Civil Engineering Association

THESIS - Design of walls with linear elastic finite element methods

Abstract

This thesis focuses on the design of reinforced concrete walls with the use of linear elastic finite element methods. Since the introduction of Eurocode EN1992, the set of design standards in which design requirements related to concrete structures are committed to paper, it is allowed to derive the required amount of reinforcement directly from the membrane forces which follow from a linear elastic finite element analysis. This method deviates however at some points considerably from common design methods. Compared to the common design methods the moment diagram is for example no longer shifted over a specific distance during the design of beams to prevent failure due to the development of inclined bending cracks. In addition, the assumed linear elastic isotropic material behavior in the finite element analyses results in the computation of load transfer mechanisms which deviate considerably from mechanisms which are expected to develop in practice. These deviations gave rise to analyze this recently approved design method in further detail, indicated by the term linear elastic finite element method (LE-FEM) henceforth.

The linear elastic finite element method is verified by considering a large number of single- and several two-span beams. The required reinforcement of these beams is determined with LE-FEM by taking all relevant provisions of the Eurocodes into account. In a subsequent step the structural behavior of the considered beams was analyzed by means of a non-linear finite element analysis, in which a similar level of reliability was taken into account as during the design process. These nonlinear analyses, which are performed in ATENA, are capable to predict the actual behavior of concrete.

Structural analyses of the considered specimen led to the following main conclusions:
· Assuming linear elastic material behavior of concrete for reinforcement design with LE-FEM of structures does not approximate concrete behavior in an accurate way.
· No direct relation is found between the limited amount of longitudinal reinforcement which reaches the supports and the observed failure mode. Concrete crushing in the compressive zone, caused by flexural deformations, turned out to be the normative failure mode.
· Reinforcement designs according to LE-FEM of the considered beams do not meet requirement related to crack control in the serviceability limit state. It is not possible to determine the stresses in the required distributed reinforcement without the application of advanced (non-linear) methods, since there is no direct relation between the applied load and stress development in individual reinforcement bars.
· Design of structures with LE-FEM which are loaded by a compressive force and contain symmetrical reinforcement, such as columns, results in an overestimation of the concrete compressive strength since eccentricities and second order effects are left out of consideration.
· Redistribution of considered two-span beams in case differential support settlements appear is insufficient to withstand settlements which are allowed by the codes.

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