Reinforced Concrete Flexural Members Research Articles

Modeling of flexural behavior of RC beams strengthened with mechanically fastened FRP strips

An alternative to fiber reinforced polymer (FRP) materials adhesively bonded to the concrete substrate is the implementation of mechanically fastened FRP (MF-FRP) systems using steel anchors to secure the laminate to the substrate. The benefit of MF-FRP, compared to adhesive bonding for FRP flexural strengthening, is the speed of installation with unskilled labor, minimal or absent surface preparation under any meteorological condition and immediate use of the strengthened structures. Some of the potential shortcomings are: possible concrete damage during anchoring and limited opportunity of installation in the presence of congested internal reinforcement in the members to be strengthened. Laboratory testing and a number of field applications have shown the effectiveness of the MF-FRP method. In this paper, an analytical model is discussed for reinforced concrete (RC) members strengthened with MF-FRP strips. The model accounts for equilibrium, compatibility and constitutive relationships of the constituent materials; in particular, it accounts explicitly for the slip between the substrate surface and the FRP strip due to the behavior of the fasteners. The proposed flexural model, coupled with the computation algorithm, is able to predict the fundamentals of the behavior of RC flexural members strengthened with MF-FRP strips, in terms of both ultimate and serviceability limit states. Comparisons between the analytical predictions and the experimental results have been successfully performed.

Predicting the Response of FRP-Strengthened Reinforced-Concrete Flexural Members with Nonlinear Evolutive Analysis Models

To design efficient and economical strengthening solutions, the structural performance before and after the intervention must be accurately evaluated. In the case of statically indeterminate structures or when the structure has suffered damage or deterioration, linear elastic analysis methods are not adequate to obtain the residual capacity and the structural effects of the intervention because of the nonlinear response of the structure. In such cases, refined analytical models able to capture the structural nonlinear behavior, the effects of previous damage, and those produced by any intervention are required to design safe and economical strengthening solutions. In this paper, a nonlinear and time-dependent evolutive analysis model, previously developed by the authors, is applied to the prediction of the response of fiber-reinforced polymer (FRP)-strengthened concrete structures in flexure. The model can take into account the structural effects of changes in geometry, structural scheme, material properties, and applied loads that may occur along the structure service life, including those attributable to strengthening. A criterion to predict peeling failure in FRP-strengthened beams on the basis of nonlinear fracture mechanics consisting in evaluating the maximum shear force that can be transmitted to the concrete by the FRP laminate between cracks or at the laminate end is incorporated in the model. Two previous experimental programs have been used to validate the model. First, four RC continuous beams, three of them strengthened with FRP laminates and tested to study the influence of the FRP arrangement, are analyzed. Second, two beams previously precracked owing to service loads and strengthened with FRP are analyzed under increasing load up to failure. In all cases, very good agreement between the theoretical and the experimental results is obtained in terms of deflections, strains, reactions, internal forces, and failure mode, showing the capabilities of the model to evaluate the efficiency of proposed strengthening solutions.

Tension-Stiffening Model Attributed to Tensile Reinforcement for Concrete Flexural Members

Adequate modeling of reinforced concrete (RC) cracking and, particularly, post-cracking behavior (tension-stiffening), as one of the major sources of a nonlinearity, is the most important and difficult task of the deformation analysis. Present investigation aims at deriving a steel-related tension-stiffening relationship based on the smeared crack approach. The analysis uses the results of the experimental program performed by the authors. It consisted of three beams reinforced with three deformed bars of 18, 14 and 10mm in diameter. Other characteristics of the beams were almost identical. An inverse technique has been developed to derive a steel-related tension-stiffening model from the moment-curvature diagrams of the beams. The constitutive relationship recommended by Eurocode 2 was assumed for the compressive concrete, whereas the elastic-brittle behavior was taken for the concrete in tension. The tensionstiffening effect was modeled by the stress-strain relationship of the tensile reinforcement. For the model assumed, total stresses in the tensile reinforcement consist of genuine stresses corresponding to the average strain of the steel and the additional stresses due to tension-stiffening. It was found that the tension-stiffening stresses, normalized in regard to reinforcement area, have become almost independent on the amount of reinforcement. The proposed technique is capable of investigating the tension-stiffening behavior in RC flexural members.

