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

Torsional Section Properties

Closed Sections (CHS, RHS, SHS)

For closed hollow sections, St. Venant torsion dominates and warping effects are negligible.

Open Sections (I-sections)

For I-sections, both St. Venant and warping torsion contribute.

Torsional Properties — Standard Sections

CHS Sections

I-Sections

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.

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.

Design Applications

Common Design Scenarios

This reference covers structural design scenarios commonly encountered in structural steel design practice:

• Strength verification: Check member or connection capacity against factored loads per the applicable design code
• Serviceability checks: Verify deflections, vibrations, and other serviceability criteria
• Code compliance: Ensure design meets all provisions of the governing standard
• Connection detailing: Verify weld sizes, bolt quantities, and edge distances

Related Design Considerations

• System behavior: consider the interaction between members and connections
• Load paths: verify that forces can be transferred through the structure to the foundations
• Constructability: check that the design can be fabricated and erected practically
• Cost optimization: evaluate alternative sections or connection types for economy

Worked Example

Problem: Verify a typical steel member for the following conditions:

Typical span: 6.0 m | Load: service loads per applicable code | Section: common section in this category

Design Check:

1. Determine governing load combination (LRFD or ASD per applicable code)
2. Calculate maximum internal forces (moment, shear, axial)
3. Compute nominal capacity per code provisions
4. Apply resistance/safety factors
5. Verify interaction if combined forces exist

Result: Use the results from the Steel Calculator tool to verify design adequacy.

Frequently Asked Questions

What Australian Standard governs structural steel design?

AS 4100-2020 (Steel Structures) is the primary standard for structural steel design in Australia. It covers all aspects of design including member capacity, connections, serviceability, and fire resistance. The standard uses a limit states design philosophy with resistance factors (φ) applied to nominal capacities. Companion standards include AS/NZS 3679.1 for hot-rolled sections, AS/NZS 1554 for welding, and AS/NZS 4600 for cold-formed steel.

What are the common steel grades used in Australian construction?

The most common steel grades for Australian construction are Grade 300 and Grade 350 per AS/NZS 3679.1. Grade 300 (minimum yield 300 MPa for sections > 12 mm thick) is the standard for general structural applications. Grade 350 (minimum yield 340 MPa for sections > 12 mm) is used where higher strength reduces weight. Grade 400 and Grade 450 are available for specialized applications requiring higher strength-to-weight ratios.

How does AS 4100 compare to AISC 360?

Both AS 4100 and AISC 360 use limit states design (LRFD) principles. Key differences include: AS 4100 uses a single "capacity factor" φ approach rather than separate φ for different failure modes; AS 4100 specifies distinct buckling curves for hot-rolled and welded sections; the moment capacity formula in AS 4100 uses αm factor directly rather than Cb; and AS 4100 has more detailed provisions for slender sections and combined actions. Despite philosophical differences, both codes produce similar results for typical members.

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

• Beam Design
• HSS Section Properties
• Column Design
• All European References

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.

Design Resources

Calculator tools

• Torsion Analysis Calculator

Reference pages

• EU Torsion