Size Effects for Reinforced Concrete Beams Strengthened in Shear with CFRP Strips

The principal motivation of this study is to obtain a clear understanding of size effects for fiber-reinforced polymer (FRP) shear-strengthened beams. The experimental program consists of seven beams of various sizes grouped in three test series. One beam of each series is used as a benchmark and its behavior is compared with a beam strengthened with a U-shaped carbon FRP (CFRP) jacket. The third test series includes an additional beam strengthened with completely wrapped external CFRP sheets. The experimental results show that the effective axial strains of the CFRP sheets are higher in the smaller specimens. Moreover, with a larger beam size, one can expect less strain in the FRPs. A nonlinear finite-element numerical analysis is developed to model the behavior of the CFRP shear-strengthened beams. The numerical model is able to simulate the characteristics of the shear-strengthened beams, including the interfacial behavior between the concrete and the CFRP sheets. Three prediction models available in current design guidelines for computing the CFRP effective strain and shear contribution to the shear capacity of the CFRP shear-strengthened beams are compared with the experimental results.     

钢筋混凝土结构裂缝分析与防治

多年来,在工程建设领域一直存在着钢筋混凝土结构的裂缝问题,这是个相当普遍的质量问题也是个迫切需要解决的技术难题,本人从设计、施工、材料等方面结合自己的实践经验分析了成因并提出防治办法。     

Torsional Capacity of CFRP Strengthened Reinforced Concrete Beams

Many buildings and bridge elements are subjected to significant torsional moments that affect the design, and may require strengthening. Fiber-reinforced polymer (FRP) has shown great promise as a state-of-the-art material in flexural and shear strengthening as external reinforcement, but information on its applicability in torsional strengthening is limited. Furthermore, available design tools are sparse and unproven. This paper briefly recounts the experimental work in an overall investigation of torsional strengthening of solid and box-section reinforced concrete beams with externally bonded carbon fiber-reinforced polymer (CFRP). A database of previous experimental research available in literature was compiled and compared against fib Bulletin 14. Modifications consistent with the space truss model were proposed to correct the poor accuracy in predictions of CFRP contribution to strength. Subsequently, a design tool to analyze the full torsional capacity of strengthened reinforced concrete beams was validated against the experimental database.     

Flexural Behavior of Continuous GFRP Reinforced Concrete Beams

The results of testing two simply and three continuously supported concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars are presented. The amount of GFRP reinforcement was the main parameter investigated. Over and under GFRP reinforcements were applied for the simply supported concrete beams. Three different GFRP reinforcement combinations of over and under reinforcement ratios were used for the top and bottom layers of the continuous concrete beams tested. A concrete continuous beam reinforced with steel bars was also tested for comparison purposes. The experimental results revealed that over-reinforcing the bottom layer of either the simply or continuously supported GFRP beams is a key factor in controlling the width and propagation of cracks, enhancing the load capacity, and reducing the deflection of such beams. Comparisons between experimental results and those obtained from simplified methods proposed by the ACI 440 Committee show that ACI 440.1R-06 equations can reasonably predict the load capacity and deflection of the simply and continuously supported GFRP reinforced concrete beams tested.     

Analytical Method for Evaluating Ultimate Torque of FRP Strengthened Reinforced Concrete Beams

The behavior of fiber reinforced polymer (FRP) strengthened reinforced concrete beams subjected to torsional loads has not been well understood compared to other loads. Interaction of different components of concrete, steel, and FRP in addition to the complex compatibility issues associated with torsional deformations have made it difficult to provide an accurate analytical solution. In this paper an analytical method is introduced for evaluation of the torsional capacity of FRP strengthened RC beams. In this method, the interaction of different components is allowed by fulfilling equilibrium and compatibility conditions throughout the loading regime while the ultimate torque of the beam is calculated similarly to the well-known compression field theory. It is shown that the method is capable of predicting the ultimate torque of FRP-strengthened RC beams reasonably accurately.     

Fundamental Frequency Testing of Reinforced Concrete Beams

Tests were conducted to measure the fundamental frequencies of reinforced concrete beams. Beams were tested prior to load application and after they had been loaded to various fractions of their ultimate moment capacity. Dynamic testing was performed in an unloaded state in both the direction of loading and in the direction perpendicular to loading. Resulting fundamental frequencies were used to determine the dynamic flexural stiffness (EdI) relative to the undamaged flexural stiffness. Results show that fundamental frequency tests can effectively measure decreases in dynamic flexural stiffness caused by flexural cracking. However, the effective moment of inertia in the relaxed state is not accurately predicted by American Concrete Institute recommendations for computing static beam deflections. Equations were developed to describe the effective flexural stiffness of unloaded, cracked beams. A relative dynamic flexural stiffness value of 70 provides a conservative prediction that a beam has failed by being loaded to its ultimate moment capacity.     

