Abstract The cable-suspended bridges differ from the elastic structures because of the inherent nonlinearity of the suspension cables. The primary focus of the available theories is to investigate the effect of nonlinearities associated with the distributed self-weight of the cable and its finite elastic displacements. The main point of departure of this paper is to study the effect of the configurational nonlinearity of the weightless linear elastic suspension cables undergoing small elastic displacements. Based upon authors’ theory of weightless elasto-flexible planar sagging cables, a new Beam with Elasto-Flexible Support (BEFS) model of the cable-deck interaction is proposed here. Rate-type constitutive equations and third order differential equations of motion are derived for a simple four-node cable-suspended beam structure undergoing small elastic vertical displacements. Static and dynamic analysis of the cable-suspended structures is carried out to reveal their characteristic configurational response. The proposed theory is critically evaluated in the context of existing theories of suspension bridges.

Abstract In this Paper, a theory of single sagging planer weightless elasto-flexible cables is proposed. In reference to the instantaneous natural state, hypoelastic rate- type constitutive equations and third-order nonlinear differential equations of planer motion for massless cables with nodal masses are derived. New concepts like configurational complementary potential and contra-gradient principles are proposed. Typical dynamic response of these elastic cables with different sustained loads, axial rigidity and sag/span ratios is determined. Modal, subharmonic and internal resonances, jump and beat phenomena, etc., a re predicted. A new mode of damping of 'free' vibration of the system perturbed from its equilibrium state is identified. Significance of the proposed theory of weightless sagging elasto-flexible cables is discussed.