Authored by Shervin Maleki*
Abstract
Using spatial cable arrangement to mitigate seismic responses of long cable-stayed bridges is investigated in this study. The innovative cable system strengthens the bridge using cross arrangement of secondary cables. First, a survey on the constructed cable-stayed bridges was performed to establish the dimensions of typical cable-stayed bridges for analyses. Then, a parametric study was carried out in order to achieve appropriate characteristics for the components of the spatial cable system such as, the layout of the cable system, cable effective area and post tensioning forces. Finally, twelve cable-stayed bridges with different cable layouts and main span lengths of 300, 400 and 500 meters were modeled and analyzed. Analyses were carried out using elastic nonlinear direct integration time-history method under six scaled near-fault earthquake ground motion records in the longitudinal and transverse directions, simultaneously. The main purpose of this study is to investigate the effect of supplementary spatial cable system on the seismic performance of cable-stayed bridges. Effectiveness of spatial cross system cable arrangement was assessed by the reduction observed in the seismic responses of the critical parts of the cable-stayed bridges. It was concluded that supplying cable-stayed bridges with spatial cross system cable arrangement decreases the longitudinal seismic response of the deck and it lowers the shear forces and moments in the pylons, especially in longer span cable-stayed bridges.
Keywords: Cable-stayed bridges; Spatial cable; Cable arrangement; Seismic performance
Introduction
Cable-stayed bridges are the most practical and economical solution for the span lengths ranging from about 200 to over 1000 meters [1]. Despite the popularity of cable-stayed bridges in recent decades, research about their seismic behavior is still ongoing. The role of the cables with distinctive architecture and nonlinear behavior leads to the complexity of seismic behavior in both the lateral and longitudinal directions. Due to high construction and maintenance expenses of such bridges, the need for further research about the seismic behavior and its improvement is obvious. Both dynamic and static response of cable-stayed bridges have also been addressed by many studies since the early 1980’s [2-7]. Karoumi [8] investigated modeling techniques for the stay cables under dynamic moving loads. Kawashima & Unjoh [9] showed the importance of damping and complications related to its estimation originating from the cable-stayed bridge elements (towers, cablesystem and deck), their configuration and interactions between the elements. Fleming & Egeseli [10] discussed the dynamic response of a cable-stayed bridge to seismic, wind and simulated traffic loads. They considered non-linear behavior of the cables and concluded that the non-linearity of the cable-stayed bridges must be considered in determining the stiffness of the structure, even under static gravitational loads. Abdel-Ghaffar [11] and Abdel-Ghaffar & Khalifa [12] studied the dynamics of cable-stayed bridges with special attention to nonlinear behavior, the sensitivity to support conditions, cable-vibration phenomena and spatial variability. Wilson & Walker [13] investigated natural modes of vibration of cable-stayed bridges, through numerical analyses. Bruno & Leonardi[14] also studied the lateral and torsional vibration modes of cable-stayed bridges. They observed small contribution of the minor deck stiffness and the tower shape to flexural oscillations, with the exception of torsional modes, which were considered clearly affected by afore-mentioned factors. He et al [15] considered semi-active damper, passive viscous and constant friction dampers between deck and bridge pylon to mitigate seismic response of a cable-stayed bridge. They showed that the type of the connection between the deck and the towers is a key factor in the static and dynamic behavior of cable-stayed bridges. The case-studies of Fujino & Siringoringo [16] about Yokohama Bay bridge (Japan), Liu et al [17] about Hangzhou bridge (China), Morgenthal [18] about Rion Antirion bridge (Greece) and Nazmy and Abdel-Ghaffar [19] considered the effect of different deck to pylon connections as well as two extreme cases of floating and fixed connections. As a new proposal, innovative using of spatial cable-system for seismic response mitigation and rehabilitation of cable-stayed bridges is investigated in this paper. The idea came from the system with two transversally inclined cable planes, which is used in some pipeline bridges (e.g., the bridge across the Labe River in the Czech Republic) as shown in Figure 1 [20]. The main purpose of this study is to investigate the effect of supplementary spatial cable system on the seismic performance of cable-stayed bridges. The seismic consequences of different spatial cable-system arrangements considering key parameters like the main span length and deck to pylon connection are investigated. Among possible spatial cablesystem configurations, it is found that the cross-system cable arrangement has a better performance in mitigating lateral and longitudinal seismic responses of the deck. In addition, the crosssystem arrangement is effective in improving the longitudinal seismic response of the pylons (Figure 1).
