New Constructions in Graphical Statics (Classic Reprint)

Excerpt from New Constructions in Graphical Statics

The possibility of obtaining a direct and complete solution of the various forms of the stiff arch rib is found to depend upon a theorem not hitherto recognized, as to the manner in which the equilibrium curve due to the applied weights is made to coincide as nearly as possible with the curve of the arch, which itself acts as a partial equilibrium curve. It is the difference in position of these two curves which is the measure of the bending moment in the arch. The solution of the arch is further simplified by showing that it depends upon that of a straight girder of the same cross section.

The theorem above referred to, which may be properly named the Theorem Respecting the Coincidence of Closing Lines, may be considered to occupy in re lation to this subject, a place analogous to Gauss' Theorem of Least Constraint in Dynamics, or Moseley's Theorem of Least Resistance in Statics, and we may'

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