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Over the last few decades, shell structures have become bigger--they cover larger areas without intermediate supports and thinner. Because of this, the problem of buckling of shells has grown in importance. This paper contains an overview of the general problem of stability of reinforced concrete shells. The buckling phenomenon is defined and its manifestations in columns, plates, and shells are discussed. The linear critical load concept is reviewed first, followed by a consideration of geometric nonlinearities and of geometric imperfections of the shape of the shell as built. Next, the material properties of reinforced con-crete and its response under load are reviewed. The properties of inelastic behavior of concrete and reinforcement, the cracking of concrete, the amount of reinforcement, and the effects of concrete shrinkage and creep are discussed. These factors make the buckling behavior of reinforced concrete shells significantly different from metallic shells and cause a reduction in the load-carrying capacity of the shell. Current approaches to shell stability analysis and design are commented on.

A state-of-the-art review of the stability of cylindrical shells is presented. The copious theoretical results available in the literature are discussed and compared with available experimental results. Reasons for the well-known discrepancies between theory and experiment are indicated and various design formulas which take these discrepancies into account are given. Most of the available experimental data are for linearly elastic metallic or plastic specimens. The behavior of these can differ markedly from the behavior of reinforced concrete structures which are subject to cracking and material nonlinearity. The applicability of linearly elastic shell data to the buckling analysis of concrete shells is discussed briefly on the basis of a comparison of the few test results for reinforced concrete shells with those for elastic shells.

The purpose of this paper is to present a state-of-the-art review of the stability of reinforced concrete domes and hyperbolic paraboloids aimed principally at presenting useful information to the designers of such shells. Analytical results, experimental results, and applications to design, together with appropriate references, will be reviewed and summarized for each of the following shell types: (1) spherical domes, (2) translational and other double curvature domes, (3) hyperbolic parab-loids, and (4) groin vaults. The effects of the following important parameters on the buckling of reinforced concrete shells are discussed: (1) geometric imperfections, (2) creep, (3) cracking of concrete and amounts of reinforcement, and (4) material non-linearity. A design approach is suggested to account for these effects. A number of examples of existing large span reinforced concrete shells are cited to illustrate the range of dimensions which have been used successfully in the past.

A review of research activities directed to evaluating the onset of buckling of reinforced concrete folded plate stru-tures is presented. Guidelines and recommendations to the designer as to when buckling might be a problem and how to consider this in the design are also presented. The review includes a description of the development of methods of analysis and, for a limited application, specific formulas suitable for use with mini-computers. The validity of the analytical methods is discussed in view of a number of studies made on small, elastic models and tests on buckling of reinforced concrete plates. The results of the various studies, which were almost solely limited to prismatic structures, indicate local plate buckling, as opposed to lateral stability, is indeed a problem which should be considered for long-span structures. The present methods of analysis for buckling which consider the inelastic material response of concrete, are approximate but felt to be conservative.

The objectives of this review of the buckling of cooling tower shells are to survey available experimental results, to discuss various analytical and numerical approaches, and to evaluate current practice for buckling predictions in design. The paper focuses on the problem of stability of large, concrete hyperboloids subject to wind loadings. There exists only a small body of experimental results relevant to this problem. Three categories of analysis approach are identified and reviewed: (a) scaled-up wind tunnel tests, (b) methods based on axisymmetry, and (c) methods not based on axisymmetry. No single approach is universally accepted or used, and various views of structural modeling are discussed. For example, some designers and research-ers advocate a local buckling criterion as opposed to a global stability treatment. Some other differences include: bifurcation predictions as opposed to limit-point analyses, reduced shell theories to obtain lower bounds rather than full shell theories, and axisymmetric simplifications instead of full nonaxisymmetric methods. It appears that bifurcation calculations with well-verified methods can provide an acceptable estimate of wind-loaded hyperboloid buckling for routine design purposes. The prediction of buckling for the design of cooling tower shells could be improved by more experimental evidence for the verification and comparison of prediction methods.