روش تحلیلی جهت پیش بینی رفتار پیچشی تیر بتنی مسلح با مواد FRP تقویت شده

ABSTRACT Analytical approach for predicting full torsional behavior of reinforced concrete beams strengthened with FRP materials

Reinforced concrete members in a structure may be subjected to loads with magnitudes higher than those considered as design loads. Axial forces, shear forces, bending moments, torsion, or a combination of these effects, are considered to design a safe structural member. For most design situations, bending moments and shear forces are considered as primary effects, whereas torsion is regarded as secondary [1]. For this reason, the torsional behavior of reinforced concrete beams is not studied as much in depth as their behavior under bending and shear stresses [1]. Torsion becomes a primary effect, however, for situations such as spandrel or curved beams [2].

The torsional strengthening of RC beams has been conducted by some techniques, such as steel plate jacketing, increasing cross sections, and adding extra steel bars. The advantages of Fiber-Reinforced-Polymers (FRPs), such as their relatively high strength to weight ratio, high resistance in corrosive regions, and their easy-to-apply character, caused engineering interest in extending the application of this material for strengthening demands [3]. While the literature on torsional strengthening is quite limited, initiated just in 2001, the flexural and shear strengthening of RC beams with FRP materials has been studied since the early 1990s [3]. Since then, flexural and shear capacity has only been included in design guides and recommendations (FIB [4], JSCE [5], ACI [6] and CSA [7]). In the case of torsional strengthening with FRP materials, only FIB proposed design equations based on shear strengthening models have been proposed [3].

Previous research on the torsional behavior of FRP-strengthened reinforced concrete beams encompassed experimental, analytical and numerical investigations. Experimental investigations on the torsional behavior of concrete beams with and without stirrups, including rectangular and T-shaped sections strengthened using FRP sheets and strips as external transverse reinforcement, have been conducted by Chalioris [8]. An analytical model based on the softened truss model in conjunction with the smeared crack theory was then proposed by Chalioris [3] to obtain the entire behavior of RC beams strengthened by FRP under torsion. The Chalioris analytical model is comprised of two distinctive steps to obtain the torsional behavior of strengthened beams in pre and post cracking stages. Ghobarah et al. [2] conducted experimental tests on FRP-strengthened reinforced concrete beams subjected to torsion and a small value of flexure, to study the effect of various strengthening configurations with carbon and glass FRP sheets and strips. To validate their experimental tests with an analytical approach, Deifalla and Ghobarah [9] utilized the compression field theory and established a series of equations for computing the contribution of FRP sheets to the torsional resistance of beam. Ameli et al. [10] presented the results of experiments together with a numerical study on reinforced concrete beams under pure torsion that were strengthened with FRP sheets in a variety of configurations. Ameli and Ronagh [11] introduced an analytical method for evaluating the ultimate torque of FRP-strengthened reinforced concrete beams based on the compression field theory. Their computational procedure only capable of predicting the torsional strength of strengthened beams and, consequently, an entire response is not obtained. Solid and box-section reinforced concrete beams with externally-bonded CFRP strips were studied through experimental and numerical work that was carried out by Hii and Al-Mahaidi [12]. Panchacharam and Belarbi [13] studied the behavior and performance of reinforced concrete members strengthened with GFRP sheets with a variety of fiber orientation, the number of beam faces strengthened, the number of FRP plies, and the wrapping configuration during experimental tests.

According to experimental tests, strengthening with continuous FRP sheets provides more efficient confinement than that of the strip, due to less crack openings [2], [8], [10], [13]. U-jacketing configuration was experimentally investigated in [8], [10], [13]. Since shear flow stresses take a circular shape during torsional load, torsion would not be well resisted in the case of U-jacketing strengthening. As expected, the torsional capacity of U-wrap strengthened beams increases less compared to full-wrap strengthened beams [8], [10], [13]. An experimental study on the effect of fiber orientation revealed that FRP sheets with fibers oriented parallel to the longitudinal axis of the beam would not contribute to the post-cracking stiffness of the beam [13].

The aim of this paper is to present an analytical model to obtain the full torsional behavior of reinforced concrete beams strengthened by FRP based on the Softened Membrane Model for Torsion (SMMT); a new model which has been recently proposed by Jeng and Hsu [14]. In fact, the contribution of this paper is an attempt to extend and modify the SMMT algorithm for the case of FRP strengthened beams. As yet, analytical models which have extended for FRP-strengthened RC beams are Compression Field Theory, Modified Compression Field Theory, and Softened Truss Model. Among these models, SMMT can predict the entire torque-twist curve by considering tension stress in equilibrium equations. Thanks to the proposed analytical approach, it is possible to predict the entire torsional behavior (pre-cracking and post-cracking stages) of FRP strengthened reinforced concrete beams.

The validation of SMMT for 81 experimental tests on reinforced concrete beams with steel bars and stirrups in [14] shows the high acceptable results. In the present study, this methodology is extended and properly modified in order to include the influence of FRP materials on torsional behavior as external reinforcement.

To obtain a reliable validation of the proposed model, reported experimental data available from the literature were considered collectively in an attempt to check the accuracy of the proposed method, based on test results of a range of parametric studies. Extensive comparisons between analytical and measured data, which also include full torsional curves of reinforced concrete beams strengthened with carbon or glass FRP materials (continuous sheets and strips) in various retrofitting configurations, are also presented and discussed herein.