Relative Flexure Factors for Analyzing Continuous Structures

An effective method of analyzing the moments in continuous structures, by using the geometrical properties of elastic curves, is offered in this paper. In using the method, a graph consisting of a series of lines connecting these centers of rotation is substituted for a graph consisting of a series of moment diagrams. Each angle between the lines represents a moment area, both as to its magnitude and also as to the location of its center of gravity. It is not necessary that the graph be drawn to scale as the work is analytical. The method also involves use of the familiar mechanical requirements that the moments about a joint must balance, for equilibrium, and that the shear in a member must equal its combined end moments divided by its length. The series of lines referred to is designated as a “traverse of the elastic curves,” because the lines which pass through points of support or joints in the structure will be, in fact, tangents to the curves formed by the flexed structure.