A column is considered to be slender if its cross-sectional dimensions are small compared with its length. The degree of slenderness or slenderness ratio (λ) is defined in Eurocode 2 art. (5.8.3.2) as a function of the effective length (l0) and the radius of gyration (i) of a rectangular uncracked concrete section. Slender structures with optimized cross-section are elegant aesthetically, reduce the dead weight of the structure and allow for efficient use of floor plans with possibilities for more higher and open space. However, the insufficiency in the knowledge of the real resistance to buckling, total design moment including second-order effects, bending stiffness and time-dependent behaviour of slender reinforced concrete columns still often leads to an exaggeration of the cross-section and therefore limit the design possibilities and new developments.
Slender structures, in which second-order effect cannot be ignored, are analyzed for practical designs with Simplified Methods according to Eurocode 2 “Design of concrete structures”. One of such methods is the Nominal Stiffness Method NEN-EN 1992-1-1 art. (5.8.7). However, the research results provided by Hageman showed that the method of Nominal Stiffness is not adequate and therefore it is overruled in the Dutch National Annex by the standard NEN6720. The calculated total bending moment including second-order effect may result in an overestimation of the failure load and therefore form an unsafe structure.
Within this report, detailed analytical research of the five Simplified Methods is performed in order to gain a deeper knowledge of the design models, relevant parameters and their backgrounds. The differences between the methods are presented considering different structural cases. The extensive overview of the results and differences between the methods provide insight into the behaviour of the design models and the significance of the parameters in a bigger structural domain. In addition, the results provide a solid starting point for the nonlinear finite element analysis and allow engineers to validate the outcomes. The magnitude of the underestimations is then research by means of nonlinear finite element analysis, incorporating both physical and geometric nonlinearity. The cracking of reinforced concrete is simulated using the principle of smeared cracking.
The results showed significant deviations between the analytical results and the nonlinear analysis performed in DIANA. It has been shown for multiple structural cases that the Dutch National Annex Method overestimates the bending stiffness of a slender column whether Nominal Stiffness method (eq.5.22) showed safe but conservative results. The developed finite element model is suited for the analysis of pure bending problems and a combination of a normal force and bending. The provided Python-scripts allow the researcher for an easy adjustment of the parameters in order to study more cases in the future. Together with the additional research it would be possible to improve the current methods for the revision of Eurocode 2.
