Shear Capacity Of Reinforced Concrete Beams Research Articles

Size effect in shear failure of RC beams with stirrups: Simulation and formulation

The objectives of the present study are to discover the influences of stirrup ratio and shear-span ratio on the shear failure and size effect of reinforced concrete (RC) beams having different sizes, and to build a theoretical formula for quantitatively describing the size effect on shear failure of RC beams. A three-dimensional meso-scale simulation method for modelling the failure of RC beams is established, and it is utilized to explore the failure behavior of geometrically-similar RC beams. In addition, the influences of shear-span ratio and stirrup ratio on the size effect of shear failure was examined. Finally, a novel size effect law (SEL) for predicting the nominal shear strength of RC beams having different sizes is established and verified. The results indicate that, (1) the shear-span ratio has a great influence on the shear capacity of RC cantilever beams, but has ignorable effect on the size effect; (2) the increase of stirrup ratio increases the shear capacity of RC cantilever beams and weakens the size effect of the shear strength; (3) stirrups cannot increase the shear capacity of RC beams indefinitely, and the increase of shear strength is obvious under the condition of small stirrup ratio; (4) the developed SEL for shear failure of RC beams can well describe the quantitative influence of stirrup ratio and shear-span ratio, and it is consistent with the available test date.

Experimental Study on Shear Strengthening of RC Beams with an FRP Grid-PCM Reinforcement Layer

This paper investigates the shear strengthening effect of a number of reinforced concrete (RC) beams strengthened by a reinforcement layer which combines carbon fiber reinforced polymer (CFRP) grid and polymer cement mortar (PCM). A total of ten RC beams, including three types of specimens as Series A and seven kinds of specimens as Series B, were prepared and investigated. The test variables in both series of experiments included various reinforcement ranges and different reinforcement amounts that consisted of CFRP grids’ spacing and cross-section areas. The experimental results suggest that the shear strengthening effect of the CFRP grid-PCM layer for RC beams is obvious and adequate. Meanwhile, better performance is observed if the CFRP grid-PCM reinforcement layer is used for the full sectional reinforcement of RC beams with an I-shaped profile, in contrast to RC beams with reinforcement of the web only. In addition, a new evaluation method based on the effective strain of the CFRP grid is developed to determine the shear capacity of RC beams strengthened by a CFRP grid-PCM layer.

Repair and strengthening of shear-deficient reinforced concrete beams using Carbon Fiber Reinforced Polymer

This paper presents the results of an experimental investigation on the behavior of Reinforced Concrete (RC) beams repaired and strengthened using Externally Bonded Carbon Fiber Reinforced Polymer (EB-CFRP). The experimental program involved 19 static tests on 16 simply supported rectangular RC beams in which seven were tested without CFRP and 12 were wrapped with one or two layers of CFRP. Out of the 12 beams, six were first tested to failure, repaired with epoxy, then wrapped with CFRP sheets before the second and final test. The remaining six were wrapped with CFRP, while virgin, before testing. Among the objectives of this study was the analysis of the effectiveness of EB-CFRP as a strengthening method for shear strengthening of damaged RC beams and the identification of interaction between conventional shear reinforcement and the EB-CFRP strips. Analysis of test results suggests that the EB-CFRP strengthening of damaged beams repaired using epoxy injection not only helps the beams to recover but also significantly increase their shear capacity. Moreover, one layer of CFRP discrete strips improved the overall capacity of the shear-deficient beams by more than 60% and an additional layer further increased the shear capacity by another 30%. The results also confirmed that an interaction exists between steel stirrups and EB-CFRP strips when carrying the applied load. For instance, test results demonstrated that the contribution of CFRP in shear strength is affected by the quantity of steel stirrups. Finally, when compared to test results, the ACI and fib formula provided reasonable estimation of the additional shear strength contributed by the EB-CFRP discrete strips, except for the beams with moderate ratio of steel stirrups. However, Chen et al. model better estimated the EB-CFRP contribution to the shear capacity of RC beams with moderate ratio of steel stirrups.

Experimental Study on the Shear Performance of Reinforced Concrete Beams Strengthened with Bolted Side-Plating

To investigate the residual shear capacity of post-fire bolted side-plated (BSP) reinforced concrete (RC) beams with different depths of steel plate and types of anchor adhesive, i.e., magnesium oxychloride cement (MOC) and HIT-RE500, a control beam and five BSP beams were fabricated, of which two were exposed to fire in accordance with ISO834 temperature curve. Four-point bending shear tests were conducted to investigate the influence of elevated temperature on the failure mode, cracking load, shear capacity, stiffness, ductility and strain development, etc. The shear capacities of RC beams were found to be improved significantly by using the BSP technique. However, the stiffness of BSP beams was seriously degraded after exposed to fire, but the reduction in shear capacity was negligible, whereas the ductility and the strain of longitudinal reinforcement were obviously increased. Thus, the failure-mode was changed from shear failure to flexural failure. Regarding the adhesive mortar used for bolt anchorage, magnesium oxychloride cement (MOC) achieved higher shear capacity and better ductility but lower stiffness for BSP beams compared with HIT-RE500. Additionally, increasing the depth of bolted steel plates effectively improved the shear performance of BSP beams. In the tests, uneven relative slips were observed on the plate-RC interface due to the shear deformation of bolt shafts and the plates’ tensile principal stress perpendicular to the main diagonal crack, which proved the deformation lag of the bolted steel plates with respect to the RC beam. The outcomes of this study provide a better understanding on the shear performance of BSP beams at room temperatures and at fire conditions.

SHEAR CAPACITY PREDICTION FOR STIRRUP-CORRODED RC BEAMS STRENGTHENED WITH FRP

Corrosion of steel reinforcement represents one of the main causes of deterioration and degradation of reinforced concrete (RC) structures. Shear reinforcements (stirrups) as an outer reinforcement in RC beams are more susceptible to corrosion problems and damage. This paper describes an analytical procedure for predicting the shear capacity of stirrup-corroded RC beams strengthened in shear using FRP laminates. The procedure shows how to incorporate the effects of the damages due to corrosion of stirrups into the design equations. An experimental investigation has been conducted to provide experimental data on the shear capacity of RC beams with corrosion-damaged stirrups strengthened using carbon fiber reinforced polymer (CFRP) sheets. The experimental study comprised three beams of 200 mm wide, 350 mm deep, and 2800 mm long. The steel stirrups in the beams were corroded using an accelerated corrosion technique. After CFRP strengthening, the beams were tested in four-point bending under a simply supported span of 2400 mm. The shear capacity of the strengthened beams was predicted using the proposed procedure and compared with the experimental ones. Good correlations were found between the predicted and experimental shear strength of the beams.

Shear Strengthening of Reinforced Concrete Beams Using CFRP Wraps

The need to retrofit existing reinforced concrete (RC) structures have increased over the decades due to corrosion of steel reinforcement inside the concrete, neglect and overuse, and increased loading. Experimental and numerical studies in this research field showed that using fiber-reinforced Polymer (FRP) materials to strengthen RC members in shear, flexure, and column confinement applications is an effective method to retrofit RC structures. This strengthening technology has numerous advantages over conventional steel plating, such as providing high strength-to-weight ratio, versatility, durability, and ease of use to strengthen RC members. The purpose of this paper is to study the effect of strengthening shear deficient RC beams with externally bonded (EB) carbon fiber-reinforced polymer (CFRP) sheets with different wrapping configurations. Two shear strengthening wrapping schemes of CFRP sheets will be investigated; U-Wrapped and completely Wrapped. Although the completely wrapped scheme is more effective, however, due to its limitations, the U-Wrapped scheme became the most commonly used method in shear strengthening of RC structures. The drawback of this strengthening scheme is the premature failure caused by debonding of the CFRP laminates, without utilizing its full strength. The main aim of this study is to compare the performance of a U-Wrapped T-beam with two completely wrapped rectangular beams. The first strengthened rectangular specimen (WBR1) has a depth equivalent to the T-beam’s web height, while the second strengthened rectangular specimen (WBR2) has a depth equivalent to the T-beam’s total depth. In addition, a control T-beam and two rectangular beams were cast and tested as benchmark specimens. The experimental test results showed that the beam strengthened by U-Wrapped CFRP sheets increased the control beam’s shear strength by 114.82%, while the increase in shear capacity of the completely wrapped equivalent WBR1 and WBR2 beams over their control unstrengthened specimens was 69.28% and 201.63%, respectively. In addition, the completely wrapped scheme provided more ductility compared to that of the U-Wrapped T-beam specimen, that failed by CFRP sheets debonding in a brittle manner. Thus, it could be concluded that an ideal way to increase the shear capacity and ductility of RC beams is to completely wrap the beams using CFRP sheets. However, if the completely wrapping scheme is not possible due to geometrical obstructions, U-wrapping scheme could be effective in increasing the shear capacity of RC beams but will fail in a brittle mode by sheet debonding without utilizing its full strength. Anchoring the CFRP U-Wraps could be a viable solution to enhance the performance of strengthened RC beams that should be investigated in future research studies.

Use of Aluminum Alloy Plates as Externally Bonded Shear Reinforcement for R/C Beams

Fiber Reinforced Polymers (FRP) and steel had proven to be very effective as externally bonded shear strengthening materials However, they both have their shortcomings. Recently developed high strength Aluminum Alloy (AA) plates possess desirable characteristics that may overcome some of the shortcomings of FRP and steel. The aim of this paper is to study the behavior of Reinforced Concrete (RC) beams strengthened with externally bonded AA plates as shear reinforcement. Three RC beams were designed to fail in shear and two of them were strengthened with externally bonded AA plates that were oriented at 90o and at 45o. The beams were tested under four-point bending until failure while magnitudes of loads and mid-span deflections were recorded. The results of the tested beams showed an increase in the load carrying capacity of up to 38% compared to the capacity of un-strengthened control beam. All beams failed in shear with diagonal shear cracks followed by de-lamination/de-bonding of AA plates near the support and near the applied load. This study demonstrated that AA plates can be used as externally bonded material to enhance the shear capacity of RC beams, however, further investigation is needed to further validate these results.

A new approach for predicting the shear capacity of FRCM strengthened RC beams in shear

In spite of the availability of different models proposed to predict the shear capacity of reinforced concrete (RC) beams strengthened in shear using fabric reinforced cementitious matrix (FRCM) system, accurately predicting this value remains a challenge. The simplified compression field theory has shown to accurately predict the shear capacity of RC beams. This paper presents an analytical model based on the simplified compression field theory for predicting the shear capacity of RC beams strengthened in shear using FRCM strengthening system. The model has been validated against a data series of over sixty RC beams strengthened in shear using different FRCM types with different strengthening configuration and orientation. The results showed that the model can reasonably predict the load carrying capacity of the beams. The ratio of theoretically predicted and experimental results for the load carrying capacity ranged between 0.67 and 1.33 while average of this ratio was 1.01 with a coefficient of variation of 0.16.

Experimental study on the residual shear capacity of fire-damaged reinforced concrete frame beams and cantilevers

The mechanical properties of concrete and steel degrade after exposure to fire, thus the fire-damaged reinforced concrete (RC) members may not be able to satisfy the prescribed performance. Therefore, it is of great significance to identify the degree of fire damage for RC members or even the entire RC structure. For RC beams, comprehensive studies have been conducted on the residual flexural capacity after fire, but those related to the post-fire shear properties are barely found in the literature. In this paper, the shear tests of twenty-five beams––including frame beams and cantilevers––were carried out to investigate the difference in their shear behaviors before and after fire exposure. The parameters controlling shear capacity, such as shear span ratio, the concrete slab (i.e. the flange of the beam), and the stirrup spacing, were investigated. The experimental results indicated that both the shear capacity and the stiffness of the RC beams degraded after fire. The diagonal cracks of frame beams with fewer stirrups concentrated seriously, and their crack width increased considerably. Based on the test results, a simplified evaluation process was developed to evaluate the shear capacity of RC beams after fire, and the proposed formula was proven to be able to predict the residual shear capacity of fire-damaged RC beams with sufficient accuracy.

Study on design formula of shear capacity of RC beams reinforced by CFRP grid with PCM shotcrete method

The objective of this study was to evaluate the shear capacity of reinforced concrete (RC) beams by using carbon-fiber-reinforced-polymer (CFRP) grid with polymer-cement-mortar (PCM) shotcrete. A new evaluation method of shear capacity based on the concept of effective strain of CFRP grid was proposed by RC beam tests, which were carried out with the reinforced arrangement of CFRP grid as parameters. In order to make this new evaluation method more applicable, we conducted a 3-dimensional finite-element (FE) analysis by incorporating factors such as the influences from shear span ratio of RC beams. Our results suggested that the proposed evaluation method by considering both vertical and horizontal grid was highly effective, and that the share ratios of shear capacity between vertical and horizontal grid presented a nonlinear relationship according to the shear span of RC beams.

Shear strength of RC beams subjected to axial load

Due to the complex mechanism of the shear failure, most shear design equations in codes and guidelines are based on empirical approaches and consequently should only be used within the bounds of the test population from which they were developed. To accommodate this issue, a mechanics-based segmental approach, which can simulate a reinforced concrete (RC) beam with any type of concrete and reinforcement and which can explain the physical process of shear failure has been proposed to determine the shear capacity of RC beams with and without stirrups. In this paper, this segmental approach is extended by incorporating axial load in the mechanics-based model; furthermore, a closed form solution for assessment is also derived. By simulating 61 published test specimens, the proposed approaches are validated with good correlation between the predicted and measured strengths. Being mechanics based, this approach has a great potential to be developed for all types of RC structures with all combinations of loading for use in the development of or refinement of simplified design approaches.

SHEAR BEHAVIOR OF REINFORCED CONCRETE SLENDER BEAMS

Major factors contributing to the shear behavior in reinforced concrete (RC) beams have been identified as compressive strength of concrete, shear span to effective depth ratio, and longitudinal reinforcement. Though significant, few of these factors are not fully incorporated in ACI code provisions for design of minimum shear reinforcement. To investigate the effect of these parameters, an analytical and experimental study was undertaken on the shear behavior of ordinary strength RC slender beams with moderate longitudinal reinforcement. The experimental program consisted of testing of eight simply supported RC slender beams subjected to two concentrated loads at a shear span to depth ratio (a/d) of 2.5 and equipped with varying shear reinforcement according to four different criteria. Ultimate shear strengths obtained in this experimental program are compared to the analytical shear strengths calculated according to existing as well as proposed equations. Test results exhibit that, the modified equation proposed in this work gives more accurate prediction of shear capacity of RC beams.

Assessment of epistemic uncertainties in the shear strength of slender reinforced concrete beams

Selection of an appropriate model for shear capacity of reinforced concrete (RC) slender beams poses a number of challenges. First, different models with different levels of conservatism have been proposed in an attempt to describe shear resistance. Second, according to Reineck et al. (2014), code provisions for shear capacity of RC beams with shear reinforcement have been primarily derived from test data with respect to the required amount of shear reinforcement and the calculation of maximum shear capacity. Third, current models have been developed based on databases presenting two major drawbacks: (i) most data points are crowded in the small size range, and (ii) the means of the subsidiary influencing parameters are very different within different intervals of beam size (or beam depth). In this study, a filtered database is used in such a way to circumvent the drawbacks mentioned above. A random variable “model error”, i.e. ratio experimental to predicted shear strength, is associated to each of the shear models analyzed in this work (NBR 6118, ACI 318, EUROCODE 2, and CSA A.23.3). It was observed that in some cases, most notably for the effective depth, a trend exists for a decrease in the “model error” as the effective depth increases. Considering the limitations of the four analyzed models, a nonlinear regression model was proposed. The database presented by Reineck et al. (2014) was used in the assessment of the effectiveness and accuracy of the proposed regression model. No trend was found associated to the most significant variables in the shear strength prediction, i.e. a uniform level of conservatism is attained throughout the range of these variables. The regression model proposed herein and the attendant statistics of the model error (mean, coefficient of variation and type of distribution) can be easily used in a reliability analysis procedure to assess safety levels implicit in different design procedures.

Shear Strength of RC Beams with Steel Stirrups

AbstractBecause of the complexity of the shear failure mechanism, most current design codes and guidelines are based on highly empirical approaches and consequently should only be used within the bounds of testing regimes from which they were derived. Hence this limitation restricts their applicability to innovative materials such as high-strength concrete and fiber-reinforced polymer (FRP) reinforcement. To solve this issue, a mechanics-based segmental approach, which can analyze a reinforced concrete (RC) beam with any type of concrete and reinforcement and which can explain the physical process of shear failure, has been developed to quantify the shear capacity of RC beams without stirrups. In this paper, with the partial interaction analysis of transverse reinforcements directly linked with that of longitudinal reinforcements, the segmental approach is extended by incorporating steel stirrups in the mechanics-based model; furthermore, a simplified closed form solution for design is derived. By evaluat...

Design model for shear capacity of RC beams strengthened with two-side CFRP wraps based on effective FRP strain concept

A simple design model based on effective strain of fibre-reinforced polymer (FRP) to predict shear capacity of reinforced concrete (RC) beams strengthened with two-side FRP wraps is proposed. Five two-side carbon FRP wrapped and five control unstrengthened RC beam specimens were tested, and the obtained results in addition to the experimental results of 32 two-side wrapped RC beams selected from the literature were used to calibrate the model. Performance of the proposed model was compared with fib Bulletin 14 and ACI 440.2R design models. It was shown that fib Bulletin 14 and ACI 440.2R mostly overestimate the FRP contribution to the shear capacity of two-side wrapped RC beams, while ACI 440.2R model is incapable of predicting effective FRP strain for shear-strengthened shallow beams. Results of 20 independent tests on RC beams strengthened in shear with two-side wraps verified that the proposed model fairly estimates the shear capacity of the strengthened RC beams. It was justified and concluded that since the simple proposed model provides more accurate and safe predictions compared with existing guideline models, it may be capable to be used for design purposes.

SHEAR REPAIRED RC BEAM BY FRP BONDING WITH EXTERNAL POST-TENSIONING

Various factors, including increase in traffic volume and weight, structural aging, and environmental impact, cause damage in structural members. This raises the importance of the maintenance, rehabilitation, and strengthening of reinforced concrete members. External post-tensioning is one of the widely-used strengthening techniques in many countries due to its advantages over other strengthening methods. Although flexural strengthening of existing structural members is a well-established method, shear strengthening of structural members, especially with existing shear cracks, has attained very little attention from researchers. Similarly, external fiber-reinforced polymer (FRP) bonding for shear strengthening of structural members, especially with existing shear cracks, is a relatively new area of research. This paper presents the results of an experimental study on the shear strengthening of reinforced concrete (RC) beams with existing shear cracks by external post-tensioning and external FRP bonding. The test result showed that the combined strengthening technique of external post-tensioning and external FRP bonding can effectively increase the shear capacity of RC beams with existing shear cracks.

Shear capacity in concrete beams reinforced by stirrups with two different inclinations

A model for the estimation of shear capacity in Reinforced Concrete (RC) beams with web reinforcement is provided by introducing a generalization of classical plastic Nielsen’s model, which is based on the variable-inclination stress-field approach. The proposed model is able to predict the shear capacity in RC beams reinforced by means of stirrups having two different inclinations and longitudinal web bars.A numerical comparison with the results of experimental tests and those provided by a Finite Element Model (FEM) based on the well known theory of Modified Compression Field Theory (MCFT) is carried out for validating the robustness of the proposed model.Finally, a set of parametrical analyses demonstrates the efficiency of the proposed double transverse-reinforcement system in enhancing the shear capacity of RC beams.

Shear Capacity of RC Beams with Web Openings Strengthened with Multi Layers of CFRP

In some cases a cut-out web opening in a reinforced concrete (RC) beam is required to facilitate the passage of electrical and mechanical pipes and ducting from one side to another. The presence of cut-out web openings will lead to decreasing in the load carrying capacity of these RC beams. Therefore, strengthening the vicinity of these openings by using Carbon Fiber Reinforced Polymer (CFRP) will represent the best practical solution. In this study, thirteen RC beams with different sizes of cut-out web openings and with different layers of CFRP strengthening and also one solid RC beam (control) were prepared and tested to failure. The outcome of this experimental and analytical study showed that the modified Eurocode 2 model can reasonably be used in computing the shear forces of RC beams having the vicinity of their cut-out web openings strengthened with single/multi layers of CFRP. In addition, for safe design purposes, a reduction factor has been suggested as well.

Finite element modeling of the shear capacity of RC beams strengthened with FRP sheets by considering different failure modes

In this study, three-dimensional (3D) finite element (FE) analyses were carried out to study the effects of several variables on the failure modes and ultimate shear capacity of reinforced concrete (RC) beams strengthened with fiber-reinforced polymer (FRP) sheets. Fifty-eight cases were analyzed by FE modeling. The parameters considered to affect the failure modes and the shear capacity included the beam width, the concrete strength, the height and thickness of the FRP sheet, the elastic modulus of the FRP and the strengthening configuration (complete wrapping, U-jacketing, and side bonding). A model for predicting the failure mode and the shear capacity were proposed on the basis of the results of the parametric analysis. Experimental results for 307 beams collected from previously published work were analyzed to verify the accuracy of the proposed model. The results show that the failure modes of RC beams are affected by the parameters considered and can be predicted by the proposed model. The results also indicate that the proposed model can be used to calculate the shear capacity of RC beams strengthened with FRP sheets and to predict the failure mode with greater accuracy than existing models.

Strut and tie modeling for RC short beams with corroded stirrups

Corrosion of steel reinforcement is one of the major problems that shorten the service life of reinforced concrete (RC) structures. Steel stirrups, due to their location as an outer reinforcement, are more susceptible to corrosion problems and damage. However, there is limited research work in the literature on the effects of stirrup corrosion on the shear strength of RC beams. This paper attempts to evaluate analytically the residual shear strength of RC short beams with corrosion-damaged stirrups. The shear strength of short or deep beams are generally determined using the strut and tie model. The corrosion effects were implemented in the model to make it capable of predicting the residual shear capacity of RC beams with corroded stirrups. The effect of corrosion is implemented considering the reduction in geometry of the concrete cross section due to spalling and reduction in effective compressive strength of concrete due to corrosion cracks. The proposed strut and tie model which accounts for the corrosion effects was verified using the experimental data available in the literature, and good agreement was found.