Moment Redistribution in FRP and Steel-Plated Reinforced Concrete Beams

Research on retrofitting reinforced concrete (RC) beams and slabs using externally bonded (EB) fiber reinforced polymer (FRP) or steel plates has reached the stage where the flexural strength can be determined with confidence. Research has also shown that EB plated structures tend to debond at relatively low strains and to such an extent that guidelines often preclude moment redistribution which can severely restrict the use of plating. However, recent research on retrofitting using FRP and steel near surface mounted plates (NSM) has shown that NSM plates tend to debond at high strains which can allow substantial amounts of moment redistribution. A moment redistribution approach has been developed for both NSM and EB plated beams that allows for the wide range of debonding strains that can occur. This allows RC beams to be retrofitted for both strength and ductility which should help expand the use of this convenient and inexpensive form of retrofitting.     

Flexural and Interfacial Behavior of FRP-Strengthened Reinforced Concrete Beams

Although there is a large amount of experimental data available on the fiber-reinforced polymer (FRP) strengthening of concrete structures, a full understanding of the various debonding phenomena is somewhat lacking. As a contribution to fill this need, two-dimensional and three-dimensional (3D) nonlinear displacement-controlled finite-element (FE) models are developed to investigate the flexural and FRP/concrete interfacial responses of FRP-strengthened reinforced concrete beams. Interface elements are used to simulate the FRP/concrete interfacial behavior before and after cracking. The analysis is carried out using two different relations for the interface; namely, nonlinear and bilinear bond–slip laws. The results predicted using these two laws are compared to those based on the full-bond assumption. The FE models are capable of simulating the various failure modes, including debonding of the FRP, either at the plate end or at intermediate cracks. The 3D model is created to accommodate cases of FRP-strengthened reinforced concrete beams utilizing FRP anchorage systems. In addition, the models successfully represent the actual interfacial behavior at the vicinities of cracks including the stress/slip concentrations and fluctuations. Results are presented in terms of the ultimate load carrying capacities, failure modes and deformational characteristics. Special emphasis is placed on the FRP/concrete interfacial behavior and cracking of the concrete. The numerical results are compared to available experimental data for 25 specimens categorized in six series, and they show a very good agreement.     

Fatigue of Reinforced Concrete Beams Strengthened with Steel-Reinforced Inorganic Polymers

Steel-reinforced polymer (SRP) composite materials are very attractive due to their low weight and high strength. The ease of installation which significantly reduces repair time and expense is another major advantage. One of the main disadvantages of SRP materials is that the matrices used for their fabrication are typically organic and thus they are susceptible to fire. In this study, a newly developed retrofit system is being used. It consists of high strength steel fibers impregnated in a fireproof inorganic matrix. The objective of this study is to examine the effects of this hybrid rehabilitation system on the fatigue performance of strengthened reinforced concrete beams. Sixteen 100?mm×150?mm×1200?mm reinforced concrete beams with enough transverse reinforcement to avoid shear failure were used in this study. Nine beams were strengthened with steel fiber sheets on their tension faces. The results from the present study indicate that the fatigue life of reinforced concrete beams, subjected to the same cycling load, can be significantly extended using externally bonded sheets. A rather important finding is that although the strengthening system increases the fatigue life of the beams, the failure mechanism remains the same in both strengthened and nonstrengthened beams. Thus, it is possible to predict the fatigue life of a cyclically loaded beam using existing fatigue models. Furthermore, no delamination failures were observed due to fatigue loading.     

Experimental Behavior of Reinforced Concrete Beams Strengthened with Prestressed CFRP Shear Straps

One promising means of increasing the capacity of existing shear-deficient beams is to strengthen the structure using external prestressed carbon fiber reinforced polymer (CFRP) straps. In this system, layers of CFRP tape are wrapped around a beam to form a strap that acts like a discrete unbonded vertical prestressing tendon. Experiments were undertaken to investigate the influence of the strap spacing, the strap stiffness, the initial strap prestress level and/or any preexisting damage on the strengthened behavior, and mode of failure. An unstrengthened control beam was tested and failed in shear. In contrast, all of the strengthened beams showed a significant increase in their ultimate load capacity with several of the strengthened beams failing in flexure. A number of different failure modes were noted and initial guidelines on the design parameters that influence the propensity for a particular failure mode were developed.     

