Verification Example - RC Column

Eurocode Verification: NCM vs Nonlinear Analysis

Overview

Slender reinforced concrete columns require consideration of second-order effects — the additional moments arising from lateral deflections under axial load (P-δ effects). Eurocode 2 provides two approaches: simplified methods (NCM) that estimate these effects indirectly, and general methods that capture them directly through nonlinear analysis.

This example verifies Awatif's implementation against a published Eurocode reference example for a highly slender column (λ = 100), comparing:

Linear + NCM

First-order analysis with Nominal Curvature Method
(EN 1992-1-1 §5.8.8)

Nonlinear

Geometrically nonlinear analysis with nominal stiffness
(EN 1992-1-1 §5.8.7)
Reference: DBV, Beispiele zur Bemessung nach Eurocode 2 – Band 1: Hochbau, Berlin: Ernst & Sohn, 2011.

Problem Summary

Geometry

  • Height: 6.20 m
  • Section: 400 × 450 mm

Materials

  • Concrete: C30/37
  • Steel: S500

Loading

  • NEd: 633 kN
  • M0: 99.5 kNm
Column geometry showing 6.2m tall RC column with dimensions, loading (633 kN axial, 99.5 kNm moment), and cross-section detail with reinforcement
Figure 1: Column geometry and cross-section detail

NCM Verification Details

Step-by-step comparison of Nominal Curvature Method calculations:

Parameter Symbol Reference Awatif (NCM) Ratio Awatif (Nonlinear)
First-order moment M0 100.00 kNm 99.50 kNm 0.995 —
Imperfection eccentricity ei 2.10 cm 2.07 cm 0.986 2.07 cm
Effective length l0 13.02 m 13.02 m 1.000 6.2 m
Slenderness ratio λ 100.23 100.23 1.000 —
Correction factor Kr 1.000 1.000 1.000 —
Second-order eccentricity e2 19.90 cm 19.97 cm 1.004 —
Second-order moment M2 126.00 kNm 126.44 kNm 1.003 —
Design moment MEd 239.00 kNm 239.02 kNm 1.000 226.35 kNm
Steel area As 1620 mm² 1580 mm² 0.975 1471 mm²

Steel area: Reference uses ω-method (graphical interpolation) leading to reading inaccuracies (1620 mm²). Awatif uses iterative calculation (1580 mm²). All other ratios within 1%

Verification Summary

✓
NCM Implementation Validated

All NCM calculation steps match the Eurocode reference within 1% tolerance. The step-by-step parameter comparison confirms correct implementation of slenderness checks, curvature calculations, and second-order moment amplification per EN 1992-1-1 §5.8.8.

✓
Nonlinear Analysis Verified

The geometrically nonlinear analysis with nominal stiffness (EN 1992-1-1 §5.8.7) produces physically consistent results. The 5% reduction in design moment (226.35 kNm vs 239.02 kNm) reflects the method's direct equilibrium calculation versus NCM's conservative amplification approach. Steel area requirement reduced from 1580 mm² to 1471 mm².

→
Both Methods Eurocode-Compliant

This verification example demonstrates that Awatif correctly implements both Eurocode-approved methods for second-order effects. Users can select the appropriate method based on project requirements, with confidence in the implementation accuracy.