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    Abstract
    This paper presents the results of an experimental investigation on the response of reinforced concrete box beam under combined actions of bending moment, shear and cyclic torque, strengthened with externally bonded carbon fiber reinforced polymer sheets (CFS). Three strengthened box beams and one reference box beam were tested. The main parameters of this experiment were the amount of CFS and the wrapping schemes. The failure shapes, torsional capacities, deformation capacities, rigidity attenuations and hysteresisbehaviours of specimens were studied in detail. The experimental results indicated that the contribution of externally bonded CFS to the aseismic capacity of box beam is significant. Based on the text results and analysis, restoring force model of CFS strengthened R.C. Box beam under combined actions of bending moment, shear and cyclic torque was established. _ 2005 Elsevier Ltd. All rights reserved.4266
    Keywords: Strengthening; Cyclic torque; Box beam; Carbon fiber sheets; CFS; Torsional capacity; Restoring force model1. Introduction
    In current practice, torsional strengthening of concrete members is achieved by one of the following methods [1]:
    (1) increasing the member cross-sectional area combined with adding of transverse reinforcement, (2) using externally bonded steel plates and pressure grouting the gap between plate and concrete element, and (3) applying an axial load to the member by post-tensioning.
    Although these methods will continue to be used in many more instances, fiber reinforced polymer (FRP) composites provide another option for strengthening. Strengthening structural elements using FRP enable the designer to selectively increase their ductility, flexure, and shear capacity in response to the increasing seismic and service load demand. Shear strengthening or flexural strengthening of reinforced concrete beams using composite materials were studied by several researchers and investigators at several institutions. However, studying the torsional strengthening of structural elements using FRP has not received much attention [2,3]. The reasons for the lack of research in the area include the specialized nature of the problem and the difficulties in conducting realistic tests and representative analyses. It is also a reason that few practical structures need to be strengthened to increase the torsional capacity under cyclic
    torque.In designs of great bridge structures, the transversal torsional deflection and bending torsional deformation of bridge girder due to transversal seismic action or lateral wind force maybe have great influence [4]. For this reason, many researchers have paid more attentions on the studies of torsional capacity, bending torque coupling effect and loss of stability due to lateral inclination [5,6]. The present project is rather unique in addressing torsional retrofit of reinforced concrete (RC) box beams under bending, shear and cyclic torque using carbon fiber
    reinforced polymer sheets (CFS). Three CFS strengthened box beams and one unstrengthened box beam were tested. The results were compared and addressed the following factors: The amount and fiber orientation of the CFS composites.
    2. Experimental program
    2.1. Test specimens and test setup
    This experimental program consisted of four identical RC single cell rectangular box beams with a box-shape cross section of 600 mm • 400 mm with 50 mm wall thickness (as shown in Fig. 1). The total span of the beam was 3400 mm long. All the four specimens were reinforced with 3–20 mm diameter longitudinal bars in bottom wall and 3–12 mm diameter longitudinal bars in top wall (fy = 310 N/mm2). The hoops of 6.5 mm diameter were spaced 100 mm apart on center throughout the test region of beam length (fyv = 210 N/mm2). Nine hundred millimeter long of the beam, from concentrated loading point to the end of the beam, were reinforced with hoops of 6.5 mm diameter at space of 50 mm on center, which assure that this part does not crack at first. The cube compressive strength of concrete was 40 N/mm2. The homogeneous unilateralism carbon fiber reinforced polymer (CFS) was used with the following material properties: The ply thickness is 0.111 mm, modulus of elasticity is 233 GPa and ultimate tensile strength is 4100 MPa. The control and strengthened beams were tested on a self-design torsional test setup. Cyclic torque moment was applied through a lever arm at one end of specimen by a MTS hydraulic actuator. The specimen was also loaded at the point of 3/4 span lengths by a jack. This concentrate vertical force results in the bending moment and shear force on the beam. The schematic of test setup was shown in Fig. 2.
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