DYNAMIC BEHAVIOUR OF AXISYMMETRIC STRUCTURES

Abstract

This investigation deals with the dynamic behaviour of axisymmetric structures with emphasis on the effects due to strong ground motion. A linear elastic analysis in time domain using timewise mode superposition method has been.used to evaluate the earthquake response of some structures. Finite element method of analysis has been employed and the adequacy of simple beam method in relation to finite element method has been examined. The method of analysis has been applied to analyze a large variety of practical problems such as nuclear reactor building, intake tower, cooling tower, chimney, and also a class of electrical systems. Interaction effects due to surrounding water or soil on the structures have also been considered. To represent the large extent of water or soil in the lateral direction, infinite elements in conjunction with finite elements have been used. Computer programs have been developed to analyze the axisymmetric structures to earthquake loading. For the purpose of analysis two ground motions normalized to the same spectral intensity have been used. Various axisymmetric finite elements have been chosen to determine their relative competence in solving the thin and thick axisymmetric shell structures. The elements are, (i) paralinear, (ii) element with relative displacement degrees of freedom, (iii) cubilinear, (iv) 4-noded element iii with incompatible modes, (v) parabolic element, (vi) 9-noded Lagrangian element, and (vii) the shell element proposed by Ahmad. Also, the performance of 2-noded beam element in relation to the above elements has been investigated. Evaluation of earthquake response using the entire earthquake time-history requires large computer time. A nevtechnique has been proposed for finding earthquake response which is efficient and economical. The technique, instead of using the full time-history, uses only the effective part of total time history termed as the "time window". The method of determining the time window has been given. Interaction effects on the dynamic response of circular cylindrical cantilever structures due to surrounding water have been determined employing finite element method. Hydrodynamic pressure distribution diagrams have been obtained theoretically for different slenderness ratios of the cylindrical structure and are compared with the Indian Standard Code of practice for Earthquake Resistant Design of Structures, IS: 1893-1975. Recommendations to improve the Code values for different range of parameters have been given. Free vibration characteristics of cylinders have been evaluated for different ratios of outside radius to height and for different levels of submergence. To verify the theoretical results, experiments have been conducted in the laboratory on some model pipes for finding the fundamental frequency in air IV as well as under water with different water depths. A close comparison between the theoretical and experimental values has been observed for fundamental frequencies. A simple method of finding the fundamental frequency of circular cylindrical structures has also been presented. Interaction effects due to surrounding soil on the structures have also been investigated. In this, a detailed parametric study involving different values of shear wave velocity of soil has been done on a mathematical model of nuclear reectox building to estimate the interaction effects. Axisymmetric finite element as well as beam methods have been used for the analysis and the results from the two have been compared. Since rocking mode of beam model is not explicitly defined in the finite element model, a new concept has been proposed to simulate the rocking mode in the axisymmetric model. The earthquake response analysis of the reactor building demonstrates that the beam method is not suitable for such structures as it can not take into account the interaction effects between shell and slab. Axisymmetric finite element analysis is necessary for analyzing such complex structures. The significant contribution of the thesis is to suggest the earthquake withstand criteria for static electrical equipment (i.e., equipment which have no rotating parts like motors). The earthquake hazard is important not only for civil engineering structures but for electrical equipment also. The V damage to power station equipment due to earthquakes has necessitated tne study of dynamic behaviour of electrical systems. A prototype voltage transformer has been theoreti cally analyzed and experimentally tested in the laboratory on s shaking table under steady state sinusoidal vibrations simulating a particular earthquake environment. New test criteria have been developed,based on dynamic response of the system during a postulated earthquake, to assess the earth quake withstand capability of the system. The criteria involve experimental-cum-theoretical approach to simulate the real earthquake in the laboratory. These electrical equipment are mounted in the field on steel frame work which introduces some flexibility in the system and thus changes the dynamic behaviour of the equipment. This has been observed by making free vibration tests on a voltage transformer both in the laboratory as well as in a switchyard in the actually mounted condition. The proposed method takes into account such type of flexibility of the system. Another method of simulation of earthquake loading has been proposed which involves the testing of equipment in the static condition by applying lateral loads simulated to the required dynamic loading. Amethod to simulate the dynamic loading in a rational manner by static loading has been given. To validate the structural models assumed in the computational analysis, wind-excited in.situ experiments have VI been carried out on two actual civil structures, namely, cooling tower and chimney, to find their fundamental mode periods. The theoretically predicted fundamental periods in respect of both the structures exhibit a close agreement with the experimentally obseived fundamental periods, indicating the adequacy of the method of analysis. It has been found that the two ground motions normalized to the same spectral intensity do not necessarily result in the same response of the structure. It is, therefore, preferable to choose a shape of acceleration response spectrum and then to generate ensemble of earthquake time-histories to match the given spectrum which then can be used in the analysis.