Flexural Fatigue Behavior of Reinforced Concrete Beams Strengthened with FRP Fabric and Precured Laminate Systems

Rehabilitation of existing structures with carbon fiber reinforced polymers (CFRP) has been growing in popularity because they offer resistance to corrosion and a high stiffness-to-weight ratio. This paper presents the flexural strengthening of seven reinforced concrete (RC) beams with two FRP systems. Two beams were maintained as unstrengthened control samples. Three of the RC beams were strengthened with CFRP fabrics, whereas the remaining two were strengthened using FRP precured laminates. Glass fiber anchor spikes were applied in one of the CFRP fabric strengthened beams. One of the FRP precured laminate strengthened beams was bonded with epoxy adhesive and the other one was attached by using mechanical fasteners. Five of the beams were tested under fatigue loading for two million cycles. All of the beams survived fatigue testing. The results showed that use of anchor spikes in fabric strengthening increase ultimate strength, and mechanical fasteners can be an alternative to epoxy bonded precured laminate systems.     

Prediction of the Failure Time of Glass Fiber Reinforced Plastic Reinforced Concrete Beams under Fire Conditions

A model is proposed to predict the time to failure of reinforced concrete beams in a fire. The model is developed specifically to predict the lifetime of beams reinforced with glass fiber reinforced plastic rebar, but is applicable to beams with any form of reinforcement. The model is based on the calculations for flexural capacity and shear capacity of beams embedded within ACI design codes where time and temperature dependent values for rebar modulus and strength and concrete strength replace the static design values. The base equations are modified to remove safety factors and where necessary the temperature induced reductions in strength for concrete and steel are derived using the equations presented by EUROCODE 2. In order to validate the model it was used to predict the failure times of steel rebar reinforced beams that had been documented in the literature. There was excellent agreement between the model and the reported lifetimes for these conventional beams. The model was applied to predict the lifetimes of two beams that had been manufactured and tested for destruction in a fire by the research group. The model predicted that the failure mode of the beams would be because of rebar rupture as opposed to the design condition of concrete crushing and this was confirmed by the experimental test results. The model provided reasonable agreement with experimental results with a lifetime of 108?min predicted based on flexural failure and 94 and 128?min observed in the experiments.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. II: Computation

Following the formulation of the constitutive model in the preceding Part I in this issue, the present Part II addresses the problems of computational algorithm and convergence of iterations. Typical numerical responses are demonstrated and the parameters of the model are calibrated by test data from the literature.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. I: Theory

Presented is a new microplane model for concrete, labeled M5, which improves the representation of tensile cohesive fracture by eliminating spurious excessive lateral strains and stress locking for far postpeak tensile strains. To achieve improvement, a kinematically constrained microplane system simulating hardening nonlinear behavior (nearly identical to previous Model M4 stripped of tensile softening) is coupled in series with a statically constrained microplane system simulating solely the cohesive tensile fracture. This coupling is made possible by developing a new iterative algorithm and by proving the conditions of its convergence. The special aspect of this algorithm (contrasting with the classical return mapping algorithm for hardening plasticity) is that the cohesive softening stiffness matrix (which is not positive definite) is used as the predictor and the hardening stiffness matrix as the corrector. The softening cohesive stiffness for fracturing is related to the fracture energy of concrete and the effective crack spacing. The postpeak softening slopes on the microplanes can be adjusted according to the element size in the sense of the crack band model. Finally, an incremental thermodynamic potential for the coupling of statically and kinematically constrained microplane systems is formulated. The data fitting and experimental calibration for tensile strain softening are relegated to a subsequent paper in this issue, while all the nonlinear triaxial response in compression remains the same as for Model M4.     

Fracture Analysis of FRP Reinforced Concrete Beams

Carbon∕epoxy FRP (Fiber Reinforced Plastic) rebars were produced with the pultrusion technique. Concrete beams reinforced with these rebars were subjected to static and cyclic 3-point bending. Flexural cracking is arrested by an adequate bond between the FRP and the concrete because of the use of a carbon fiber overwrap on the otherwise smooth pultruded rods. In spite of the brittle nature of the FRP rods and the concrete, their combined behavior demonstrate ductility in excess of what is typically expected from reinforced concrete. An analytical evaluation of the fracture energy shows that such ductility is due to the large fraction of the total strain energy that is consumed in the formation of distributed cracking in concrete. Therefore, if an adequate bond can be provided, the strain-to-failure of the FRP determines the ductility and failure mode of FRP reinforced beams.     

Prediction Models for Debonding Failure Loads of Carbon Fiber Reinforced Polymer Retrofitted Reinforced Concrete Beams

This study focuses on debonding failure in reinforced concrete beams with carbon fiber reinforced polymer composite bonded on the soffit using the wet lay-up method. An experimental study, which involved 26 tests, was carried out. The experiments showed two failure modes: Intermediate span debond and end debond. The first failure is the result of the high bond stress near the tip of a flexure-shear crack, whereas the second type of failure is due to the high shear stress developed in the weakest concrete layer at the tension reinforcement level. The experiments have shown that U-straps can be effective in preventing intermediate span and end debond. Based on experimental observations, two simple and practical theoretical models were developed and verified with the experimental data, together with a large database of other existing tests.     

Deflection Calculation of FRP Reinforced Concrete Beams Based on Modifications to the Existing Branson Equation

Fundamental concepts of tension stiffening are used to explain why Branson’s equation for the effective moment of inertia Ie does not predict deflection well for fiber reinforced polymer (FRP) reinforced concrete beams. The tension stiffening component in Branson’s equation is shown to depend on the ratio of gross-to-cracked moment of inertia (Ig/Icr), and gives too much tension stiffening for beams with an Ig/Icr ratio greater than 3. FRP beams typically have an Ig/Icr ratio greater than 5, leading to a much stiffer response and underprediction of computed deflections as observed by others in the past. One common approach to computing deflection of FRP reinforced concrete beams has been to use a modified form of the Branson equation. This paper presents a rational development of appropriate modification factors needed to reduce the tension stiffening component in Branson’s original expression to realistic levels. Computed deflections using this approach give reasonable results with the right modification factor, and compare well with a more general unified approach that incorporates a realistic tension stiffening model. Comparison is made with the existing and past correction factors recommended by ACI 440 for predicting deflection of FRP beams. The method presently used by ACI 440 gives reasonable estimates of deflection for glass and carbon FRP reinforced beams. However, this method underestimates deflection of aramid FRP reinforced beams and is restricted to rectangular sections. A proposal is made for adoption of a simple modification factor that works well for all types of FRP bar and beam cross-sectional shape.     

Modeling of an Unbonded CFRP Strap Shear Retrofitting System for Reinforced Concrete Beams

A retrofitting technique has been developed that uses carbon fiber-reinforced polymer (CFRP) straps to increase the shear capacity of reinforced concrete beams. The vertical straps are not bonded to the beam but are instead anchored against the beam, which makes this technique potentially more effective than bonded FRP retrofitting techniques. However, it also means that models for bonded FRPs are not appropriate for use with the straps. Instead, a model based on a shear friction approach has been developed where the strain in the straps is calculated based on a term that accounts for the effects of prestress and additional strain in the strap due to shear crack opening. The model can either consider the shear reinforcement to be smeared along the length of the beam or discrete elements. The “smeared” model was checked against an experimental database consisting of rectangular, T-, and deep beams, both in terms of predicted capacity and predicted strain in the straps. Overall the smeared model predicted the capacity of the specimens and, with some adjustments, the strains quite accurately. There were, however, cases when it was more appropriate to use the “discrete” model such as when the transverse reinforcement ratio was low or when the transverse reinforcement spacing was high. Further experimental data are required to fully validate the models and to determine appropriate limits on the use of the smeared model and the discrete model. However, the initial results are promising.     

Numerical Modeling of FRP Shear-Strengthened Reinforced Concrete Beams

An attractive technique for the shear strengthening of reinforced concrete beams is to provide additional web reinforcement in the form of externally bonded fiber-reinforced polymer (FRP) sheets. So far, theoretical studies concerning the FRP shear strengthening of reinforced concrete members have been rather limited. Moreover, the numerical analyses presented to date have not effectively simulated the interfacial behavior between the bonded FRP and concrete. The analysis presented here aims to capture the three-dimensional and nonlinear behavior of the concrete, as well as accurately model the bond–slip interfacial behavior. The finite-element model is applied to various strengthening strategies; namely, beams with vertical and inclined side-bonded FRP sheets, U-wrap FRP strengthening configurations, as well as anchored FRP sheets. The proposed numerical analysis is validated against published experimental results. Comparisons between the numerical predictions and test results show excellent agreement. The finite-element model is also shown to be a valuable tool for gaining insight into phenomena (e.g., slip profiles, debonding trends, strain distributions) that are difficult to investigate in laboratory tests.     

Flexural Behavior of Reinforced Concrete Beams Strengthened with CFRP Sheets and Epoxy Mortar

Experiments were conducted to study the effect of using epoxy mortar patch end anchorages on the flexural behavior of reinforced concrete beams strengthened with carbon fiber-reinforced polymer (CFRP) sheets. More specifically, the effect of the end anchorage on strength, deflection, flexural strain, and interfacial shear stress was examined. The test results show that premature debonding failure of reinforced concrete beams strengthened with CFRP sheet can be delayed or prevented by using epoxy mortar patch end anchorages. A modified analytical procedure for evaluating the flexural capacity of reinforced concrete beams strengthened with CFRP sheets and epoxy mortar end anchorage is developed and provides a good prediction of test results.