Improved model for plate-end shear of CFRP strengthened RC beams Omar Ahmed, Dionys Van Gemert * , Lucie Vandewalle Department of Civil Engineering, Katholieke Universiteit Leuven, W. De Croylaan 2, B-3001 Heverlee, Belgium Received 27 August 1999; accepted 21 September 2000 Abstract In case of RC members strengthened by means of externally bonded reinforcement, a premature failure can be detected in addition to the conventional modes of failure observed in RC unstrengthened beams. The premature failure occurs mainly both shear and normal stresses induced in eitherthe externalreinforcement±concrete interfaceor at the level of steel reinforcement. This research is part of a complete programme aiming to set up design formulae to predict the strength of strengthened beams, particularly when premature failure through laminates-end shear or concrete cover delamination occurs Series of RC beams were strengthened with carbon-®ber-reinforced plastic (CFRP) laminates and tested to estimate the e the applicability ofthe formulae proposed by the authors, as well as to study the in¯uence ofthe layoutof the external reinforcement in termsof unsheeted length (the distance between CFRP laminates-end and the nearer support)and cross- sectional area,on the behaviour of strengthened beams. The predictions using the proposed formulae are compared with the obtained experimental results,as wellas with the calculated design limit states. The interfacial shear stress and the maximum de¯ection corresponding to the predicted values at maximum and service loads are also studied. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Carbon-®ber-reinforced plastic (CFRP) laminates; Anchorage shear stress; Strengthening; Shear-span; Unsheeted length 1. Introduction Carbon-®ber-reinforced plastic (CFRP) laminates are becoming a powerful technique for strengthening RC beams.The technique intends to enhance the ¯exural capacity of the original beam. However, when applying the CFRP laminates to the beam, geometrical as well as materialdiscontinuities are introduced into the com- posite system (beam/adhesive/laminates). Similarly, as in the steel plate bonding technique, the unsheeted length in the shear zone near the beam sup- ports has an important eect on the general behaviour and strength of the system. Due to higher strength of the laminates,their cross-sectional area is reduced,and therefore the geometrical relation between concrete and laminates is completely dierent from the one in bonded steel plates. In steelplate bonding only exceptionally more than one layer of plates are used. However,in CFRP lami- nates bonding, it is very easy to comprise of multiple laminates and laminate layers with dierent lengths. The use of dierent lengths can be applied to alleviate stress concentration at the laminates anchorages [1]. This paper deals with mathematical modelling and prediction ofbehaviourand strength ofCFRP lami- natesstrengthened beams, in particularwhen failure occursdue to laminates-end shear or concrete cover delamination, taking into account the in¯uence of un- sheeted length and the cross-sectional area of CFRP. This paper does not deal with other failure mechanisms like peeling-o of laminates at the laminates ends or at intermediate locations such as large shear or ¯exural cracks [2]. Tests on a series of RC beams with externally bonded CFRP laminates have been used in thisresearch to con®rm the validity of the proposed formulae to be applied in the case of CFRP strengthened beams in both ultimate and design limit states. Cement & Concrete Composites 23 (2001) 3±19 www.elsevier.com/locate/cemconcomp * Corresponding author. Fax: +32-016-32 19 76. E-mail address:dionys.vangemert@bwk.kuleuven.ac.be (D. Van Gemert). 0958-9465/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 8 - 9 4 6 5 ( 0 0 ) 0 0 0 5 1 - 2