TOOLS / STRUCTURAL

Beam bending stress and required section modulus calculator

Screen a beam section: bending stress from the maximum moment, how much of your allowable stress it uses, and the section modulus it would need — as a screening check, not a design.

Bending stress σ = M / S100.0 MPa

Maximum moment: 20.00 kN·m · Utilisation of your entered allowable: 66.7% · Required section modulus at that allowable: 133.3 cm³.

SAFETY-CRITICAL SCREENING ONLY — not a structural design, approval or compliance check. The allowable stress above is entered by you; no code limit is built into this tool. Deflection, shear, buckling, lateral-torsional stability, connections, load factors and the governing code must all be checked by a qualified structural engineer before any real structure is built.

Formula

Bending stress σ = M ÷ S. Maximum moment M: simply supported uniform load, M = wL² ÷ 8; simply supported centre point load, M = PL ÷ 4; or entered directly. Required section modulus S_required = M ÷ σ_allowable. Utilisation = σ ÷ σ_allowable.

Standard / source

Bending-stress principles per AISC 360 and EN 1993-1-1. No code allowable stress is hard-coded in this tool: the allowable is entered by you from your project specification or engineer, because limits depend on the code, load combination and member type.

Worked example

Uniform load 10 kN/m over a 4 m simply supported span: M = 10 × 4² ÷ 8 = 20 kN·m = 20,000,000 N·mm. With S = 200 cm³ = 200,000 mm³: σ = 20,000,000 ÷ 200,000 = 100.0 MPa. At a user-entered allowable of 150 MPa: utilisation = 100 ÷ 150 = 66.7%, and S_required = 20,000,000 ÷ 150 ÷ 1,000 = 133.3 cm³. These are the calculator's default inputs, so it shows 100.0 MPa on load.

Safety note — qualified-person gate

SAFETY-CRITICAL SCREENING ONLY — not a structural design, approval or compliance check, and never labelled as such. Deflection, shear, buckling, lateral-torsional stability, connections, load factors and the governing code are all outside this tool. A qualified structural engineer must check the member before any real structure is built, and a result over your entered allowable must not be used.