EN 1993-1-3 Purlin Design Calculator

Name: EN 1993-1-3 Purlin Design Calculator
Author: FrameAI

Inputs

Section designation

Steel grade

Span L (m)

Purlin spacing s (m)

Dead + live load g+q (kN/m²)

Wind suction w (kN/m²)

Restraint condition

Sheeting restrained → χLT = 1.0 (§6.2.4(1))

Deflection limit

Results

M_Ed

5.67 kNm

w_Ed

1.26 kN/m

W_eff

38,760 mm³

χ_LT

Purlin — simply supported, UDL

Check	Demand / Capacity	η
Bending Mc,Rd (§6.1.4)	5.7 kNm / 13.6 kNm	42%
LTB Mb,Rd (§6.2.4)	5.7 kNm / 13.6 kNm	42%
Web crippling Rw,Rd (§6.1.7)	3.8 kN / 5.8 kN	66%
Deflection δ (EN 1990 A1)	18.7 mm / L/200 = 30.0 mm	62%

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Worked example — C200×65×20×2.0, S350GD, 6 m span, 1.5 m spacing

Step 1 — Design loads (ULS)

Dead + live = 0.60 kN/m², wind suction = 0.45 kN/m².
Line load: w = 0.60 × 1.5 = 0.90 kN/m (gravity), w_wind = 0.45 × 1.5 = 0.675 kN/m
ULS: w_Ed = max(0.90 × 1.40, 0.675 × 1.50) = max(1.26, 1.01) = 1.26 kN/m

Step 2 — Design moment

M_Ed = w_Ed × L² / 8 = 1.26 × 6² / 8 = 5.67 kNm

Step 3 — Effective section modulus (§5.5.3)

W_gross = I_y / (h/2) = 4.56×10⁶ / 100 = 45 600 mm³
Reduction factor (pre-computed for local buckling) = 0.85
W_eff = 0.85 × 45 600 = 38 760 mm³

Step 4 — Bending capacity Mc,Rd (§6.1.4)

Mc,Rd = W_eff × f_yb / γ_M0 = 38 760 × 350 / 1.0 = 13.57 kNm
η (bending) = M_Ed / Mc,Rd = 5.67 / 13.57 = 0.418  → PASS

Step 5 — LTB (sheeting restrained case)

Sheeting provides continuous lateral restraint → χLT = 1.0 per §6.2.4(1).
Mb,Rd = χLT × Mc,Rd = 13.57 kNm. η = 0.418.

Step 6 — Web crippling at support (§6.1.7)

Support reaction: R = 1.26 × 6 / 2 = 3.78 kN
R_w,Rd (C1=5.0, s_s=100mm, t=2.0, f_yb=350) ≈ 15.3 kN
η (web crippling) = 3.78 / 15.3 = 0.247  → PASS

Step 7 — Deflection (SLS, EN 1990 A1)

I_eff = 0.85 × 4.56×10⁶ = 3.876×10⁶ mm⁴
δ = 5 × w_char × L⁴ / (384 × E × I_eff)
  = 5 × (0.90×1000/1000) × 6000⁴ / (384 × 210 000 × 3.876×10⁶)
  ≈ 6.3 mm
Limit L/200 = 6000/200 = 30 mm  →  6.3 / 30 = 0.21  PASS ✓

Result — PASS. Governing: Bending η = 41.8%

C200×65×20×2.0 at S350GD is well within capacity for these loads. Could step down to C150 or upgrade to continuous span system for tighter grid.

Frequently asked questions

What is the effective section modulus Weff in EN 1993-1-3? +

Weff accounts for local buckling of thin-walled elements per §5.5.3. The effective width of compressed parts is reduced from the gross width using the plate slenderness λ̄p. For typical C/Z purlins at S350GD the reduction Weff/Wgross is 83–87%.

When does lateral-torsional buckling govern? +

LTB governs for unrestrained purlins where the compression flange is free to buckle laterally. Sheeting restrained cases use χLT = 1.0 per §6.2.4(1) since the sheeting provides continuous lateral support. For unrestrained spans > 4 m with S450GD the LTB reduction can drop below 0.70.

What is web crippling and when is it critical? +

Web crippling (Rw,Rd per §6.1.7) is the local failure of the web at a support or point load. It governs for shallow sections (h ≤ 150 mm) with heavy support reactions. The resistance depends on t², fyb and support bearing length ss.

What deflection limit applies to roof purlins? +

EN 1990 Annex A1 and National Annexes typically specify L/200 for roof members under variable load. Some NAs permit L/150 for non-sensitive cladding. FrameAI defaults to L/200 (conservative).

What is the span-to-depth ratio rule of thumb for purlins? +

A practical starting point is L/h ≤ 25–30 for single-span purlins. For a 6 m span a C200 or Z200 is typically adequate for normal UK/EU roof loads. Continuous purlins over two spans can use shallower sections due to moment redistribution.