Earthquake Analysis of Concrete Structures

The present Ph.D. dissertation provides a contribution to the development of rational and simplified design procedures in order to facilitate the task of seismic design of reinforced concrete structures. It is widely accepted that it is neither economic nor necessary to design most part of reinforced concrete structures so that they remain in the elastic domain during the course of an extreme earthquake event. Currently, seismic design for strong earthquakes comprises of selecting a suitable collapse mechanism and determining an adequate distribution of strength and stiffness so that the corresponding overall structural performance in a representative seismic action lies within desired limits, i.e. Performance based-seismic design. Non-linear time-history analysis (NLTHA) is generally accepted as the most suitable method to determine the seismic demand on structures designed to develop non-linear behaviour when subjected to earthquake motion. However, despite its superior accuracy and rationality, its use at a practical level is limited to structural assessment. Therefore, the need for simplified design procedures is still valid. Unfortunately, most of the existing simplified methods available for seismic design still make use of the Elastic Spectrum to determine seismic demand and therefore are beset with serious inconsistencies related to the inelastic nature of the dynamic response of ductile systems. In this thesis, a new seismic design procedure for systems expected to perform in the non-linear range during a lifetime earthquake event, the Rigid-Plastic Seismic Design method (RPSD), is proposed. The procedure is founded on the theory of Plasticity (Rigid-plastic structures), follows modern seismic design philosophy and combines: a) The rationality of NLTHA for the estimation of the seismic demand solely based on the properties of the structure, and b) The simplicity and practical value of spectral analysis for the estimation of the required dissipation capacity. Firstly, a collapse mechanism is chosen and the dissipation capacity of the structure is determined with respect to a pre-defined performance parameter using a rigid-plastic response spectrum. The latter is characteristic of the ground motion alone. Then, a safe admissible stress field is found in parts of the structure outside the yield zones in order to enforce the chosen collapse mechanism. The latter task is facilitated to a great extent by applying the extreme loading scenarios approach, which takes advantage of the fact that the strength demand at any point of rigid-plastic structures is solely dependent on the intensity of the ground motion. Any artificial coefficients intended to adjust results according to empirical observations are avoided, which from a conceptual point of view is considered to be an advantage over other simplified design procedures for seismic design. Moreover, there is an effective separation between the properties of the structure and those of the ground motion, which contributes to the straightforwardness of the RPSD method. Two examples of the application of the procedure to the design of reinforced concrete frames are given. Results are compared with refined NLTHA and found to be encouraging.