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UBC Theses and Dissertations

Optimum Michell frames Johnson, Eric William

Abstract

The theory underlying the design of minimum volume space frameworks is reviewed. Fundamental theorems and relations proposed and developed by Maxwell, Michell, Cox, Chan, Hemp, Johnson and Barnett are discussed and examined from a practical viewpoint. Two dimensional frames, which are close geometric approximations to the theoretical concepts of Michell, are defined and formulas established for their design and complete solution. Computer programmes are established for the analysis of pin jointed trusses having a wide range of parameters. The effect of changing parameters on the structural properties is discussed. Rigid frames are analyzed by the use of STRUDL, [STRUctural Design Language], a multi-purpose computer programme for the calculation of forces and displacements in rigid structures. The effects of biaxial stress in the joints and other deviations from the theoretical concept are examined. Comparison is made with other structural designs to establish the superiority and economy of the Michell design. Birefringent models are made, using a numerically controlled milling machine, and tested under load in a polariscope, to confirm the predicted stress levels in the members and stress concentrations in the joints. Examples are given of practical application of Michell space frames. The design of a high tension transmission tower and of a lightweight astronomical mirror support are considered. Alternative solutions to both problems are suggested to provide a basis for more detailed design.

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