Reciprocal Conjugate Method for Space Curved Bars

Abstract

By means of a correspondence between two systems, each consisting of a space curved bar resting on an external medium, a complete reciprocal formulation of the conjugate structure method is herein presented. The method allows us to transform (internal and external) forces and deformations of one of the two systems into deformations and forces respectively of the conjugate one. This can be done by interchanging the field equilibrium and the mechanical boundary conditions in the two systems with the field compatibility equations and the kinematical boundary conditions and vice versa. The reciprocal correspondence descends from the Principle of Virtual Work and it can be regarded as a particular form of this principle. The Culmann and Ricci ellipse theories and the Cross column analogy are shown as particular aspects of the unified method. The equilibrium, compatibility equations and constitutive laws of the one‐dimensional space member supported on an external medium are derived in a suitable form. An application to influence lines of circular bridge, also taking into account the shear deformation effect, is developed.