Free Tool · EN 1992-1-1 §5.8.8

EN 1992-1-1 Concrete Column Design Calculator

RC column design per EN 1992-1-1 §5.8.8 nominal curvature method. Computes slenderness λ and limit λlim (§5.8.3 Eq.5.13N), second-order eccentricity e2 from Kr·Kφ·(1/r0) (Eq.5.34–5.37), total design moment MEd, and plots the N-M interaction envelope with the demand point. Rebar detailing per §9.5. C20/25–C50/60 · B500B · i18n EN/NL/DE.

Section diagram & N-M envelope (updates on compute)

b h
M_Ed (kNm) N_Ed (kN)

Column Parameters

Cross-section width. For square columns b = h.
Cross-section depth in the bending direction.
Effective buckling length. For braced fixed-pin: l₀ = 0.7·L; braced pin-pin: l₀ = L; cantilever: l₀ = 2·L.
Design axial force (compression positive).
First-order design moment. Do not add imperfection eccentricity — the calculator adds e₀ = max(l₀/400, h/30, 20 mm) per §5.2(7).
Number of main bars on each face (tension and compression). Total bars = 2 × n.
Nominal cover to the centre of the main reinforcement bar.
EN: α_cc = 1.0 (recommended)
λ_lim factors (A, B, C) — click to expand
Creep factor A = 1/(1+0.2·φ_ef). Use default 0.7 if effective creep ratio is unknown.
Reinforcement factor B = √(1+2ω). Use default 1.1 if ω is unknown.
Moment ratio C = 1.7 − r_m. Conservative default 0.7 (r_m = 1 → equal end moments same sign).

Design Results

154%
M_Ed / M_Rd utilisation
FAIL
Slender — 2nd order required
λ (slenderness)46.2
λ_lim (limit §5.8.3)11.8
M₀Ed (kNm)80
M_Ed total (kNm)141.96
M_Rd at N_Ed (kNm)92.36
N_Rd,max (kN)2346.4
A_s total (mm²)1257
f_cd (MPa)20
f_yd (MPa)434.8
A_s,min §9.5.2 (mm²)345
Link φ_min / s_max
2nd Order (§5.8.8)
e₀ (imperfection)20 mm
K_r0.52
K_φ1.411
e₂ (2nd order eccentricity)21.31 mm
M₂ (kNm)31.96

Worked Steps

Step 1 — Slenderness §5.8.3 Eq.5.13N
Radius of gyration i = h/√1286.6 mm
λ = l₀/i46.2
n = N_Ed/(A_c·f_cd)0.833
λ_lim = 20·A·B·C/√n11.8
Conclusion Slender — 2nd order required
Step 2 — Second-Order Effects §5.8.8 Nominal Curvature
e₀ = max(l₀/400, h/30, 20 mm) [§5.2(7)]20 mm
K_r [Eq.5.36]0.52
K_φ [Eq.5.37]1.411
e₂ = (1/r)·l₀²/π² [§5.8.8.3]21.31 mm
M₂ = N_Ed·e₂31.96 kNm
Step 3 — Total Design Moment
M_Ed = M₀Ed + N_Ed·e₀ + M₂141.96 kNm
Step 4 — N-M Interaction Check
N_Rd,max (pure compression)2346.4 kN
M_Rd at N_Ed (interpolated)92.36 kNm
Utilisation = M_Ed/M_Rd 153.7% → FAIL
Step 5 — Rebar Detailing §9.5
A_s,min [Eq.9.12N]345 mm² (governs: axial (0.10·N_Ed/f_yd))
A_s,max3600 mm²
A_s provided1257 mm²
Link φ min / spacing s max

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FAQ

When is a concrete column considered slender per EN 1992-1-1?
A column is slender when λ > λ_lim. The slenderness λ = l₀/i where i = h/√12 for a rectangular section. The limit is λ_lim = 20·A·B·C/√n (§5.8.3.1 Eq.5.13N), where n = N_Ed/(A_c·f_cd) is the relative axial load. The conservative default coefficients are A=0.7 (no creep info), B=1.1 (unknown reinforcement), C=0.7 (equal end moments). Below λ_lim only first-order moments and imperfections need to be considered; above λ_lim the nominal curvature method (§5.8.8) adds a second-order moment M₂ = N_Ed·e₂.
What is the nominal curvature method (§5.8.8)?
The nominal curvature method (§5.8.8) is the recommended approach for isolated columns with constant cross-section. It estimates the deflection at midheight as e₂ = (1/r)·l₀²/c, where c = π² ≈ 9.87 for sinusoidal deformation. The curvature 1/r = K_r·K_φ·(1/r₀) uses: 1/r₀ = ε_yd/(0.45·d) as the basic curvature; K_r = (n_u−n)/(n_u−n_bal) ≤ 1.0 correcting for axial load level (Eq.5.36); K_φ = 1+β·φ_ef accounting for creep (Eq.5.37). The total design moment is M_Ed = M₀Ed + N_Ed·e₂, where M₀Ed already includes imperfection eccentricity.
How is the N-M interaction diagram constructed?
The N-M interaction diagram is built by strain compatibility sweep: the neutral axis depth x varies from pure tension to full compression. At each position, concrete stresses follow the rectangular stress block (§3.1.7, depth λ·x, stress η·f_cd), and reinforcement stresses are bilinear elastic-plastic (capped at ±f_yd). Resultant N_Rd and M_Rd are computed at each step. The demand point (N_Ed, M_Ed) must lie inside the envelope. If it lies outside, the column fails the N-M check and a larger section or more reinforcement is needed.
What imperfection eccentricity does the calculator add?
The calculator adds e₀ = max(l₀/400, h/30, 20 mm) per EN 1992-1-1 §5.2(7) as a geometric imperfection. This is added to the first-order moment before computing second-order effects. You should NOT manually add imperfection to M₀Ed — the calculator handles this. e₀ accounts for unavoidable construction tolerances and replaces the equivalent horizontal load approach for isolated columns.
How does the German National Annex differ?
The main difference is the concrete strength reduction factor α_cc. EN recommends α_cc = 1.0; the German National Annex (DIN EN 1992-1-1/NA) uses α_cc = 0.85. This lowers the design compressive strength f_cd = α_cc·f_ck/γ_c from f_ck/1.5 to 0.85·f_ck/1.5, reducing both the concrete contribution to N_Rd,max and the interaction envelope. Select "DE" in the National Annex toggle to apply this. The Netherlands (NL) follows the EN recommended value of α_cc = 1.0.
What rebar detailing checks are performed?
Per EN 1992-1-1 §9.5.2, the calculator checks: A_s,min = max(0.10·N_Ed/f_yd, 0.002·A_c) [Eq.9.12N]; A_s,max = 0.04·A_c; minimum 4 bars for rectangular sections; minimum bar diameter 8 mm. Per §9.5.3, it recommends link diameter φ_link ≥ max(6 mm, φ_long/4) and link spacing s ≤ min(20·φ_long, b_min, 400 mm). These are output alongside the capacity check results.