Steel Design · 9 min read
How to design and check a steel beam (Eurocode 3 basics)
A practical walk-through of designing a steel beam to BS EN 1993: section choice, bending, shear, deflection, and lateral-torsional buckling.
Designing a steel beam is one of the most common structural tasks you'll do. The good news: the Eurocode 3 process is logical and repeatable. This guide walks through how to size a simply supported steel beam to BS EN 1993-1-1, including the checks engineers most often forget.
What you need before you start
- Span L (m) and support conditions
- Permanent (Gₖ) and variable (Qₖ) loads
- Deflection limits (often L/360 for total or L/200 for imposed)
- Steel grade — usually S275 or S355
- Restraint conditions to the compression flange
Step 1 — Find the design action effects
Combine loads with partial factors from EN 1990. The standard ULS combination is 1.35·Gₖ + 1.5·Qₖ. From the design load wₑd, calculate the maximum design moment Mₑd and shear Vₑd.
Mₑd = wₑd · L² ÷ 8 Vₑd = wₑd · L ÷ 2Step 2 — Trial section selection
Pick a trial UB based on a quick plastic modulus estimate. Required Wₚₗ ≈ Mₑd · γₘ₀ ÷ fy. For S275, fy = 275 N/mm². Check the section properties table and choose a UB whose Wₚₗ,y exceeds the requirement.
Step 3 — Section classification
Class 1 and 2 sections develop their full plastic moment. Class 3 sections are limited to elastic moment, and Class 4 sections need effective properties. Most rolled UBs in S275/S355 are Class 1 in bending — but always check, especially with high axial load.
Step 4 — Bending resistance check
Mc,Rd = Wₚₗ,y · fy ÷ γₘ₀ (Class 1 or 2)γₘ₀ = 1.0 in the UK National Annex. The check is simply Mₑd ÷ Mc,Rd ≤ 1.0. If utilisation is below ~0.5, you're probably oversized and should try a lighter section.
Step 5 — Shear resistance check
Vc,Rd = Av · (fy ÷ √3) ÷ γₘ₀Shear rarely governs for typical floor beams, but it does for short, heavily loaded transfer beams or beams with large point loads near supports.
Step 6 — Lateral-torsional buckling (LTB)
If the compression flange is not fully restrained between supports, the beam can buckle sideways before reaching its plastic moment. Calculate the slenderness λ̄LT, look up the reduction factor χLT, and compute Mb,Rd = χLT · Wₚₗ,y · fy ÷ γₘ₁. If LTB governs, options are: shorter restraint spacing, deeper section, or a section with higher Iz.
Step 7 — Deflection (SLS)
Switch from ULS to SLS loads (typically just Gₖ + Qₖ, no factors). Calculate δ using the standard formula for your load case. Compare against the limit — usually δtotal ≤ L/250 to L/360, depending on what the beam supports.
δ = 5 · w · L⁴ ÷ (384 · E · Iy)Quick worked example
Span L = 6.0 m, wₑd = 18 kN/m (after factoring). Mₑd = 18 · 6² ÷ 8 = 81 kNm. For S275, required Wₚₗ,y ≈ 81 × 10³ ÷ 275 = 295 cm³. A 305×127×42 UB has Wₚₗ,y ≈ 614 cm³ — plenty of capacity, but check deflection: with Iy ≈ 8200 cm⁴ and unfactored w ≈ 12 kN/m, δ ≈ 14 mm = L/430. Comfortably within L/360. Done.
Frequently asked questions
When does lateral-torsional buckling not need to be checked?
When the compression flange is fully restrained — for example, by a composite slab acting compositely with the top flange, or when restraint spacing is short relative to the section's iz. EC3 also gives a simplified check using λ̄LT ≤ 0.4, below which LTB effects can be ignored.
What deflection limit should I use?
EN 1993 doesn't specify limits — they come from the National Annex or client requirements. Common UK values: L/360 for imposed deflection on beams supporting brittle finishes, L/250 for total deflection generally, and L/200 for cantilever tips.
Should I use elastic or plastic section modulus?
Plastic (Wₚₗ) for Class 1 and 2 sections, elastic (Wel) for Class 3, and effective (Weff) for Class 4. Most standard UB and UC sections in S275 are Class 1 in pure bending.