A Closed-Form Refined Model of the Cables' Nonlinear Response in Cable-Stayed Structures

Abstract

In this paper a refined second-order model for the analysis of the elastic response of cables in cable-stayed structures is proposed. Starting from the exact catenary theory, the Dischinger-Ernst formulation is rationally deduced and, performing a second order approximation both with respect to the stress variation and the apparent chord-strain one, a refined explicit equivalent constitutive relationship for elastic stays is obtained. Moreover, the geometrical non-linearities induced on the cable by the deformation of the stay-supported structure are taken into account through a second order displacement approach. Accordingly, a closed-form formulation describing nonlinear cable-structure interaction effects is obtained which, unlike the classical secant model, does not need iterative procedures, opening the possibility to develop refined analytical solutions for cable structures. Several numerical examples and benchmarks on different stay configurations are presented, showing the effectiveness and the accuracy of the proposed model.

Flutter Performance of the Emergency Bridge with New‐Type Cable‐Girder

“…Based on a quasi-secant large-displacement formulation, a nonlinear continuous model for the analysis of long-span cablestayed bridges was proposed; the model opens the possibility to develop more refined closed-form solutions for the analysis of cable-stayed structures [25]. In order to consider nonlinear response of cable-stayed structures, a closed-form refined model was proposed [26]. To simplify the dynamic analysis of emergency bridge, the equivalent modulus of elasticity (Ernst 1965) [27][28][29][30] had been used to consider the sag effect of main cable.…”

Tension Analysis of Submarine Cables during Laying Operations

“…Hao et al [19] adopted the extrapolation method to analyze the effects of bending stiffness of the cable and current drag forces on cable tension and configuration, which required iterative computation until the accuracy satisfied permissible error. Similarly, Vairo [20] proposed a refined second-order model to obtain the elastic response of cables. Unlike the model mentioned in [19], the procedures had no need to iterative computation with taking into nonlinear cable-structure interaction effects.…”

Convex analysis and ideal tensegrities

“…As notation, x u and x o denote the unstressed and the reference element lengths, respectively, and F o is the pre-stress value of F . the unstressed configuration 3 and are characterized by a non-linear lengthening response essentially due to sag effects [18]. Therefore, cables equivalent force-extension response can be suitably described by a piecewise-linear relationship corresponding to a zero stiffness in compression and to an equivalent linear behavior in tension.…”