Axial-moment interaction diagram per EN 1992-1-1:2004 §6.1. Full P-M curve swept from pure tension to pure compression. §5.8 slenderness check, second-order eccentricity e₂ (nominal curvature §5.8.8), design point plotted with utilization ratio.
| λ (slenderness) | 43.3 | Slender |
| λlim §5.8.3.1 | 28.47 | |
| e₀ = MEd/NEd (mm) | 75 mm | |
| emin = max(h/30, 20) (mm) | 20 mm | |
| e₂ second-order (mm) | 24.7 mm | 2nd-order |
| e_total (mm) | 99.7 mm | |
| MEd,total (kNm) | 199.4 kNm |
| As,total (mm²) | 2513 mm² | |
| As,min §9.5.2 (mm²) | 460 mm² | ✓ |
| As,max §9.5.2 (mm²) | 6400 mm² | ✓ |
Rectangular stress block §3.1.7
λ = 0.8, η = 1.0 (fck ≤ 50 MPa). Depth of stress block = λ·x, intensity = η·fcd.
Strain profile
Plane sections remain plane. εcu3 = 0.0035. ε_i = εcu3·(x−d_i)/x for each bar layer.
Slenderness §5.8.3.1 Eq(5.13N)
λlim = 20·A·B·C/√n, A = 1/(1+0.2φef), B = √(1+2ω), C = 1.7−rm.
Nominal curvature §5.8.8
1/r = Kr·Kφ·eyd/(0.45·d). e₂ = (1/r)·l₀²/10. Kr per Eq(5.36).
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A P-M (or N-M) diagram plots the combination of axial load N and bending moment M that a cross-section can resist at ULS. Points inside the curve are safe; outside means failure. The calculator sweeps the neutral axis depth from near-pure-tension to near-pure-compression to generate ≥ 60 points of the curve.
Per EN 1992-1-1 §5.8.3.1, second-order effects may be ignored if λ ≤ λlim. The limit λlim = 20·A·B·C/√n accounts for creep (A), reinforcement (B), moment profile (C), and relative normal force n = NEd/(Ac·fcd). If λ > λlim, the nominal curvature method (§5.8.8) computes an additional eccentricity e₂ = (1/r)·l₀²/10.
Plane sections remain plane. For a given neutral axis depth x, the compressive strain at the top fiber is set to εcu3 = 0.0035 (for fck ≤ 50 MPa, Table 3.1). The strain in each bar at depth d_i is ε_i = εcu3·(x−d_i)/x, capped at εud (design steel fracture strain).
Per §9.5.2, the minimum is As,min = max(0.10·NEd/fyd, 0.002·Ac) and the maximum is As,max = 0.04·Ac (or 0.08·Ac at laps). These limits prevent brittleness at low axial load and prevent congestion at high reinforcement ratios.
EN 1992-1-1 §6.1(4) requires a minimum eccentricity e₀,min = max(h/30, 20 mm) to account for construction tolerances and unintentional eccentricity. The design moment includes this even if the calculated eccentricity is smaller.
The RC Beam tool (§6.1 + §6.2) covers pure bending and shear in beams. This column tool adds the axial-moment interaction diagram needed when significant compression (NEd) is present. Together they cover the basic EN 1992-1-1 member set for columns and beams.