Finite Element Modeling
Detailed review of the section dimensions and proportions of several constructed cable-stayed bridges was performed to establish the base models for this study. The main span, as the key parameter defining the dimensions of the rest of the bridge, was considered as 300,400 and 500 meters. The models were assumed to have two H-shaped towers, as most of the constructed cablestayed bridges do. These models herein are named the base models and are designated as H300, H400 and H500, which have no spatial cable arrangement. The deck was assumed to hold four traffic lanes with a total width of 22 meters. The cross section of the deck for all bridge models was considered the same as that assumed by Pedro et al [21]. It consisted of a 0.25 m thick slab in composite action with two 2.5 m deep steel girders at two sides and steel cross-girders spaced at 10 m supporting the slab together with steel subsidiary beams. Figure 2 demonstrates a schematic 3D view of the deck elements. Figure 3 represents the schematic model of the considered bridges. Based on the review of constructed bridges, the height of the tower above the deck was considered to be 0.3 times the main span length and the height of tower below the deck was assumed to be 50 meters. The main cables were considered to have semi-fan configuration, which connect the whole length of the deck to the upper half of the towers. Post-tensioned multi-wire helical strands with total area of 19.6 cm2 were considered as the main cables. Nonlinear cable elements were used for modelling cables. The cable elements were assumed to be capable of withstanding tensile forces only and cannot carry compression. Figure 4 represents the finite element model of the H400 base bridge. The type of the connection between the deck and the pylons has major effects in the seismic behavior of cable stayed bridges. The constructed cable-stayed bridges in seismic areas usually possess deck to tower connections that are different from the usual floating connection. In the floating type of connection, the deck is free to move in the longitudinal and lateral directions and rotate in torsional mode. Hence, no reaction is directly exerted to the tower under lateral earthquake forces. In this connection, the displacement of the deck is partially constrained between both towers, by cables. In the restrained connection system, the longitudinal, lateral and torsional degrees of freedom are considered to be fixed between the deck and the tower. However, the rotation about the longitudinal and transverse axes of the bridge are released. In this study, the restrained type of deck to tower connection was employed in the base models (Figures 2-4).
Spatial lateral cable system
A solution to the problems associated with lateral loads on cable supported bridges with long and slender spans is to modify the cable system so that it can resist not only vertical, but also lateral loads. As an innovative solution, a new spatial cable system is proposed herein, similar to the spatial cable systems, which have been already used in pipeline bridges [20] (see Figure 1). Two transversely inclined main cables have been considered on either side of the cable-stayed bridges to improve the seismic performance of such bridges. To achieve reasonable seismic performance, it is crucial to use cross-type cable system to connect the deck to the main spatial cables. The pretension force in the cross-type cables give a curved shape to the main spatial cables. Post-tensioned multi-wire helical strands of total 78 cm2 with arc curvature of 8% and 15% in horizontal inclination are used to model the main spatial cables, in all span lengths. Two spatial cable systems are proposed, as illustrated in Figure 5, namely ‘XSC’ and ‘MXSC’ systems. The XSC system consists of a cable-stayed bridge (base model), in which only the longitudinal constraints connecting deck to towers are released completely, supplemented by spatial lateral cables through the whole length of the deck, and anchored in the abutment foundations. The MXSC system consists of cable-stayed bridge base model, in which all longitudinal, lateral and torsional constraints connecting the deck to towers are released completely, supplemented by spatial lateral cables covering the distance between the pylons and anchored to the pylons foundations. These bridge models are compared with the base model having no spatial cable system with fixed deck to tower connection. Also, another version of the base model (called NLT model) in which the lateral and torsional constraints of the deck to towers are released are considered to investigate the effects of deck-pylon connection type on the transverse responses (Figure 5).
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