Fatigue analysis of box-girder webs subjected to in-plane shear and transverse bending induced by railway traffic Carlos Sousa a,⇑ , João Francisco Rocha b,1 , Rui Calçada b,1 , Afonso Serra Neves a,1 a LABEST, Faculty of Engineering, University of Porto, rua Dr. Roberto Frias, 4200-465 Porto, Portugal b CEC, Faculty of Engineering, University of Porto, rua Dr. Roberto Frias, 4200-465 Porto, Portugal article info Article history: Received 31 May 2012 Revised 8 April 2013 Accepted 10 April 2013 Available online 23 May 2013 Keywords: RC structure Concrete bridge deck Box girder Fatigue analysis Damage accumulation method abstract The analysis of slender reinforced concrete box-girder webs, in bridge decks, must be carried out consid- ering the effects of in-plane shear and transverse (out-of-plane) bending. In the case of structures sub- jected to important cyclic loads, such as railway bridge decks, fatigue must also be taken into account. This paper presents a numerical methodology for fatigue analysis of reinforced concrete girder webs, con- sidering the combined effects of in-plane shear and transverse bending. Fatigue lives are calculated by using the damage accumulation method, which makes it possible to analyse variable amplitude stress histories due to real traffic. The main specificity of the proposed methodology lies in the algorithm for calculation of stress histories in the stirrups and in the web concrete. This algorithm is validated through the comparison with experimental results reported in the bibliography, which demonstrates that the pro- posed approach provides results on the safe side. The interest and practical consequences of employing this methodology in fatigue analyses of new structures are illustrated through the application to a real case study. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The main function of girder webs consists of providing adequate capacity to resist in-plane shear forces. However, these elements are also subjected to other secondary forces. In the case of box girders, important transverse (out-of-plane) bending moments oc- cur in the girder webs, associated to the structure behaviour in the transverse direction, under the effect of both permanent and live loads. Several methodologies have been proposed for taking into ac- count the combined effects of in-plane shear and transverse bend- ing in ultimate limit state (ULS) analyses. These effects were initially handled in a very simplistic way, by considering that the required cross-sectional area of stirrups should be equal to the maximum between the reinforcement required for in-plane shear and that required for transverse bending, as proposed by Robinson [1]. On the other hand, the AFGC [2] recommends a more conserva- tive approach, which consists of the independent analysis of both effects and the subsequent sum of the required areas of reinforcing steel. These are simplified approaches, and none of them is consis- tent with the actual structural behaviour. The former might lead to unsafe results. On the other hand, the latter gives rise to: (i) excessive amounts of reinforcement steel in the case of moderate concrete stresses; (ii) incoherent superposition of the concrete compressive stresses due to both effects, which might lead to un- safe results in the case of elements subjected to high concrete com- pressive stresses. However, coherent approaches (in which equilibrium conditions are satisfied) for taking into account the combined effects of in-plane shear and transverse bending, in ULS analyses, are already available. The methodology proposed by Menn [3] is based on the experimental observations by Kaufmann and Menn [4]. Alternative approaches were proposed by Lefaucher [1] and Gaspar [5]. The EN 1992-2 [6] adopted a dif- ferent methodology, based on the sandwich model. Considerably less attention has been paid to fatigue analyses. To the authors’ knowledge, only Gaspar and Stucchi [5,7] have inves- tigated the fatigue behaviour of girder webs under the combined effects of longitudinal shear and transverse bending. These authors carried out laboratorial experimental studies and proposed a methodology for fatigue design. The fatigue analysis of girder webs considering the influence of transverse bending is particularly critical in the case of railway bridge decks built with precast U-shaped girders (Fig. 1). On the one hand, cyclic effects associated to railway traffic loads give rise to important fatigue damage. On the other hand, precast girders usually have thin webs, which give rise to high shear stresses (owing to in-plane shear forces) and make these elements sensitive to transverse bending. In view of the relevance of this type of 0141-0296/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2013.04.008 ⇑ Corresponding author. Tel.: +351 22 508 1901; fax: +351 22 508 1446. E-mail addresses: cfsousa@fe.up.pt (C. Sousa), joao.francisco.a.rocha@gmail.com (J.F. Rocha), ruiabc@fe.up.pt (R. Calçada), asneves@fe.up.pt (A. Serra Neves). 1 Tel.: +351 22 508 1901. Engineering Structures 54 (2013) 248–261 Contents lists available at SciVerse ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct