Sizing a steel beam when stiffness, not strength, is the limit
Checking bending capacity and serviceability deflection together, and reading which of the two actually governs the member.
The engineering question
A beam can pass every strength check and still deflect enough to crack ceilings or distort glazing. What decides the section size?
Worked example
The figures below were produced by running the Steel Beam Capacity Calculator with the same inputs — during the build, from its authoritative engine.
| Applied moment | 96 kN·m |
|---|---|
| Bending capacity | 278.817 kN·m |
| Demand / capacity | 0.3443 – |
| Governing criterion | deflection (L/240) |
| Allowable load (governing) | 26.9875 kN/m or kN |
| Deflection under the applied load | 14.8217 mm |
- Applied moment for a uniformly distributed load is wL²/8.
- Bending capacity is 0.66·Fy·Sx — an allowable-stress check, not a code limit state.
- Compare with the load that keeps deflection inside L/240; the smaller of the two governs.
Sanity check
Short spans are usually governed by strength and long spans by deflection. If the deflection limit never governs, the span is too short for it to matter.
Tools for this problem
These are the EngiMetric calculators that compute the numbers in this topic. Each one shows its formula, its units and its limits rather than returning a bare result.
- Steel Beam Capacity Calculator Allowable bending and deflection check for a simply supported steel beam, reporting which criterion governs.
- Beam Deflection Calculator Elastic beam deflection for six support and loading arrangements, compared with the L/240 serviceability limit.
- Section Properties Calculator Area, second moments of area, radii of gyration and section moduli for rectangles, boxes, pipes, I-sections and channels.
Engineering review required
This topic supports professional engineering work; it does not replace a sealed design. The result depends on site data, the governing standard and engineering judgement, and should be confirmed by a competent engineer before it is built.
References & standards
- EN 1993-1-1 (Eurocode 3) — bending and serviceability
- AISC 360 — Specification for Structural Steel Buildings
- SCI P358 / P363 — properties of universal beams and sections
Related problems
Why a column fails long before the steel reaches its yield strength
Euler and Johnson behaviour, the slenderness ratio, and recognising the member that will buckle rather than crush.
Checking a retaining wall will not overturn, slide or sink
The three limit states every retaining wall must satisfy, and which one usually fails first on a narrow base.
Also: Geotechnical