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Abstract: Arch bridges are generally considered widely as esthetically pleasing bridges and its different variations can be found from both historical and modern times all over the word. Arch bridges can be divided into several different types by different definition. One possibility to divide them is through the spandrel. Spandrel can be open or closed. When it is open, there are usually columns to transmit the loads from the deck to the arch. The purpose of this study is to determine the optimum design of arch longitudinal no prismatic single-cell section. In this study, Cetina Bridge, which is a long span open reinforced concrete arch bridge spanning Cetina river canyon near the town of Trilj. The arch is of span 140m with a rise of 21.5 m, giving rise-to-span ratio of 1/6.5. The FE model of the Cetina open spandrel arch bridge was constructed using the Ansys. The main span and columns was simulated with Beam4, and element solid45 was used for reinforced concrete non prismatic single cell arch. For definition of arch geometry in longitudinal sections, parabolic conic functions are employed. In this present work the optimum design is carried out by taking total material volume of substructure of bridge as objective function. Substructure includes of column and reinforced concrete arch. Height of skewback abutment, Height of crown of arch, back and soffit radii of arch and position of crown respect to global axes are considered as design variables. The distance between the columns is assumed constant and equal to 21.6 m in optimization process. Also the cross sections of column are not taken as design variables. Instead of this, cross section of piers is selected proportionally with these of application project. During problem formulation most of practical design variables and constraints are considered. Three type of design constraints were taken into account: stress constraints of arch, transversal displacement constraints of arch crown and geometric constraint. Initially, a program is developed in MATLAB in order to generate coordinate of nodes, then is taken finite element software ANSYS for modelling the geometry of an arch dam. Finally, the optimization technique is performed by Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. Shape optimization for each of the arch web thickness to be examined (i.e. t_w=0.3-0.5m ). The following, some of important conclusions are drawn from the present work: It is concluded that SPSA can be effectively used in the shape optimization of the bridges. The total reinforced concrete volume obtained in this study is 23% less than the application project. For each t_w, the optimum arch geometry is obtained, when the volume of the arches and columns is minimized. Minimum volume of substructure achieved for t_w=0.35m with 1131 m3 . Keywords: long span; Open Arch Bridge; SPSA algorithm; Finite Element Analysis; substructure; shape optimization;

Keywords: long span, Open Arch Bridge, SPSA gradient based algorithm, substructure, shape optimization

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