Thesis (M.S.)--University of Wisconsin--Madison, 1960. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 140-141).

Thesis (M.S.)--University of Wisconsin--Madison, 1962. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 149-150).

Thesis (M.S.)--University of Wisconsin--Madison, 1961. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 33).

Thesis (M.S.)--University of Wisconsin--Madison, 1960. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 71).

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This study of the bending of a spherical shell of constant thickness consists of five chapters. In the first chapter, general differential equations of the problem are derived and presented with the variables in dimensionless form. The second chapter deals with the solution of the two second order differential equations in terms of Bessel Functions. The solution is applicable for shells with a colatitude of about 25 degrees or less. Expressions are given for the internal stresses and displacements in terms of these values at the boundary. The third chapter gives a numerical solution of the problem. Solutions are found for three cases of radius to thickness ratio, namely 30, 100 and 500, and for colatitudes from 8 to 90 degrees. In the preparation of tables the Alwac III-E Electronic Digital Computer was used. The flow diagram and programme for the Alwac III-E are given. The fourth chapter compares the numerical method with one of Timoshenko's approximate solutions. The wave lengths, deflections, rotations and moments are calculated by two methods and compared. As the conclusion to these comparisons a graph is given, which shows the approximate error in the damped harmonic solution. In the last chapter, a numerical example is solved using tables from the digital computer. The ratio of radius to thickness is 500; radius being 125 feet and the colatitude 30 degrees. The edges are considered as being on rollers. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The linear analysis of a specific framed dome is mapped for the unsymmetric loadings of half snow and wind. The joints of the dome, to which the loads are applied, lie on a spherical surface but the connecting members are straight. Several parameters, such as the perimeter ring size, the web member area, geometric conformity, and joint fixity, are changed and the effects of these changes are compared and discussed. It is shown that membrane shell theory closely approximates the member forces induced by wind. An approximate system to find the member forces is presented and compared with the exact analysis. This system is based on overall structure equilibrium and an assumed distribution of edge shear. All analyses were made using a space frame program based on the stiffness method with six degrees of freedom per joint; An IBM 7040 computer was used for calculations. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

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