Steel · Members & beams
Steel I-beam in torsion with warping calculator
UB or UC simply supported with fork ends (twist prevented, warping free) carrying an eccentric point load at midspan plus a UDL. The torque is resisted by St Venant and warping torsion in proportion set by a = √(EIw/GJ). The tool gives the twist at midspan, warping normal stress (E·Wn·φ″), St Venant and warping shear at the supports, the minor-axis stress induced by the twist (φ·Mx/Zy), and combines them with the bending and shear stresses.
Standard: SCI P385 (torsion of steel beams) closed forms for a central point torque with fork supports · AS 4100 elastic stress limits (0.9fy, 0.9 × 0.6fy)
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Section | 310UC118 | |
| Span | 6 | m |
| Design point load at midspan P* | 60 | kN |
| Load eccentricity from the shear centre | 50 | mm |
| Design UDL (on the shear centre) | 5 | kN/m |
| Yield stress (0 = section value) | 0 | MPa |
| Twist limit (serviceability, at P/1.4) | 2 | ° |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Torque T* = P*·e | 3.00 | kNm |
| J / Iw | 1,504.8×10³ mm⁴ / 1,980.1×10⁹ mm⁶ | |
| Torsional bending constant a = √(EIw/GJ) | 1,814 | mm |
| Twist at midspan | 0.94 | ° |
| Warping normal stress E·Wn·φ″ | 29.0 | MPa |
| Major-axis bending stress | 64.8 | MPa |
| Minor-axis stress from twist φ·Mx/Zy | 3.1 | MPa |
| Combined normal stress | 96.9 (limit 252) | MPa |
| St Venant shear at support G·tf·φ′ | 11.8 | MPa |
| Warping shear at support | 0.5 | MPa |
| Web shear from V* | 12.0 | MPa |
| Twist at service (P*/1.4) | 0.67 | ° |
- ✓ Combined normal stress ≤ 0.9fy — 38 %
- ✓ Combined shear stress ≤ 0.9 × 0.6fy
- ✓ Service twist ≤ limit — 0.67°
Method, formulas and assumptions
- Fork supports, central torque (SCI P385): φ(L/2) = T/2GJ·[L/2 − a·tanh(L/2a)], φ″(L/2) = T/(2GJa)·tanh(L/2a), φ′(0) = T/2GJ·(1 − sech(L/2a)), φ‴(0) = T/(2GJa²)·sech(L/2a).
- Warping stress σw = E·Wn·φ″ with Wn = hs·bf/4; warping shear τw = E·Sw·φ‴/tf with Sw = hs·bf²·tf/16; St Venant shear τt = G·tf·φ′.
- Twist couples the major-axis moment into minor-axis bending (φ·Mx/Zy). Elastic combination limited to 0.9fy; check LTB separately (the twisting load reduces φMb).
- Section properties from plate dimensions (root radii ignored).
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.