Column interaction diagram calculator
A column is not sized by axial load alone: the moment it carries reduces the axial capacity it can offer. This calculator builds the P–M interaction curve from strain compatibility, interpolates the capacity at your moment, and applies Bresler’s method when both axes are loaded.
| Point | φPn (kN) | φMn (kN·m) |
|---|---|---|
| Pure axial | 2498 | 0 |
| Balanced | 146 | 28 |
| Mid-height | 2248 | 133 |
| Pure bending | 0 | 267 |
| Demand | 1200 | 120 / 0 |
Points come from strain compatibility with the ACI φ transition between 0.65 and 0.90.
Pn, Mn from a sweep of c · Concrete block plus elastic-perfectly-plastic steel.
0.65 → 0.90 as εt goes 0.002 → 0.005 · ACI Table 21.2.2.
1/Pn = 1/Pnx + 1/Pny − 1/P0 · Bresler reciprocal load method.
A clear path from inputs to results.
A column is not sized by axial load alone: the moment it carries reduces the axial capacity it can offer. This calculator builds the P–M interaction curve from strain compatibility, interpolates the capacity at your moment, and applies Bresler’s method when both axes are loaded.
How to use
- Enter the section and reinforcement.
- Set f′c, fy and the cover to the bar centroid.
- Enter the factored axial load and moments.
- Read the capacity at your moment and the utilisation.
The formula
Reference: ACI 318-19 §22.2 (stress block), Table 21.2.2 (φ transition), Bresler reciprocal load method.
Worked example
400 × 400 mm, 8 × 20 mm bars, 1,200 kN at 120 kN·m
- 400 × 400 mm, 8 bars of 20 mm (2,513 mm²).
- f′c 28 MPa, fy 420 MPa, cover 50 mm.
- Pu 1,200 kN, Mux 120 kN·m.
- 1
Pure axial capacity: 2,498 kN (capped at 0.80φP0).
- 2
Pure bending capacity: 267 kN·m.
- 3
At 120 kN·m the curve gives 2,316 kN of axial capacity.
- 4
Utilisation: 1,200 / 2,316 = 51.8%.
- 5
Adding 120 kN·m on the other axis drops the capacity further through Bresler.
Capacity 2,316 kN at 120 kN·m · utilisation 51.8%.
Interpreting the result
The curve explains why a column that looks lightly loaded axially can still fail: moment eats axial capacity along a steep slope. The balanced point, where the tension steel yields as the concrete crushes, is where the curve turns — below it the section is compression-controlled and φ falls to 0.65.
Assumptions & limitations
- Rectangular section with steel split evenly between two faces.
- Uniaxial and Bresler biaxial screening; no second-order magnification.
- No seismic confinement requirements.
Frequently asked questions
What is the balanced point?
The strain state where the tension steel reaches yield exactly as the concrete reaches 0.003.
Is Bresler exact?
No. It is a conservative approximation; a full biaxial design uses the interaction surface.
Why does φ change along the curve?
ACI ties φ to the tension strain, from 0.65 compression-controlled to 0.90 tension-controlled.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.