Nonlinear Analytical Solution for Cable Truss

In this technical note the nonlinear closed-form static solution of the suspended biconvex and biconcave cable trusses with unmovable, movable, or elastic yielding supports subjected to vertical distributed load applied over the entire span is presented. Irvineʹs linearized forms of the deflection and the cable equations are modified because the effects of the nonlinear truss behavior needed to be incorporated in them. The concrete form of the system of two nonlinear cubic cable equations is derived and presented. From a solution of a nonlinear vertical equilibrium equation for a loaded cable truss, the additional vertical deflection is determined. The transformation analytical model serves to determine the response, i.e., horizontal components of cable forces and deflection of the geometrically nonlinear truss, due to the applied loading, considering effects of elastic deformations, temperature changes, and elastic supports. The deflection of asymmetric prestressed cable trusses has been compared with Irvineʹs linear solution as well as the nonlinear finite element model results.