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Home > Publications > International Concrete Abstracts Portal
The International Concrete Abstracts Portal is an ACI led collaboration with leading technical organizations from within the international concrete industry and offers the most comprehensive collection of published concrete abstracts.
Showing 1-5 of 9 Abstracts search results
November 1, 1988
W. C. Schnobrich
Umbrella and gable configurations are two of the most popular hyperbolic parabolic geometries. Early design of those shells was accomplished through the use of membrane theory. This determinant theory predicted overall behavior of these shells as a double cantilever beam for the inverted umbrella and as a simple beam for the gable shell. As long as the dimensions of these shells were small enough, this theory was adequate. However, with increased spans and with flatter applications, the theory proves to be inadequate. Bending solutions achieved by a finite element analysis prove to be necessary. Results from such analysis demonstrate the influence of several design parameters. The major role played by the dead weight of the edge and ridge beams is demonstrated.
The equations for a bending theory of shallow shells are specialized to the case of the hyperbolic paraboloid shell. The nature of the analytic solutions to these equations that have been achieved for this class of shells is described. Such analytical solutions involve boundary conditions that depart significantly from those present in real shell applications. Types of numerical approximate solutions present as alternatives are noted and the details of one of these, the finite element method, are described. The importance of the dead weight of perimeter or support beams is noted, demanding a bending solution with real support conditions. Some representative solutions are included as examples.
Alex C. Scordelis
The state of the art for the analysis and design of hyperbolic parabolic (HP) shells is reviewed. The necessary expressions for determining the internal membrane stresses in the shell and the internal axial forces, shears, and bending moments in the groin arch due to surface dead and live loads on the shell are given. A special-purpose computer program GROINV, for the membrane analysis of HP groined vaults with a minimum of input data, is briefly described. The program is available from the author. Numerical results for several groined vaults with varying amounts of curved shell overhang are presented and their structural behavior with respect to concrete and reinforcing steel requirements is compared. Recent developments in the nonlinear finite element analysis of reinforced concrete shells that account for membrane and bending actions are reviewed, and results obtained for HP groined vaults loaded to ultimate failure using computer programs developed at Berkeley are briefly described with respect to their design implications.
A;lex C. Scordelis
A review of the state of the art for the membrane analysis of hyperbolic parabolic (HP) shells is presented. Membrane solutions using simple statics are given for HP shells having square, rectangular, or parallelogram shapes in plan and subjected only to uniform vertical loading over the horizontal projection of the shell. Statics of shell-edge beam systems are discussed for saddle shells, inverted umbrellas, gable shells, and shells on two supports. Membrane stresses for general loadings on parallelogram-shaped HP shells obtained using a differential equation approach are described. Stress transformation formulas are given that can be used to find principal membrane stresses in the shell and boundary stresses to be transmitted to the edge members. Membrane stresses in HP shells having an arbitrary quadrilateral shape are discussed and procedures for determining them are discussed.
Editor: Jack Christiansen
Offering both utility and beauty, the hyperbolic paraboloid (HP) shell came to the attention of American designers in the early 1950's. Since that time, many hyperbolic paraboloid structures have been built both in the United States and around the world. This state-of-the-art report on hyperbolic paraboloids is the culmination of over ten years of research and fact gathering. Effort has been devoted to developing analysis and design data and techniques for hyperbolic paraboloid concrete shells, especially for umbrella, gable and saddle shells. "Hyperbolic Paraboloid Shells" offers the latest information on topics such as: bending theory, saddle shells, hyperbolic paraboloid performance and cost, groined vaults, membrane analysis and construction.
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