COLUMN INTERACTION DIAGRAM — Mx·My
EN 1992-1-1 § 5.8.9(4) — BIAXIAL CAPACITY CONTOUR AT CONSTANT NEd — BST500C
| Caz | MEdx (kN·m) | MEdy (kN·m) | |
|---|---|---|---|
| LC1 |
Tool information
What this calculator checks
The calculator plots the Mx·My capacity envelope of a rectangular reinforced-concrete column, at a constant axial force \(N_{Ed}\), according to EN 1992-1-1 §5.8.9(4). It is the other section through the column's interaction surface: where the N·M diagram cuts at moment about a single axis, this one cuts horizontally, at fixed \(N\), and shows which combinations of moment about the two axes the section can carry.
Why it is not a simple ellipse
In biaxial bending, a column cannot carry the maximum moment about the x-axis and about the y-axis simultaneously — the two "consume" each other. The capacity envelope in the \(M_x\)–\(M_y\) plane is a closed curve around the origin, and Eurocode approximates it by the interaction expression (5.39):
\(\left(\frac{M_{Edx}}{M_{Rdx}}\right)^a + \left(\frac{M_{Edy}}{M_{Rdy}}\right)^a \le 1\)
The exponent \(a\) is not constant: it depends on the axial load level \(N_{Ed}/N_{Rd}\). At low compression, \(a \approx 1\) (an almost rhombic envelope); at high compression, \(a\) rises toward 2 (an almost elliptical envelope). This variation in shape is why the envelope is computed, not approximated by a fixed ellipse.
How to read it
- \(M_{Rdx}\) and \(M_{Rdy}\) are the moment capacities about each axis taken separately, at the given axial force \(N_{Ed}\) — that is, the points where the envelope crosses the two axes.
- An action point \((M_{Edx}, M_{Edy})\) inside the envelope passes.
- Changing \(N_{Ed}\) changes both the size and the shape of the envelope — which is why the calculation is done at a fixed value.
Input data
- Section geometry — the sides, the arrangement and diameter of the bars.
- Materials — the concrete class, the steel grade (BST500C by default).
- \(N_{Ed}\) — the constant axial force at which the envelope is plotted.
- Action points — the pairs \((M_{Edx}, M_{Edy})\) to check.
Assumptions and limitations
- Rectangular section with symmetric reinforcement.
- The envelope is valid for a single \(N_{Ed}\); for the variation with axial force, see the N·M diagram.
- The input moments are assumed to be the design ones, already including second-order effects and imperfections where relevant.
Related calculations
- N·M diagram — the vertical section through the interaction surface
- Reinforced section — bending about a single axis, without axial force
- Section analysis — the moment-curvature behaviour