Plastic Hinge Length in Reinforced Concrete Flexural Members

For reinforced concrete (RC) flexural members, the plastic deformation is localized in a small zone namely the plastic hinge zone after the yielding of the member. The performance of the plastic hinge zone is critical for flexural members as it governs the load carrying and deformation capacities of the member. Therefore, plastic hinge has been of great interest to structural designers and researchers for decades. The length of the plastic hinge zone is an important design parameter where intense confinement should be provided to increase the ductility of the member for survival from extreme events such as earthquakes. The behavior of plastic hinges is very complicated due to the high nonlinearity of materials, interaction and relative movement between the constituent materials, and strain localization. As a result, most researchers investigated the problem through experimental testing. Restricted by the time and cost involved in large tests, very limited knowledge has been obtained up to date. This work tries to investigate the problem analytically with Finite Element Method (FEM) using the computational software DIANA. A computational model is built and verified with existing experimental data including load deflection response, rotational capacity, and strain and stress distributions of reinforcement. With the calibrated FEM model, the extent of the rebar yielding zone, concrete crush zone, curvature localization zone and the real plastic hinge length are studied. Parametric studies are subsequently employed to investigate the plastic hinge length in terms of material properties of rebar and concrete, dimensions of the member, and reinforcement ratio.

Deflection Calculation of Frp-Strengthened Reinforced Concrete Flexural Members

SummaryExternally bonded fibre-reinforced polymer (FRP) composite plates can enhance the flexural strength, as well as stiffness to a limited degree, of reinforced concrete (RC) flexural members. Understanding the behaviour of these strengthened members at the serviceability and ultimate load ranges of response is of particular importance to engineers. The description of such behaviour is best described via plotting of the complete moment-curvature, as well as load-deflection responses from initial load to member failure. Based on the assumption of a tri-linear moment-curvature relationship, closed-form analytical solutions are presented in this paper for calculating the complete load-deflection response of FRP flexurally-strengthened one-way RC slabs and beams, which are simply-supported (three- and four-point bending), as well as cantilevered (free-end point load). The analytical predictions compare well with test results and the basis of a new “quad-linear” moment-curvature relationship is proposed that may better capture a so-called “pseudo-ductile” response occasionally observed in experiments. The influence of anchorage of the FRP strengthening for the prevention or delaying of debonding and a procedure for its inclusion in the analytical model is also discussed. Finally, the results of parametric studies are presented.

Deformation-Controlled Design of Reinforced Concrete Flexural Members Subjected to Blast Loadings

Both maximum displacement and displacement ductility factors should be considered in the design of a blast-resistant structure since both parameters correlate with an expected performance level of a reinforced concrete (RC) structural member during a blast event. The blast-resistant design procedure discussed in this paper takes into account both the maximum displacement and displacement ductility responses of an equivalent single-degree-of-freedom (SDOF) system, while the response of the SDOF system is made equivalent to the corresponding targets of design performance. Some approximate errors are present when comparing the actual responses of the structural member, which has been designed for blast loading, and their corresponding design performance targets. Two indices are defined to quantify the approximation errors, and their expressions are obtained through comprehensive numerical and statistical analyses. By using the error indices, the design procedure is then modified such that the approximate responses of the RC member are equivalent to the targets of the design performance. The modified procedure is implemented in three design examples and numerically evaluated. It is concluded that the modified procedure can be used more effectively in order to ensure that the actual responses of designed members reflect the respective targets of design performance.

