Williot Equations for Statically Indeterminate Structures in Combination With Moment Equations in Terms of Angular Displacements
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VIEW THE REPLYPublication: Transactions of the American Society of Civil Engineers
Volume 100, Issue 1
Abstract
If the Williot diagram served only as the graphic solution for the deflections of a truss, it would still hold a prominent place among the analytic methods used by the designing engineer; but its usefulness is by no means so circumscribed. When combined with Maxwell's theorem of reciprocal displacements it is the quickest solution for statically indeterminate reactions in continuous spans, two-hinged arches, and similar structures. It also serves in determining the angular displacements of members in secondary stress analysis.
Another inherent quality in the Williot diagram recently discovered should be of consider able assistance in stress analysis. So far as known, itis a new idea in the theory of structures. Like many other inventions, necessity was the mother of this one. In studying a large and unusual structure, the writer encountered a problem in stress distribution that would not yield to an exactor even to a satisfactory solution because of the lack of sufficient equations, until he discovered them in the geometric properties of the Williot diagram.
This paper recites the circumstances lea ding up to this dilemma, describes the development of the Williot strain equations (Equations (1 3) to (21), inclusive, and Equations (29), (30), (3 6), and (37)), and shows h ow they were combined with moment equations expressed in terms of angular displacements to meet the situation.
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Transactions of the American Society of Civil Engineers
Volume 100 • Issue 1 • January 1935
Pages: 580 - 598
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© 1935 American Society of Civil Engineers.
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Published in print: Jan 1935
Published online: Feb 10, 2021
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