STRESSES AROUND - CAVITIES OF DIFFERENT SHAPES A PHOTOELASTIC . STUDY

Abstract

one of the major problems In the design of any ' structure Is the accurate estimation of stresses at various points. Stress analysis,# therefore,, forms a major pre-requtsite for successful design of any structure, This can be achieved either by a mathe-. matical analysis or by experimentation. Zuspite of the apparantly large volume of literature on theore. tical analysts and the advent of electronic digital computers, there are still large group of problems which either cwmot at all be solved or cannot be solved with in a reasonable time by these mathematical methods* The number of problems that can be solved by the mathematical methods are limited to those involving relatively simple boundary conditions. Lzperiment, . analysis s provides the only guide is wueb cases. Experimental methods of stress analysis are of particular sign .ficanee for the analysis of river valley structures for two foudameutal reasons. Firstly, the shape of these structures are unique and do not generally conform to type design for 2 which the rues]. methods of engineering analysis are applicable. Secondly, in massive structures like those required for river valley projects structural behaviour remains more or less un- known efld. it is only through the experimental arrangement in the prototype that a real understanding of structural behaviour could be made. The experimental methods of stress analysis oan be divided into two major gatuups. The first group supplements the sly' C tic al method by furnishing quiki; and elegantly the mathematical . solutions which would have been obtained ideally with theoretl-cal formulation provided the time and facilities for working out were available. In this class fall the several Photo--elastic methods and analogues. In the second group of experimental methods the only information a vai].able for elucidation of structural behaviour is the observation of structure itself. Cavities of different shapes are the most common featu-res of river vauey projects particularly the hydroelectric projects e.g. tunnels, shafts, galleries indam-s & power houses and surge shafts. e]ysis of these cavities fall in the category of plane stress problems which reduces the analysis to two dlmenaiaaal case. For the analysis of plane-stress problems 2dimensional. photo-elasticity is the most elegant method and have been used to analyse the different shapes of cavities. There can be a very large number of shapes of cavities used In any river valley project. The anther has analysed the most common shapes and have given the results in the form of tables and graphs which can be readily used. This study shall, be very useful for an engineer in the following respect. 4~.t 3 U) This study shell give a design engineer sufficient in- formation for selecting a most favourable shape of cavity if the critical boundry stress is the criterion for design. (ii) Stress coneentstion factors for both the horizontal & vertical stress field along axes of symmetry in the form of tables and graphs shall enable an engineer to find out hoop reinforcement around cavities of given shapes. (iiI.) The study shall also help to locate critical point in case of an underground cavity for that due precautions can be ta*en in advance during excavation.