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Curved Beam Circumferential Fibre Stress Calculator

Calculate circumferential fibre stress in a curved beam using the Winkler-Bach theory.

Your inputs

Change any value to update the result instantly.

Mechanical & Civil Engineering
N·mm
mm²
mm
mm
mm

Circumferential fibre stress

5 MPa

Eccentricity e

5 mm

Centroidal radius

150 mm

Neutral axis radius

145 mm

What this calculator does

Curved Beam Circumferential Fibre Stress Calculator: Applies the standard mechanics-of-materials relationship for this load case so a student can see how the stress, strain or deflection follows from the geometry and the load.

What your result means

The headline figure tells you how hard the material is being worked, or how much it moves, under the load you entered. Compare it with the allowable value for your material and required factor of safety.

Formula and working

σ = M(R - rn) / (A·e·r)

  1. 1

    Collect the inputs

    Bending moment = 500,000 N·mm; Cross-section area = 1,000 mm²; Centroidal radius = 150 mm; Neutral axis radius = 145 mm; Fibre radius = 100 mm

  2. 2

    Apply the formula

    σ = M(R - rn) / (A·e·r)

  3. 3

    Result

    Circumferential fibre stress = 5 MPa

Frequently asked questions

Symbols and assumptions

M
Bending moment (N·mm)
A
Cross-section area (mm²)
R
Centroidal radius (mm)
rn
Neutral axis radius (mm)
r
Fibre radius (mm)
  • • The material is homogeneous, isotropic and loaded within its linear-elastic range.
  • • Inputs are entered in a consistent unit system, as labelled on each field.

Sources and review

Reviewed 2026-09-22 · Next review 2027-09-22

Mechanics of Materials — axial stress and strain, torsion, bending, combined loading and stress transformationEngineering LibreTextsShigley's Mechanical Engineering Design — stress, deflection, fatigue, shafts, springs, gears, bearings and fastenersBudynas & Nisbett, McGraw-HillNIST Special Publication 811 — Guide for the Use of the International System of UnitsUS National Institute of Standards and Technology
  • • This is an educational estimate for learning and checking, not a design deliverable.
  • • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
  • • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.

Important limitation

This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.

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