Conjugate Analogy for Space Structures

A theorem of conjugate analogy is derived which generalizes the well-known conjugate beam method for bars, beams, and structures consisting of one-dimensional members of arbitrary shape (including curved bars) and with arbitrary supports, connections, and joints (including non-rigid ones). It also applies to thin-walled bars, for tension and shear, and for inelastic materials. It develops from the analogy between the geometry of small deformations and the equilibrium condition which is presented in vectorial integral form. This analogy permits the determination of deformations, deflection lines, influence lines, flexibility coefficients, as well as differential relations between deformations according to the equilibrium conditions of the conjugate structure which is obtained by replacing all supports and connections with their conjugates and loaded by conjugate loads (corresponding to curvature changes, extensions and shear angles at deformation).