Concrete · Columns & walls
Circular RC column: N–M interaction calculator
Circular column or pile section with bars evenly spaced round a circle. The interaction curve is built by strain compatibility for neutral-axis depths from a thin compression zone to beyond the section: the concrete block is a circular segment of depth γ·dn, the bars take ±fsy. φ varies from 0.65 above the balanced load to 0.85 in pure bending. The design point (M*, N*) is checked against φMu at N*.
Standard: AS 3600-2018 Cl 10.6 strain compatibility (εcu = 0.003, rectangular stress block α2, γ on a circular segment) · φ = 0.65 above Nub rising to 0.85 in bending
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 |
|---|---|---|
| Diameter | 600 | mm |
| Number of bars | 8 | |
| Bar diameter | 24 | mm |
| Cover to ties / spiral | 50 | mm |
| Tie / spiral diameter | 10 | mm |
| f′c | 40 | MPa |
| fsy | 500 | MPa |
| Design axial N* | 3000 | kN |
| Design moment M* (resultant) | 300 | kNm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Bar circle radius | 228 | mm |
| Steel ratio | 1.28 | % |
| Balanced load Nub | 3,336 | kN |
| Squash-side φN (deepest curve point) | 6,763 | kN |
| Design moment (≥ N*·0.05D) | 300.0 | kNm |
| φMu at N* | 475.8 | kNm |
| Utilisation M*/φMu | 63 | % |
- ✓ (N*, M*) inside the φ interaction curve
- ✓ Steel ratio 1–4 % — 1.28 %
- ✓ At least 6 bars in a circular column
Method, formulas and assumptions
- Strain compatibility with εcu = 0.003; concrete force α2·f′c on a circular segment of depth γ·dn (area R²acos((R − a)/R) − (R − a)√(2Ra − a²), centroid 2c³/3A from the centre).
- Bars at their actual depths, stress Es·ε limited to ±fsy (concrete displaced by bars ignored).
- φ = 0.65 for N ≥ Nub, rising linearly to 0.85 at N = 0 (AS 3600-2018 Table 2.2.2); minimum design moment N*·0.05D. Slender columns: magnify M* (Cl 10.4) first.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.