Concrete Component of the Rotational Ductility of Reinforced Concrete Flexural Members

Reinforced concrete flexural members inherently rely on member ductility to ensure a safe design by allowing for: redistribution of applied stress resultants; quantification of drift for determining magnified moments; and for the absorption of seismic, blast and impact energy. Structural engineers have recognised that much of the member rotation is concentrated in a small region referred to as the plastic hinge and because of the complexity of the problem this has been quantified mainly through testing. In this paper, a new plastic hinge approach that is based on well established shear-friction theory is postulated. The generic behaviour of this novel shear-friction hinge is shown to agree with that exhibited in tests. Furthermore, the shear-friction hinge explains the mechanics of the benefits of confinement, such as that due to FRP encasement or steel stirrups, on the rotational capacity of RC members.

Damping and Viscoelastic Dynamic Response of RC Flexural Members Strengthened with Adhesively Bonded Composite Materials

A theoretical approach for the dynamic viscoelastic response of reinforced concrete (RC) beams and one-way slabs strengthened with adhesively bonded composite materials is developed. The analytical model is based on variational principles, dynamic equilibrium, and compatibility of deformations between the structural components (RC beam/slab, adhesive, composite material). The model accounts for the deformability of the adhesive layer and for its high order stress and displacement fields. The equations of motion and the boundary, continuity, and initial conditions are derived via the extended Hamilton’s principle. The Kelvin-Voigt approach is adopted for the consideration of the viscoelastic response of the adhesive material and the internal damping in the composite material and the RC member. The Rayleigh damping model is used for the external viscous damping of the RC member. The dynamic governing equations are solved using the Newmark time integration and a multiple shooting algorithm is used for the so...

Shear capacity and failure behavior of DFRCC repaired RC beams at tensile region

Many shear dominant structural members in existing concrete structures have been evaluated as below serviceable standard requiring strengthening and/or repair. In order to repair these aged reinforced concrete (RC) structures, a section replacement method of removal and replacement of old concrete and/or steel reinforcements of damaged sections with new concrete and/or steel reinforcements are commonly used. However, this repairing method is used without understanding the complicated structural behavior such as shear behavior of RC structures. Also, the materials commonly used for repairing are concrete and cement mortar. In order to implement the material superiority of newly developed cement based material and to complement the disadvantages of cement-based construction materials such as brittleness of failure, Ductile Fiber Reinforced Cementitious Composite (DFRCC), a high performance cementitious composite with superior strain capacity, is currently being used as a repair material. However, the composite behavior between old substrate and new repair material is not clearly understood at present. In order to effectively apply DFRCC as repairing material on RC structure, the interface, the weakest part in the repaired system where most failures occur, must be studied in depth. In this research, the composite behavior of a RC flexural member repaired using the superior tensile capacity of DFRCC on the tensile face of a RC specimen is studied. Two types of DFRCC repaired RC specimens are tested, one is without shear stirrups and the other is with shear stirrups. By comparing these two types of DFRCC repaired specimens, the failure mechanism and interface debonding behavior as well as repairing capacity can be effectively studied.

Probabilistic response evaluation for RC flexural members subjected to blast loadings

The probabilistic responses of the maximum displacement and displacement ductility factor for a reinforced concrete (RC) flexural member against potential blast loadings are evaluated through a nonlinear dynamic analysis of its equivalent single-degree-of-freedom (SDOF) system. Monte-Carlo simulation is used in the analysis. Some differences are observed between the actual responses of the RC member and those of the equivalent SDOF system due to the complex behaviours of reinforced concrete structural members under blast conditions. Two non-dimensional indices are defined to quantify the differences and their expressions are generated through a large amount of numerical and statistical analyses. The approach of utilizing the indices into a probabilistic response assessment of RC flexural members accounting for different kinds of uncertainties is illustrated via four numerical examples which are verified through nonlinear dynamic finite element analysis. It is concluded that the probabilistic response of RC flexural members obtained from the developed approach have a similar distribution with those from probabilistic nonlinear finite element analysis.

