Statics and strength

Calculate bending stress

Determine nominal bending stress, allowable stress, utilization, and required section modulus.

σᵦSI
01

Load and section

02

Results

ƒ(x)

Set the inputs and run the calculation.

Inputs and method

Bending stress from moment and section modulus

Check elastic nominal stress of a section under uniaxial bending.

Inputs

Bending moment M, elastic section modulus W, allowable stress and safety factor are entered.

W represents how far load-carrying material lies from the neutral axis. The same moment gives lower edge stress with larger W; local notches can remove that benefit in the real part.

Calculation

Edge stress is σ = M/W. Required W follows from moment and allowable stress.

Example

10 kNm with W = 50 cm³ gives 200 MPa nominal bending stress.

Sources and limits: Linear beam theory; assess notches, stability, fatigue and combined loading separately.

Mechanical reference

Bending moment at a section

Bending moment M acts about the centroidal axis. Bending stress is zero at the neutral axis and increases linearly in magnitude to σmax at the extreme fibres. Reversing the moment swaps tension and compression.

Bent beamneutral fibreMMCompressionTension
Original schematic. The tension/compression assignment applies to the illustrated moment direction.
Purpose

What the calculator is for

Bending moment and elastic section modulus give the maximum nominal stress. This is useful for quickly comparing candidate beam sections.

Limits

What still needs checking

Valid for linear-elastic uniaxial bending. Notches, fatigue, stability, and combined loading require separate checks.