distance from the centre. That is why an I-beam puts most of its metal in the flanges and why a hollow tube is nearly as strong as the solid bar it came from — the material near the middle is barely stressed.
It also explains the d² in the section modulus for a rectangle: doubling the depth doubles the lever arm and doubles the area available at that arm.