Effect of strain ratio variation on equivalent stress block parameters for normal weight high strength concrete

Replacement of actual stress distribution in a reinforced concrete (RC) flexural member with a simpler geometrical shape, which maintains magnitude and location of the resultant compressive force, is an acceptable conceptual trick. This concept was originally perfected for normal strength concrete. In recent years, high strength concrete (HSC) has been introduced and widely used in modern construction. The stress block parameters require updating to account for special features of HSC in the design of flexural members. In future, more varieties of concrete may be developed and a corresponding design procedure of RC flexural members will be required. The usual practice is to conduct large number of experiments on various sizes of specimen and then evolve an empirical relation. This paper presents a numerical procedure through which the stress block parameters can be numerically derived for a given strain ratio variation. The material model for concrete is presented and computational procedure is described. This procedure is illustrated with several variations of strain ratio. The advantages of numerical procedure are that it costs less and it can be used with new material models for any new variety of concrete.

Experimental Study on Intermediate Crack Debonding in FRP-Strengthened RC Flexural Members

A commonly observed failure mode of reinforced concrete (RC) flexural members strengthened with a fibre reinforced polymer (FRP) plate bonded to their tension face involves debonding that initiates at a major flexural or flexural shear crack and propagates towards a plate end, which has often been referred to as intermediate crack (IC) debonding. This paper first presents the results of IC debonding tests conducted on eighteen cantilever slabs in which IC debonding initiated at or near the fixed end, and four simply-supported slabs in three-point bending where IC debonding initiated at the load position. A number of factors are covered by these tests, including the type of FRP material, the width of FRP strip, the length of FRP strip, the slab width, the concrete strength, the longitudinal steel ratio, the concrete cover, and pre-cracking of concrete. The test results are next used to assess the accuracy of four available strength models that can be used to design against IC debonding. Of these four models, Teng et al's (2003) model is shown to provide safe predictions of the test results in most cases but can lead to overly conservative results; the scatter of the predictions is also large. The other three models from recent design guidelines (JSCE, 2001, fib 2001, ACI 440 2002) are not sufficiently safe for use in design. This assessment clearly illustrates the need for much further research to develop a more accurate IC debonding strength model.

Reinforced High-Strength Concrete Beams in Flexure

An important design issue is the ductility or the ability of a reinforced concrete (RC) member to deform at or near the ultimate load without significant strength loss. This article reports on a study of reinforced high-strength concrete (HSC) beams in flexure. The study included flexural test results generated on 16 reinforced concrete beams. Test parameters considered include concrete compressive strength, ratios of tensile and compressive reinforcements, and spacing of lateral ties. The authors found that the current code provisions for serviceability requirements of maximum crack width and ultimate strength are adequate up to a concrete strength of approximately 130 MPa. The authors express concerns regarding the adequacy of current code provisions, however, for cracking moment and service load deflection. They show that stresses generated by shrinkage of concrete and the creep associated with it can significantly affect the cracking moment and service load deflection of reinforced HSC beams. The authors recommend that the ACI Code specification for maximum spacing of ties in RC flexural members need to be reduced to d/4, particularly at critical sections. This will prevent premature disintegration of the confined concrete core in the compression zone due to buckling of compression reinforcement.

Influence of Concrete Cover on Fire Resistance of Reinforced Concrete Flexural Members

Six specimens with different concrete cover (CC) thickness (10–30 mm) were tested to investigate the influence of the CC on the properties of reinforced concrete flexural members exposed to fire. The specimens were heated on their bottom and two lateral surfaces. From these test results, it is shown that the bottom CC has significant influence on the specimen ultimate loading capacity, but the extent of this influence will decrease with an increase in the CC thickness. Thus, it is improper to excessively increase the bottom CC thickness to improve the specimen fire resistance. The lateral CC has a less beneficial effect on the specimen fire resistance compared to the bottom CC. A concept of the equivalent CC thickness is proposed in this paper to better predict the effect of the CC on the flexural capacity of reinforced concrete members exposed to fire.

