One of the main goals of a good and effective structural design is to decrease, as far as possible, the self-weight of structures, because they must carry the service load. This is especially important for reinforced concrete (RC) structures, as the self-weight of the material is substantial. For RC structures it is furthermore important that the whole structure or most of the structural elements are under compression with small eccentricities. Continuous spatial concrete structures satisfy the above-mentioned requirements. It is shown in this book that a span of a spatial structure is practically independent of its thickness and is a function of its geometry. It is also important to define which structure can be called a spatial one. Such a definition is given in the book and based on this definition, five types of spatial concrete structures were selected: translation shells with positive Gaussian curvature, long convex cylindrical shells, hyperbolic paraboloid shells, domes, and long folders. To demonstrate the complex research, results of experimental, analytical, and numerical evaluation of a real RC dome are presented and discussed. The book is suitable for structural engineers, students, researchers and faculty members at universities.
Table of Contents
Introduction General concepts of differential geometry and surface theory Main concepts of differential geometry Concepts in the theory of surfaces Surface curvature Numerical examples in geometry of shells Structural principles in design of spatial concrete structures General Reinforcement schemes in shells and folders Elements of elastic shells' theory Internal forces and deformations of thin-walled shells Equilibrium equations of the shell element Convex translation shells Reinforced concrete shells with steel trusses Calculation of internal membrane forces in shallow rectangular shells Numerical examples for translation shells Long convex cylindrical shells Reinforced concrete shell structures Calculation of internal forces in a long cylindrical shell Calculating a long cylindrical shell as a simple supported beam Numerical examples for calculating long cylindrical shells Hyperbolic paraboloid shells Saddle shells Hyperbolic shells Numerical examples for hypars Shells of revolution - domes World-famous dome structures Statically determined spherical shells A dome with elastic support along its perimeter Numerical examples for domes Experimental, analytical and numerical investigations of a full-scale RC dome under vertical vibrations General Analytical investigation of long span shells due to out of phase supports' vibrations Vibration testing of the RC dome Analytical investigation of RC domes vertical vibrations Finite elements analysis of the dome natural vibration period Long reinforced concrete folders Constructive requirements The folder action in the long direction Considering the folder plates flexibility References Appendix. List of symbols