Australian Torsion Design — AS 4100 St. Venant and Warping Guide
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Reference for torsional design of steel members per AS 4100:2020. Covers St. Venant (uniform) torsion, warping torsion, combined torsion and bending for spandrel beams, crane girders, and eccentrically loaded members.
Torsional Behavior
| Section Type | St. Venant J | Warping Iw | Torsional Behavior |
|---|---|---|---|
| CHS (tube) | High | None | Pure St. Venant — most efficient |
| SHS/RHS | Medium | Low | Mostly St. Venant |
| I-section (UB) | Low | High | Warping dominates (80-90%) |
| UC (compact) | Low | Medium | Significant warping |
| Channel (PFC) | Very low | Moderate | Warping + bending |
| Angle (EA) | Very low | Very low | Avoid torsion |
Design Approach
Total torsional moment: Mz = Mt (St. Venant) + Mw (warping)
St. Venant torque: Mt = G × J × φ′ Warping torque: Mw = −E × Iw × φ′′′
Stresses:
- Shear from St. Venant torsion: τs = Mt × t / J
- Normal from warping: σw = Mw × w / Iw (w = warping function)
- Shear from warping: τw = Mw × Sw/(Iw × t) (Sw = warping statical moment)
Capacity Check — Combined Torsion + Bending
AS 4100 Clause 5.6.2 — Interaction:
σ_max = |Mx*/Zx + My*/Zy + Mw*/Ww| ≤ φ × fy
τ_max = |Vx*/Ax + Vy*/Ay + Mt×t/J + Mw×Sw/(Iw×t)| ≤ φ × 0.6 × fy
Von Mises combined: √(σ² + 3τ²) ≤ φ × fy
Worked Example
Problem: 310UB46.2 spandrel beam, 6 m span. Uniformly distributed torsion mz=0.5 kNm/m (from eccentrically supported cladding). Check torsion.
Solution:
- J for 310UB46.2: J = Σ(bt³/3) = 127×10³ mm⁴
- Iw = Iy × (d-tf)²/4 = 1.49×10¹² mm⁶
- Max torque at support: Mz = mz × L/2 = 0.5×3 = 1.5 kNm
- Warping dominates for I-section: σw typically governs at flange tips
- σw at midspan: ≈ 25 MPa (torsional normal stress)
- Compare with bending stress σx ≈ 80 MPa (assuming V* governs)
- Combined: √(80² + 3×τ²) or direct sum σ_max = 80+25 = 105 MPa < 0.90×300 = 270 MPa OK
- Note: Torsion usually not critical for this magnitude. For heavy torsion (crane girders), use CHS or closed section.
Design Resources
- [[Australian Steel Grades|/reference/australian-steel-grades/]] | [[Australian Steel Properties|/reference/australian-steel-properties/]] | [[Australian Beam Sizes|/reference/au-beam-sizes/]] | [[Australian Bolt Capacity|/reference/australian-bolt-capacity/]] | [[AS 4100 Beam Design|/reference/as4100-beam-design-example/]] | [[All Australian References|/reference/]]
FAQ
What sections resist torsion best? Closed sections (CHS, SHS) are most efficient with high St. Venant torsional constant J. I-sections are poor in torsion — warping dominates.
When is torsional analysis required? Spandrel beams (eccentric cladding), crane runway girders (eccentric wheel load), and beams supporting eccentric loads. Per AS 4100 Clause 5.6.2.
How is warping torsion different from St. Venant torsion? St. Venant produces pure shear flow (uniform). Warping produces flange bending and normal stresses (non-uniform). I-sections resist load primarily through warping.
Educational Use Only — This reference is for educational and preliminary design purposes only. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) in accordance with AS 4100:2020 and all applicable Australian Standards. Results are not for construction.