Te-Hsiung Lu

Date of Award

5-1-1972

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Civil Engineering

Abstract

This thesis has been written for the purpose of using the stiffness method to analyze an orthogonal grid composed of straight and circular members that is loaded perpendicular to the plane of grid. In the development of theory, each member is assumed to carry bending, torsion and shearing force, and the axial force is neglected.

It is much more complicated to derive the stiffness matrix for a circular member than that for a straight member. The stiffness matrix for a circular member is derived by using the strain energy and Castigliano's theorem while the stiffness matrix for a straight member is found by using the slope-deflection method. Having obtained the individual member stiffness matrix, it is then shown how the equilibrium equations of a joint are expressed in matrix form. Direct superposition of stiffness coefficients associated with each individual loading state can therefore be used in forming the equilibrium equations for the whole structure.

Based on the above, a general computer program is written for evaluating the joint displacements and end actions of each member. Then a numerical example illustrates the application of the method and permits an evaluation of its accuracy and efficiency. By checking the computed results of joint displacements and member end actions, it is indicated that the method is workable and surprisingly accurate.

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