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Column Interaction Diagram: worked example
A reinforced concrete column section with its axial load–moment (P–M) interaction diagram and a design point.
EN 1992-1-1:2004 — Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings · SI units · Calculator v1.1
These are the real results of the Column Interaction Diagram for the inputs below, read-only. Open the calculator with these values already loaded to change them.
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Inputs
| Section type | Rectangular |
| Width b | 400 mm |
| Height h | 400 mm |
| Cover to link/tie | 40 mm |
| Concrete | C30/37 |
| Reinforcing steel | B500S |
| Longitudinal reinforcement | 8×T25 |
| Design axial load NEd | 500 kN |
| Design moment MEd | 150 kN·m |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Axial load / moment design point within interaction envelope | (NEd, MEd) = (500.0 kN, 150.0 kN·m) | Utilization 52.2% | 52.2% | PASS |
P-M interaction curve — key points
| Point | N (kN) | M (kN·m) |
|---|---|---|
| Pure Compression | 4224.0 | 0.0 |
| Balanced Point | 1155.7 | 310.3 |
| Pure Bending | 0.0 | 249.6 |
| Pure Tension | -1707.4 | 0.0 |
| Design Point (Pu, Mu) | 500.0 | 150.0 |
Calculation steps
Calculation (3 steps)
EC2 §6.1
Section properties
Ac = b×h, As = Σ(area of each bar)
Ac = 160000 mm², As = Σ over 8 bars
As = 3927 mm²
EC2 §3.1.7, §6.1(5)
Maximum axial capacity (pure compression, uniform strain εc2 = 0.002)
N0 = fcd·(Ac − As) + As·min(fyd, Es·εc2)
N0 = 17.00×(160000 − 3927) + 3927×min(434.8, 400)
N0 = 4224.0 kN
EC2 §6.1
N-M interaction check
Design point must lie within interaction curve
(NEd, MEd) = (500.0, 150.00) kN, kN·m
Utilization = 52.2% — ✓ PASS
Design basis and assumptions
- National Annex: none applied as a whole — the EN recommended values are used, except where noted below. There is no National Annex selector; check the values against the annex for your project.
- αcc = 0.85 in fcd = αcc·fck/γc (the UK National Annex value; EN 1992-1-1 §3.1.6(1) recommends 1.0).
- Pure compression N0 = fcd·(Ac − As) + As·min(fyd, Es·εc2) with εc2 = 0.002 (EN 1992-1-1 §3.1.7, §6.1(5)): bars displace concrete and the steel stress is capped at 400 MPa for B500; sections fully in compression pivot about εc2 at 3h/7 (Fig. 6.1).
- γc = 1.5 and γs = 1.15 (EN 1992-1-1 Table 2.1N, persistent and transient), editable.
- Short-column check only — no slenderness or second-order moment magnification is applied; use RC Column Design for slender columns.
- Uniaxial bending about one axis only.
- Circular sections are assumed spiral-tied and rectangular sections tied (governs the ACI φ transition floor and the axial capacity cap factor) — verify this matches your actual detailing.
- Checks a single user-supplied load point (Pu, Mu) against the section’s interaction envelope — this tool doesn’t generate load combinations for you.
- Verify all provisions against the governing code edition and applicable National Annex before use.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.