Beam bending stress

How bending moment and section modulus provide a preliminary elastic stress screening value.

ENGINEERING PRINCIPLE

In elastic bending, normal stress varies linearly from the neutral axis and reaches its maximum at the outer fibre.

σ = M/Z
Structural MechanicsVerifiedReviewed 2026-08-09

Variables and units

  • σ = nominal bending stress (MPa)
  • M = bending moment (N·mm)
  • Z = elastic section modulus (mm³)

Worked example

A 25 kN·m moment on a section with Z = 250,000 mm³ gives σ = 25 × 10⁶ / 250,000 = 100 MPa.

Calculation method

  1. Obtain the governing moment from a load and support model.
  2. Convert moment to N·mm.
  3. Divide by the elastic section modulus about the bending axis.

Practical applications

  • Machine frames
  • Support beams
  • Lifting members and brackets

Review boundary and reference

  • Shear, deflection, lateral stability, connections and load combinations are separate checks.
  • Section properties must match the actual orientation and geometry.

Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.

Source: Elastic flexure formula from standard strength-of-materials references.

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