Elliptical Response Envelopes for the Design of Reinforced Concrete Structures: New Developments and Application to Nuclear Power Plant Buildings

Seismic analysis is one of the main steps in the structural design of Nuclear Power Plants (NPPs). Design is usually made by assuming linear structural behavior and using the so-called modal spectrum analysis. This method is based on the calculation of the response peaks for each earthquake direction (X, Y or Z) of several single-degree-of-freedom oscillators representing the modes of the analyzed structure. Then, the modal peaks of each response parameter for each earthquake direction are combined using, for instance, the so-called Complete Quadratic Combination-CQC (Der Kiureghian [1]). The superposed responses are, by definition, positive quantities. Hence, their sign must be defined, according to a fundamental mode shape or another reference structural configuration. Actually, signature of CQC of modal responses is not required for the approach based on the notion of “peak modal response hyper-ellipsoid envelope” (also called “envelope for seismic response vectors” by Menun and Der Kiureghian [2]). This is one of the interesting advantages of this method. For this reason, in this paper we discuss two developments based on the notion of “response envelopes”. The first one is an “equivalent static method” (ASCE [3], Nguyen et al. [4]-[5]) based on the theory of the “response envelopes”. The second development is an improved procedure for the definition of the signs of the CQC of modal peaks. Some of these proposed methods are applied to a NPP building and results are then compared with those coming from a standard modal spectrum analysis.