Abstract
Due to their architectural attraction, hyperbolic paraboloid shells have been constructed in increasing numbers during the last decade, although very little attention has been paid towards the development of accurate methods of analysis. Even the related membrane theories have not yet been summarized. This thesis is concerned with an analytical and experimental investigation of the stresses, deformations and stability of thin hyperbolic paraboloid shells subjected to uniform and non-uniform, vertical as well as horizontal loads. After a historical review, the general-shell-theory is discussed. It is not the purpose of this thesis to describe the general shell theory in great detail and it is explained here only from a certain viewpoint, by emphasizing the great importance of VLASOV's equations. It will be pointed out that these equations provide all the sufficient and necessary information on which the theoretical investigation for all the two and three dimensional problems of elasticity rests. As long as we resort to the domain of real numbers, the VLASOV equations are the bases for all the existing shell-theories as well as the further developments which can be made in this field. A comprehensive discussion for the membrane theory of hyperbolic paraboloid shells follows, where particular attention is paid to the various shapes and loading conditions. The possibility of the direct and indirect solution as well as the permissible boundary condition are discussed and the polynomial method, as a suitable approximation for indirect solution is also introduced. The edge-disturbance and the deformation of the rectangular timber shells are investigated for two different boundary conditions. A separate chapter is devoted to the analysis of laminated timber diamond shells, where particular attention is paid to the wind effect. The creep effect and the model-prototype correlation for timber shells are also investigated. It is observed, that the membrane theory seems to be a suitable approximation for timber shells, where the material can equally resist both tensile and compressive forces. The displacements, however, are critical sometimes and to reduce them the stiffness of the unsupported edge beams has to be increased. Based on test results, nomograms are presented for the determination of the necessary edge beam sizes for a given side length and predetermined vertical displacements. An additional chapter is devoted to the timber shell in general. A simplified bending theory is developed to analyse a rectangular, precast concrete hypar shell, where two opposite low corners are built-in and no edge beams are used along the perimeter. It is found that the edge-disturbance is not critical, and the failure of the shell occurs due to tangential shear. The analytical and experimental results are not in very good agreement and discrepancies are found in certain regions of the shell. This leads to the conclusion that the bending theory is not adequate for analysing all of the possible boundary conditions, and sometimes, as in the present case, it is also necessary to investigate the non-linear behaviour. Finally, the resistance of the free edge against buckling is examined. Analytical and experimental investigations are carried out on a black Perspex rectangular hypar shell, where two opposite low corners are built-in and no edge beams are used. The analytical and experimental, results are close to each other. It is observed, that the stiffness of the edge strip is of great importance and to increase the resistance of the hypar against buckling, the inertia of the edge strip has to be increased.