Bending Stress Calculator

Construction

Calculate the maximum bending (flexural) stress in a beam using the flexure formula σ = M·c / I, where M is the bending moment, c is the distance from the neutral axis to the outer fibre, and I is the second moment of area. Enter those three values to find the peak stress on the cross-section.

Formula

σ = M·c / I (equivalently σ = M / S, where S = I / c)
  • The flexure formula σ = M·c / I gives the maximum bending stress at the outer fibre of a beam cross-section.
  • M is the bending moment, c is the distance from the neutral axis to the extreme fibre, and I is the second moment of area (moment of inertia).
  • Section modulus S = I / c, so the stress can also be written as σ = M / S.
  • With M in N·mm, c in mm and I in mm⁴, the stress comes out in N/mm² (MPa).
  • This assumes linear-elastic behaviour and pure bending; compare the result against the material's allowable stress with a suitable safety factor.
  • Bending stress is different from axial stress (F/A) — it arises from a moment, not a direct push or pull.

M = 5,000,000 N·mm, c = 100 mm, I = 20,000,000 mm⁴

Inputs
  • Bending Moment M (N·mm): 5000000
  • Distance to Outer Fibre c (mm): 100
  • Moment of Inertia I (mm⁴): 20000000

σ = (5,000,000 × 100) / 20,000,000 = 25 N/mm² (25 MPa). The section modulus is I/c = 200,000 mm³.

Frequently asked questions

What is bending stress?
It's the stress in a beam caused by a bending moment. The flexure formula σ = M·c/I gives the maximum value, which occurs at the fibre furthest from the neutral axis.
How is it different from axial stress?
Axial stress (F/A) comes from a direct force along the member. Bending stress comes from a moment and varies across the cross-section, peaking at the outer fibres.
What is the section modulus?
Section modulus S = I/c is a geometric property of the cross-section. Using it, bending stress simplifies to σ = M/S — a larger S means lower stress for the same moment.
What units should I use?
If you enter the moment in N·mm, c in mm and I in mm⁴, the stress is in N/mm² (MPa). Keep the unit system consistent throughout.