JointLib

COLUMN INTERACTION DIAGRAM — N·M BIAXIAL

EN 1992-1-1 § 6.1 · § 5.8.9 — RECTANGULAR SECTION — BST500C

⚠ The N·M diagram below verifies the cross-section, with MEd exactly as entered. The slenderness check of §5.8 is performed separately, in the panel on the left, and does not propagate automatically into the diagram: if MII > MEd, enter the magnified value in the load cases yourself. The minimum eccentricity e0 = max(h/30; 20 mm) is applied automatically in each direction (§6.1(4)).
⬡ CROSS-SECTION
Ac = 15.0 cm²
⬡ REINFORCEMENT (BST500C)
▸ Faces parallel to b — top & bottom
▸ Faces parallel to h — left & right
Total bars: 10 buc
As total: 2275 mm²
As face b (top/bottom): 829 mm²
As face h (l/r): 936 mm²
ρ: 1.52 %
⬡ MATERIALS
fck
25 MPa
fcd
16.67 MPa
fyk (BST500C)
500 MPa
fyd
434.8 MPa
Ecm
31.5 GPa
fcm
33 MPa
Creep
h₀ = 2A_c/u
188 mm
φ(∞,t₀)
2.68
φ(∞,t₀) to EN 1992-1-1 Annex B, with h₀ derived from the section above. It does not enter the N·M diagram on this page — it is the quantity you need separately, for the slenderness check of §5.8, through φ_ef = φ(∞,t₀)·M_0Eqp/M_0Ed. Details on the creep and shrinkage page.
Slenderness §5.8
λ = l₀/i
20.8
φ_ef
1.87
e_i
20 mm
ω
0.396
# λ_lim N_B M_II
1 24.1 21217 99.8
λ ≤ λ_lim for every case, so second-order effects may be ignored (§5.8.3.1). M_II is shown anyway, as a point of comparison — using it remains conservative.
λ_lim is computed with C = 0.7, the recommended value when the ratio of the end moments is not known — the page receives a single M_Ed per case, not M₀₁ and M₀₂. The magnification uses the nominal stiffness method (§5.8.7). Set L = 0 to disable the check.
⬡ LOAD CASES
Caz NEd (kN) MEdx (kN·m) MEdy (kN·m)
LC1
◈
Fill in the data and press Calculate
The N–MRd curve will be generated for both axes
Tool information

What this calculator checks

The calculator plots the N·M interaction diagram of a rectangular reinforced-concrete column, according to EN 1992-1-1 §6.1, and checks the action points \((N_{Ed}, M_{Ed})\) against the capacity envelope. A column fails under a combination of axial force and moment, not under either alone, and the diagram shows exactly the boundary of that combination.

How to read the diagram

The section capacity curve joins all pairs \((N_{Rd}, M_{Rd})\) at which the section reaches its limit state, sweeping the neutral axis from pure compression (top) to pure tension (bottom). Its shape is characteristic:

  • At low axial force, extra compression closes the cracks and increases the moment capacity.
  • At high axial force (beyond the balance point), compression consumes the capacity, and the moment capacity falls.
  • The balance point is the peak of the curve — the axial load at which the concrete crushes and the steel yields simultaneously, i.e. the maximum moment capacity.

An action point inside the envelope passes; one outside does not.

Second-order effects

Besides the section capacity curve, the calculator superimposes two effects that reduce the real capacity of the column as a member:

  • Geometric imperfection (§5.2) — an initial inclination that adds a parasitic moment.
  • Buckling / second-order effect (§5.8.9) — in slender columns, lateral displacement magnifies the moment (\(P\text{-}\delta\)), so the actual action to check is larger than the first-order one.

The biaxial check accounts for the moments about both axes simultaneously.

Input data

  • Section geometry — the sides, the arrangement and diameter of the bars.
  • Materials — the concrete class, the steel grade (BST500C by default).
  • Load cases — the pairs \((N_{Ed}, M_{Ed})\), possibly several at once.
  • Buckling length and support conditions — for the second-order effect.

Assumptions and limitations

  • Rectangular section with symmetric reinforcement; other shapes need separate treatment.
  • The model uses the parabola-rectangle diagram for concrete and the bilinear one for steel (§3.1.7, §3.2.7).
  • For the \(M_x\)–\(M_y\) envelope at constant axial force, see the Mx·My diagram.
  • It does not replace a global second-order analysis of the structure where that is required.
An unhandled error has occurred. Reload 🗙