Quadrature Solutions for Large Deflection Static Cable Problems

It is shown that solutions to the governing equations for arbitrarily large static deflections of cables obeying any elastic law can be reduced to quadratures for four general types of distributed loadings. These solutions are given in closed form and ways of using them are discussed. It is observed that the final shape can be found without knowledge of the initial shape in three cases and without knowledge of the elastic law in two if the final length of the cable is regarded as known. These latter two cases considerably generalize the classical catenary and parabola solutions.