EN 1993 Torsion Design — Torsional Resistance per Eurocode 3 Cl. 6.2.7
Complete guide to torsional design of steel sections per EN 1993-1-1:2005 Clause 6.2.7. St. Venant (uniform) torsion constant J, warping torsion constant I_w, bimoment B, combined bending and torsion interaction. Torsional properties for I-sections, CHS, RHS, and SHS sections. Worked example for an eccentrically loaded cantilever beam.
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Types of Torsion
| Type | Description | Dominant in |
|---|---|---|
| St. Venant (uniform) torsion | Pure twist, free warping, shear stress only | CHS, RHS, closed sections |
| Warping torsion | Restrained warping, normal + shear stress | I-sections, open sections |
| Combined torsion | St. Venant + warping | All open sections |
Torsional Section Properties
Closed Sections (CHS, RHS, SHS)
For closed hollow sections, St. Venant torsion dominates and warping effects are negligible.
| Section | Torsion Constant J |
|---|---|
| CHS | J = pi x (D^4 - (D-2t)^4) / 32 |
| RHS/SHS | J = 4 x A_0^2 / sum(b/t) |
Open Sections (I-sections)
For I-sections, both St. Venant and warping torsion contribute.
| Section | J (approx) | I_w (warping constant) |
|---|---|---|
| I-section | J = sum(b x t^3 / 3) | I_w = I_z x h_s^2 / 4 |
Torsional Properties — Standard Sections
CHS Sections
| Section | D (mm) | t (mm) | J (cm4) | tau per unit torque (MPa/Nm) |
|---|---|---|---|---|
| CHS 88.9x5 | 88.9 | 5.0 | 236 | 0.75 |
| CHS 114.3x6 | 114.3 | 6.0 | 620 | 0.55 |
| CHS 139.7x8 | 139.7 | 8.0 | 1460 | 0.38 |
| CHS 168.3x8 | 168.3 | 8.0 | 2660 | 0.30 |
| CHS 219.1x10 | 219.1 | 10.0 | 7300 | 0.19 |
I-Sections
| Section | J (cm4) | I_w (cm6) | Behaviour |
|---|---|---|---|
| IPE 200 | 6.98 | 6360 | Warping dominant |
| IPE 330 | 20.1 | 49700 | Warping dominant |
| IPE 500 | 53.4 | 385000 | Warping dominant |
| HEA 200 | 24.8 | 43000 | Warping dominant |
| HEB 200 | 34.7 | 78800 | Warping dominant |
| HEB 300 | 112 | 491000 | Warping dominant |
Combined Bending and Torsion (Clause 6.2.7)
For sections subject to combined bending and torsion:
(M_Ed / M_c,Rd)^2 + (B_Ed / B_Rd)^2 + (T_Ed / T_Rd)^2 <= 1.0
Where:
- M_Ed = design bending moment
- M_c,Rd = design bending resistance
- B_Ed = design bimoment (warping)
- B_Rd = warping resistance = f_y x W_w
- T_Ed = design torsional moment
- T_Rd = design torsional resistance
Worked Example — Eccentrically Loaded Cantilever Beam
Cantilever beam, 3.0 m span. HEA 200, S355 steel. Point load at tip: 20 kN, 150 mm eccentricity. T_Ed = 20 x 0.15 = 3.0 kNm.
| Property | Value |
|---|---|
| W_pl,y | 583 cm3 |
| J | 24.8 cm4 |
| I_w | 43000 cm6 |
St. Venant contribution: T_T,Ed = 3.0 x (24.8 / (24.8 + 47100)) = 0.0016 kNm (negligible) Warping contribution: T_W,Ed = 3.0 - 0.0016 = 2.998 kNm (dominant)
Bimoment at support: B_Ed = 2.998 x 3.0 / 2 = 4.50 kNm2
Combined check: (60/207)^2 + 0 + (3.0/3.5)^2 = 0.084 + 0 + 0.73 = 0.81 < 1.0 OK
The torsional component dominates the interaction despite being only 3.0 kNm.
Frequently Asked Questions
What is the difference between St. Venant torsion and warping torsion?
St. Venant (uniform) torsion occurs when warping is unrestrained, with resistance through shear stress circulation (governed by J). Closed sections (CHS, RHS) have high J and resist torsion efficiently. Warping torsion occurs when warping is restrained, developing normal stresses (governed by I_w). Open sections (I-beams) predominantly resist torsion through warping action.
When is torsional design required per EN 1993-1-1?
Torsional design per Clause 6.2.7 is required for: edge beams supporting cantilever slabs, eccentrically loaded beams, crane runway girders with lateral loads, curved beams, and spandrel beams. For typical simply supported I-beams with concentric loading, torsional effects are small and may be neglected.
Related Pages
Educational reference only. Torsional design per EN 1993-1-1:2005 Clause 6.2.7. Verify combined interaction with applicable National Annex. Results are PRELIMINARY - NOT FOR CONSTRUCTION without independent verification.
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