Equivalent axial stiffness of horizontal stays

Cable-stayed structures are widely employed in several fields of civil, industrial, electrical and ocean engineering. Typical applications are cable-stayed building roofs, bridges, guyed masts, overhead electrical lines, and floating device anchorages. Since the cable behavior is often highly nonlinear, suitable equivalent mechanical cable models are often adopted in analyzing this kind of structures. Usually, like in the classical Dischinger's approach, stays are treated as straight rods offering an equivalent axial tangent stiffness, so that each of them can be substituted with an appropriate equivalent nonlinear spring or truss element. Formulae expressing equivalent stiffness provided by classical methods are satisfactory only when the cable is highly stressed, and therefore its sag is small with respect to its chord; on the contrary, when the cable is slack, they give often contradictory or meaningless results. Aiming to remove that limitation, a more refined approach based on the application of the virtual work principle is discussed. Important products of that original rational criterion are accurate and closed form innovative expressions of the tangent stiffness of the cable, whose field of application is independent on the sag to chord ratio of the cable, as well as on the magnitude of the normal stresses. Referring to some relevant case studies, the results obtained applying these new formulae are critically discussed for cables made of different materials, also in comparison with the approximate expressions provided by simplified methods.