Proceedings of the Institution of Civil Engineers Bridge Engineering 162 September 2009 Issue BE3 Pages 119–126 doi: 10.1680/bren.2009.162 .3.119 Paper 700017 Received 21/07/2007 Accepted 20/05/2009 Keywords: beams & girders/concrete structures/ mathematical modelling Job Thomas Lecturer in Civil Engineering, School of Engineering, Cochin University of Science and Technology, Cochin, India Ananth Ramaswamy Professor, Department of Civil Engineering, Indian Institute of Science, Bangalore, India Analysis of prestressed fibre-reinforced concrete beams J. Thomas PhD and A. Ramaswamy PhD This paper presents the test results of 12 partially prestressed concrete flexural beams reinforced with steel fibres that failed in flexure over partial or full depth. The variables considered were strength grades of concrete (35, 65 and 85 MPa) and the presence of steel fibres in the cross-section of the beam (web, flange or full depth). Three-dimensional finite element analysis of the pre- stressed beams was carried out to assess the non-linear behaviour of concrete, for example post-peak softening, concrete cracking strain softening, tension stiffening, bond-slip and yielding of reinforcement. Also, the effects of the addition of steel fibres in the concrete (increase in tensile strength and control of crack width due to the bridging of fibres across the crack interface) were modelled. The bond-slip behaviour of longitudinal rein- forcements (steel fibres, prestressing wire and deformed bars) was accounted for to capture the structural stiffness of the concrete beam accurately. The effects of steel fibres in the concrete beam section over partial or full depth were also modelled. All prestressed beams were analysed using Ansys. Load–deflection responses and cracks in the prestressed concrete beams were predicted and compared with experimental results. The predicted results were found to be in good agreement with the corresponding test results. The analytical model pre- dicted crack patterns in the concrete quite accurately. 1. INTRODUCTION High-strength concrete and high-strength steel are commonly used in prestressed concrete structures to achieve economical proportions. 1 At ultimate stages of loading, the constituent materials of partially prestressed structures, that is concrete, prestressing steel and deformed bars, exhibit non-linear stress– strain variation. The presence of steel fibres in the concrete induces a multi-axial state of stress, which results in a higher strength. The bridging of steel fibres across the crack increases the post-cracking tensile stiffness of concrete. However, the post- cracking tensile stiffness through the bridging of steel fibres is a function of fibre–matrix debonding. The literature on modelling of steel-fibre-reinforced concrete (SFRC) structures accounting for the non-linearity associated with the effects of steel fibres is, however, limited. 2–7 This paper discusses details of a three dimensional (3D) finite element (FE) model that accounts for the effects of steel fibres, the non-linear behaviour of constituent materials and bond-slip of longitudinal reinforcements. The stress transfer between steel and a concrete matrix in reinforced concrete structures is known to have a close inter- relation with the bond and crack formations at various stages of loading. The bond-slip characteristics between steel and the concrete matrix strongly influence the progressive cracking of reinforced beam structures. 8 The modelling of the bond-slip of longitudinal reinforcements, that is steel fibres, prestressing steel and deformed bars, is vital in capturing the behaviour of partially prestressed beam structures. 9 This study uses a linear variation as reported in the literature 9 to model the bond-slip of longitudinal reinforcements. The load–deflection response, location of critical cracks and crushing of concrete in partially prestressed concrete beams is predicted using a 3D FE model. The factors influencing the modelling and analysis of reinforced concrete structures using a FE approach have been reported. 8,10,11 The failure surface for concrete, the stress–strain behaviour of concrete in tension and compression, models for the interface bond-slip of steel with the surrounding concrete, and sophistications in crack and crack interface modelling have all been described. 7–13 However, these topics are still advancing and are the subject of many specially organised symposia and workshops around the world. A number of current software packages are based on specialised and sophisticated algorithms for the non-linear FE analysis (NLFEA) of reinforced concrete structures. For example, Ansys 14 has a dedicated 3D eight-node element with non-linear characteristics of brittle materials. The eight-node element in Ansys can be used to simulate the cracking and crushing of concrete. In this work, 12 partially prestressed concrete beams were modelled using Ansys. With this technique, the advantages of adding steel fibres to concrete are illustrated. NLFEA models and procedures remain complex and tend to be limited in their range of applications. Accurate modelling of the complex behaviour of reinforced concrete demands more attention. In this work, a NLFEA of the flexural performance of partially prestressed concrete beams was carried out using Ansys. The predicted results are compared with experimental data. 2. EXPERIMENTAL PROGRAMME Test beam specimens were cast using three different grades of concrete, that is cube compressive strengths of 35, 65 and 85 MPa, corresponding to normal strength, moderately high- strength and high-strength concrete, respectively. Four beams of Bridge Engineering 162 Issue BE3 Analysis of prestressed fibre-reinforced concrete beams Thomas N Ramaswamy 119