Abstract
The paper deals with new applications of Michell's theory for determining the layout of least-weight trusses under a single load condition and the same permissible stress for all bars. Considering cantilever trusses with a horizontal axis of symmetry, the optimal layout was derived in a closed analytical form by A. S. L. Chan and H. S. Y. Chan for a limited length: height ratio. Solutions beyond the above ratio are investigated in this paper. The results will be extended to non-symmetric cantilever trusses in Part II of this study. In both parts, a novel method is used for deriving adjoint displacements. The results are also confirmed by comparisons with discretized solutions for trusses and perforated plates.
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