Effect of axial restraint on mechanical behavior and average crack spacing of reinforced concrete flexural members

This study was performed to verify the effect of axial restraint on the mechanical behavior and average crack spacing of reinforced concrete (RC) flexural members. Experiments for mechanical behavior have been performed on axially restrained and unrestrained RC beams. And, the average crack spacing has also been investigated in other RC beam tests under the axially restrained condition. The test results show that the capacity of the axially restrained beam was higher than that of the unrestrained beam. For restrained flexural members, axial deformation was restrained, deformation capacity was decreased, plastic behavior was delayed, and possibility of compressive failure was increased due to the axial restraint force. The major variables affecting the average crack spacing were steel stress, axial force, circumference of reinforcing bar, and effective tension area of concrete. However, the effect of concrete compressive strength was minimal. A prediction equation utilizing the identified variables was proposed for determining the average crack spacing of the axially restrained RC flexural members.

New Solution for Prediction of Chloride Ingress in Reinforced Concrete Flexural Members

Control and monitoring of chloride-induced reinforcement corrosion is of practical significance if premature failure of reinforced concrete structures is to be prevented. Of all predictive models available, it appears that Fick's second law has been the most widely used in practice to determine the chloride ingress in concrete.

Effect of Force-Temperature Paths on Behaviors of Reinforced Concrete Flexural Members

Building structures subjected to fire will generally experience complex force-temperature paths. In this paper, these paths are expressed simply by two basic paths: the path of constant forces but subjected to elevated temperature (FT path), and the path of constant temperature but subjected to applying forces (TF path). A total of 13 beam specimens subjected to two such basic paths were tested. The results show that the fire resistance for the FT path is different from that for the TF path; the former is always greater than the latter, and the two are similar only when the temperature exceeds 525°C or thereabout. However, there are always great differences between their deformations. Therefore, the behaviors of reinforced concrete flexural members subjected to fire are closely dependent on the force-temperature paths they experience. Thus, in fire-resistant design, especially for statically indeterminate structures, to more accurately ascertain their fire resistances the force-temperature path factor can...

Load-Deflection Analysis of FRP Reinforced Concrete Flexural Members

This paper is devoted to the deformability investigation of concrete flexural members reinforced with fiber-reinforced polymer (FRP) rebars. The analysis is carried out both theoretically, by means of a general procedure derived from a cracking analysis founded on slip and bond stresses, and experimentally, by means of flexural tests on aramid FRP reinforced concrete beams. Predictions of the general procedure are compared with both those furnished by models usually adopted for the analysis of FRP reinforced concrete structures and available experimental results. Finally, results of comparisons are discussed to demonstrate the effectiveness of model predictions and their applicability for design purposes.

Externally Bonded FRP for Service-Life Extension of RC Infrastructure

Although the concept of repairing and strengthening reinforced concrete (RC) structures using steel plate reinforcement has been established for more than 30 years, today there is an increasing trend toward the use of externally bonded fiber-reinforced polymer (FRP) composites, such as glass FRP and carbon FRP. This paper summarizes the results of a comprehensive survey of field applications of both steel plates and FRP composites as external reinforcement for the life extension of deteriorating RC flexural members. A literature review conducted to assess the need for infrastructure rehabilitation suggests that the problem with structurally deficient or obsolete structures is one of large magnitude needing immediate attention. Based on the collective findings from a survey of field applications, a review of literature on the state of the infrastructure and a database of laboratory studies, a list of research priorities is compiled for further studies investigating the use of FRP composites as external reinforcement for RC flexural members. Overall, it is concluded that future research on the application of FRP to RC members should focus on conditions that are more similar to what is observed in the field.

Shape Optimization of RC Flexural Members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. These design examples—a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads—have been optimized. The results show a significant savings (40–56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.