Concrete · Beams
RC beam torsion with shear (AS 3600 Cl 8.3) calculator
Rectangular beam under combined torsion and shear. Checks whether torsion can be ignored (T* ≤ 0.25φTuc), web crushing (T*/φTu.max + V*/φVu.max ≤ 1), then sizes closed fitments for shear plus torsion (Asw/s = T*/(φ·fsy.f·2At·cotθ)) and the extra longitudinal steel around the perimeter, using the simplified shear method with θv = 36°.
Standard: AS 3600-2018 Cl 8.2 (simplified shear), Cl 8.3 torsion · thin-walled tube / space truss
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 |
|---|---|---|
| Width b | 400 | mm |
| Depth D | 700 | mm |
| Cover to fitments | 40 | mm |
| Fitment bar | 12 | mm |
| Main bar | 24 | mm |
| f′c | 32 | MPa |
| Fitment fsy.f | 500 | MPa |
| Longitudinal fsy | 500 | MPa |
| Design torsion T* | 60 | kNm |
| Design shear V* | 300 | kN |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Torsional modulus Jt = 0.4x²y | 44.8 | ×10⁶ mm³ |
| Tuc = 0.3√f′c·Jt | 76.0 | kNm |
| 0.25φTuc (ignore torsion below) | 14.3 | kNm |
| dv | 572 | mm |
| Vuc (kv = 0.100) | 130 | kN |
| Crushing T*/φTu.max + V*/φVu.max | 0.49 | |
| Asw/s for torsion (per leg) | 0.310 | mm²/mm |
| Asv/s for shear (two legs) | 0.687 | mm²/mm |
| Fitment spacing required / used | 173 / 150 | mm |
| Maximum spacing (0.12ut, 300) | 220 | mm |
| Extra longitudinal steel for torsion Al | 1,077 | mm² |
- ✓ Web crushing — 0.49
- ✓ Fitments at a practical spacing (≥ 75 mm) — 150 mm
- ✗ Torsion can be ignored (T* ≤ 0.25φTuc)
Method, formulas and assumptions
- Jt = 0.4x²y (Cl 8.3.3); crushing with Tu.max = 0.2f′c·Jt and Vu.max = 0.55f′c·bv·dv·cotθ/(1 + cot²θ), φ = 0.75.
- Simplified shear (Cl 8.2.4.3): kv = 200/(1000 + 1.3dv) ≤ 0.10 and θv = 36° for members with at least minimum fitments.
- Torsion steel: Tus = fsy.f(Asw/s)2At·cotθv with At enclosed by the fitment centreline; extra longitudinal steel (Asw/s)·ut·cot²θ·fsy.f/fsy distributed round the perimeter (shown orange).
- Fitments must be closed with 135° hooks for torsion.
Related concrete calculators
- RC beam (flexure + shear) — Singly reinforced rectangular beam: tension steel, ductility and shear with stirrups.
- RC T-beam flexure (flange in compression) — Rectangular stress block in a T-section: neutral axis in the flange or web, moment capacity, ductility (ku)…
- Doubly reinforced RC beam — Rectangular beam with compression steel: neutral axis by trial on compression-steel yield, capacity and…
- Continuous beams and slabs: AS 3600 simplified moment coefficients — Design moments and shears from the AS 3600 coefficients for continuous beams or one-way slabs of near-equal…
- One-way slab — Bending steel, bar spacing and deemed-to-comply span/depth for a one-way slab.
- Two-way slab — Moments in both directions for a rectangular slab simply supported on four edges.
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.