Journal of Constructional Steel Research 67 (2011) 462–470 Contents lists available at ScienceDirect Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr Modeling of curved composite I-girder bridges using spatial systems of beam elements Theodoros Adamakos a , Ioannis Vayas a,* , Stelios Petridis a , Aristidis Iliopoulos b a Laboratory of Steel Structures, National Technical University of Athens, Heroon Polytechniou 9, Zografou, Athens, Greece b Sfaktirias 4, Kato Halandri, Athens, Greece article info Article history: Received 25 May 2010 Accepted 25 September 2010 Keywords: Curved bridges Modeling Buckling Grillage analysis Composite bridges Beam elements I-girders Warping abstract A new way of modeling steel composite bridges has been presented by Vayas et al. (in press, 2010) [3,4]. The proposed model is based on the representation of steel I-girders by equivalent trusses. The concrete slab is suitably represented by a set of bar elements, and the bearings by appropriate springs. Diaphragms and stiffeners may also be taken into account. In comparison to the grillage model, which is usually used for the analysis of bridges, the proposed three-dimensional model allows a more reliable prediction of deformations, internal forces, and stresses. Curved bridges display unique behavior characteristics, and for this reason a grillage analysis is not always suitable. The new way of modeling composite bridges, using a spatial system of beam-like structural elements, is applied in this paper for the modeling of curved composite bridges. Worked examples are provided to illustrate the set-up procedure of the proposed modeling and to compare its results with those of corresponding finite element models. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction Plane grillage models are widely used for the design of steel– concrete composite bridges. Grillage analysis is used both for the analysis and the design of the bridge for the most common design situations, as well as for the construction stages [1,2]. This method is based on idealization of the slab and the I-girders using beam elements. The longitudinal composite girders are represented by beam elements with equivalent cross-sectional properties that in- clude the steel beam and the concrete flange. The deck slab is ide- alized by a series of transverse beams. Although this model is generally accepted as sufficiently accu- rate and it has the advantage of generality, it is associated with some drawbacks. Eccentricities among the structural elements of a bridge cannot be taken into account in the model, and inevitably additional internal forces and possible load distributions are ig- nored. Torsion and distortional warping effects are difficult to be taken into account, and buckling phenomena of the steel girders during erection stages cannot be easily investigated. On the other hand, the finite element (FE) analysis that is widely used in bridge engineering also has some limitations and needs more time and effort in modeling than a grillage analysis. In ad- dition, the quantity of computations and output can be enormous, * Corresponding author. E-mail addresses: tadamakos@yahoo.com (T. Adamakos), vastahl@central.ntua.gr (I. Vayas), iliop78@otenet.gr (A. Iliopoulos). and the engineer may not always check the large amount of com- puter data and the results. Furthermore, there are various sources of error that can contribute to incorrect results, like the choice of element type, its shape, or the meshing of the structure elements. 2. Bridge analysis using a three-dimensional (3D) model A bridge analysis model should be based on the following criteria. (a) It should reflect the structural response in terms of deforma- tion, strength, and local and global stability. (b) It should include as many structural elements and parts (cross- frames, stiffeners, bearings, etc.) as possible, and their possible eccentric connections. (c) It should cover all construction stages and loading cases. (d) Loads should be easily introduced. (e) It should allow the performance of dynamic analysis and in- clude the most important modes. (f) It should run with a common analysis and design software. To overcome the difficulties of grillage and FE method analyses and to fulfil the above criteria, a 3D truss model was proposed in [3] and [4] by Vayas et al. The intention of this model was to better represent the 3D behavior of composite bridges using a new method that would be neither complicated nor time consuming compared to the grillage analysis, providing at the same time useful results that would probably require an FE analysis. 0143-974X/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2010.09.008