Issue 38

P. Lonetti et alii, Frattura ed Integrità Strutturale, 38 (2016) 359-376; DOI: 10.3221/IGF-ESIS.38.46 360 important especially for new or advanced bridge configurations such as the ones proposed in the framework of cable- stayed suspension self-anchored schemes, in which, in order to guarantee the reliability of such configurations, it is important to investigate collapse behavior and load carrying capacity of the bridge [3, 4]. In the literature, many research efforts are developed to analyze the influence of geometric and material nonlinearities on the structural behavior of cable supported bridges, especially for cable-stayed configurations. In this framework, the bridge behavior was analyzed by means of two different approaches, which are known as the Bifurcation Point Instability (BPI) and the Limit Point Instability (LPI) approaches. BPI is based on an eigenvalue analysis, which predicts the buckling strength and the corresponding mode shapes of the bridge structure [5-7]. However, since initial imperfections, residual stresses and inelastic behavior of bridge members are not taken into account, this approach may lead to inaccurate results in presence of relevant nonlinearities. As a matter of fact, several studies, based on formulations, which involve both geometric and material nonlinearities, have shown that material inelastic behavior of structural members highly affects the nonlinear static behavior of the bridge structure [8-11]. Both geometric and material nonlinearities were considered in the modified BPI approach proposed by Yoo and Choi [12, 13] in which the effect of material inelasticity in the structural members was reproduced by means of classical tangent modulus theory and column–strength curves provided by current design codes. Moreover, an iterative eigenvalue analysis was adopted to calculate, at each computational step, the tangent modulus of each structural member. However, such approach evaluates only the load-carrying capacity and the corresponding collapse mode, without enter in details in the prediction of the step-by-step behavior or the service bridge configuration. Alternatively, advanced analyses based on step by step integration procedures are proposed in the literature with the purpose to evaluate the complete load-displacement curves. In this framework, the nonlinear inelastic behavior is identified by means of the plastic zone method, which reproduces material nonlinearities arising from the constitutive relationships: globally for the beam-column elements and locally for each fiber of the cross-sections [14-17]. Although plastic zone method leads to accurate results, it requires intensive computational time and cost in the numerical analysis [18]. In addition, the local approach, utilized in material description, introduces mesh dependence effects, which affect the accuracy of the proposed results. In the literature, the load carrying capacity can be also identified by using plastic hinge method, which adopts stability functions and lumped plastic effects at both ends of the elements to capture geometric and material nonlinearities, respectively [19-21]. The considerable advantage of this method is that it is simple in both formulation and implementation and it requires a relatively reduced number of mesh elements in the numerical modeling, avoiding as a result convergence problems and mesh dependence effects of the solution. However, in order to compute accurately the actual response of the structure, the location of the plastic hinges should be known before the analysis. In order to overcome weaknesses of the plastic hinge method and, at the same time, to retain the computational efficiency of the numerical procedure, an hybrid approach based on a fiber hinge beam–column method was developed in [22, 23]. Such method is based on stability functions and fiber model to predict geometric and material nonlinearities, respectively, which are introduced, at discrete number of cross-sections, divided by many fibers, to control the plastic flow in the structure. It is worth noting that the above referred studies, specifically involved in the framework of cable supported bridges, take in account mainly material nonlinearities in both girder and pylons, without introducing any source of nonlinearities in the constitutive elements of the cable system. Such contributions are considered only in rare cases and mainly in the framework of cable-stayed bridges [16, 24]. However, such effects should be taken into account especially in those bridge configurations mostly dominated by the cable system configurations, such as of pure suspension or combined cable-stayed suspension, in which, typically, the cable system plays an important role in the cable force distribution and in the ultimate bridge behavior. Therefore, parametric analyses are quite important especially in the framework of new advanced cable-supported schemes, such as the mixed cable-stayed suspension configurations, whose use, in comparison to existing conventional bridge schemes based on pure cable-stayed or suspension bridges, is quite limited due to the lack investigation and knowledge. This is the case of self-anchored cable-stayed suspension bridges, which especially in the last few years, have received much attention since they are able to combine the best properties of pure cable-stayed and suspension systems leading to structural and economic advantages [25-28]. For this reason, the purpose of present study is to propose an efficient numerical model to analyze the nonlinear static behavior of self- anchored cable-stayed suspension bridges with the purpose to quantify numerically the influence of each source of nonlinearities involved in the bridge components on the ultimate strength of the bridge. To this end, a parametric study in terms of bridge properties, geometric and mechanical characteristics including also comparisons with conventional bridges based on pure cable-stayed and suspension configurations are proposed. The outline of the paper is as follows: in Section 2 a description of the self-anchored cable-stayed suspension bridge together with the formulation of the bridge modelling and the evaluation of the initial configuration is presented. The numerical implementation is reported in Section 3, whereas in Section 4 numerical comparisons and parametric results in terms of bridge formulations, material properties and geometric characteristics are proposed.