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Guidelines for flexural design of FRP reinforced concrete beams
Abstract
This paper investigates the effects of different parameters on the live load carrying capacity of concrete beams reinforced with FRP bars. The author performed a parametric study utilizing an innovative numerical approach to inspect the effects of multiple variables such as reinforcement ratio, concrete compressive strength, span to depth ratio, FRP type, and bar diameter on load carrying capacity of FRP reinforced concrete beams. This study concluded that unless the span to height ratio is smaller than 8, tension-controlled sections are impractical as they do not meet code requirements for serviceability. In addition, it is recommended to use higher reinforcement ratios when using larger span to depth ratios and/or when using CFRP reinforcing bars. Moreover, larger number of bars with small diameter is more practical than fewer large diameter bars. Furthermore, this research suggests that increasing the concrete compressive strength is associated with a significant increase in the ultimate flexural capacity of FRP reinforced beams.
... The reinforcement ratio is an index usually used to measure whether a beam member undergoes brittle failure. Jnaid et al. [23] used an innovative numerical approach to study the effect of the reinforcement ratio on the flexural behaviour of GFRP bar-reinforced NC beams. The results demonstrated that given a reinforcement ratio lower than the balanced reinforcement ratio, an increase in the reinforcement ratio could significantly improve the flexural capacity of the studied beams, whereas given a reinforcement ratio higher than the balanced reinforcement ratio, an increase in the reinforcement ratio could only slightly increase the flexural bearing capacity of the beams. ...
Glass fibre-reinforced polymer (GFRP) bar-reinforced seawater–sea sand concrete (SWSSC) has been widely regarded as a new structural material with great potential due to its environmental friendliness. To safely and economically utilize seawater and sea sand to cast GFRP bar-reinforced flexural members in coastal areas, an experimental study was conducted to investigate the flexural behaviour of 12 GFRP bar-reinforced SWSSC beams. The various considered parameters included the (1) reinforcement ratio, (2) stirrup ratio, (3) prestress level, and (4) shear span ratio. The experimental results for the GFRP bar-reinforced SWSSC beams were verified via a comparison to the calculation models of GB 50608-20 and ACI 440.1R-15 for FRP bar-reinforced normal concrete (NC) beams. The results indicated that the prestress level is the main factor controlling the cracking load of the GFRP bar-reinforced SWSSC beams, and the cracking load of prestressed beams was 81% higher than that of nonprestressed beams. The ultimate load of the GFRP bar-reinforced SWSSC beams was strongly correlated with the reinforcement and shear span ratios (the higher the reinforcement ratio or the lower the shear span ratio was, the higher the ultimate load). Under the influence of the reinforcement and stirrup ratios, the failure mode of the GFRP bar-reinforced SWSSC beams could be transformed from GFRP bar rupturing into concrete crushing. Moreover, the calculation model of ACI 440.1R-15 overestimated the ultimate flexural capacity of the nonprestressed beams, while the calculation model of GB 50608-20 yielded conservative estimation values for the nonprestressed specimens and overestimated values for the prestressed beams. To ensure safety, the calculation model of GB 50608-20 for FRP bar-reinforced NC beams can be adopted when designing nonprestressed GFRP bar-reinforced SWSSC beams. In contrast, a prediction model for prestressed GFRP bar-reinforced SWSSC beams should be further investigated.
Abstract
Six large-scale high-strength concrete beams reinforced with basalt fiber reinforced polymer (BFRP) bars and stirrups and three corresponding beams without stirrups were constructed and tested for shear failure under four-point bending. The main parameters considered were the beam effective depth (300, 500, and 700 mm) and the stirrup spacing. The test results indicated that the size effect on shear failure could not be eliminated completely, as the initial shear crack, shear crack width, shear resistant components analysis, strain in the BFRP stirrups, and normalized shear strength were still related to the beam depth. The ACI 440-15 strain limit of 4000 µs could be relaxed with the condition that the serviceability requirement is satisfied. Furthermore, based on a collected database from the literature, an accurate and conservative equation was proposed to predict the FRP stirrup strain limit. The proposed equation includes the effects of all influencing parameters, which is more reasonable than the constant strain limit used by most design codes.
Adding fibers is highly effective to enhance the deflection and ductility of fiber-reinforced polymer (FRP)-reinforced beams. In this study, the stress and strain conditions of FRP-reinforced lightweight aggregate concrete (LWC) beams with and without fibers at ultimate load level were specified. Based on the sectional analyses, alternative equations to predict the balanced reinforcement ratio and flexural capacity for beams failed by balanced failure and concrete crushing were established. A rational equation for estimating the short-term stiffness of FRP–LWC beams at service-load levels was suggested based on Zhu’s model. In addition, the contribution of the steel fibers on the short-term stiffness was quantified incorporating the effects of FRP reinforcement ratio. The proposed short-term stiffness model was validated with measured deflections from an experimental database for fiber-reinforced normal weight concrete (FNWC) beams reinforced with FRP bars. Furthermore, six glass fiber-reinforced polymer (GFRP)-reinforced LWC beams with and without steel fibers were tested under four-point bending. Based on the test results, the proposed models and procedures according to current design codes ACI 440.1R, ISIS-M03, GB 50608, and CSA S806 were linked together by comparing their predictions. The results showed that increasing the reinforcement ratio and adding steel fibers decreased the strain of the FRP bars. The flexural capacity of the LWC beams with and without steel fibers was generally underestimated by the design codes, while the proposed model provided accurate ultimate moment predictions. Moreover, the proposed short-term stiffness model yielded reasonable estimations of deflection for both steel fiber-reinforced lightweight aggregate concrete (SFLWC) and FNWC beams.
This study investigated the punching shear behavior of full-scale, two-way concrete slabs reinforced with glass fiber reinforced polymer (GFRP) bars, which are known as noncorrosive reinforcement. The relatively low modulus of elasticity of GFRP bars affects the large deflection of flexural members, however, applying these to two-way concrete slabs can compensate the weakness of the flexural stiffness due to an arching action with supporting girders. The test results demonstrated that the two-way concrete slabs with GFRP bars satisfied the allowable deflection and crack width under the service load specified by the design specification even in the state of the minimum reinforcement ratio. Previous predicting equations and design equations largely overestimated the measured punching shear strength when the slab was supported by reinforced concrete (RC) girders. The strength difference can be explained by the fact that the flexural behavior of the supporting RC beam girders reduces the punching shear strength because of the additional deflection of RC beam girders. Therefore, for more realistic estimations of the punching shear strength of two-way concrete slabs with GFRP bars, the boundary conditions of the concrete slabs should be carefully considered. This is because the stiffness degradation of supporting RC beam girders may influence the punching shear strength.
The paper presents the computational analysis of static behavior of simply supported beam reinforced with FRP (Fiber Reinforced Polymers) bars. The available calculation procedures and design assumptions were listed. The design of FRP reinforcement procedures for flexural strength and long-term deflection according to American (ACI 440.1R-06) guidelines were analyzed. Moreover, the analysis of computations of simply supported beam reinforced with CFRP (Carbon Fiber Reinforced Polymers), AFRP (Aramid Fiber Reinforced Polymers) and GFRP (Glass Fiber Reinforced Polymers) bars based on American guidelines were done and compared. The differences between obtained properties dependent on various types of reinforcement were identified.
The flexural properties of eight 200 x 300 mm (8 x 12 in.) concrete beams reinforced with basalt fiber-reinforced polymer (BFRP) reinforcing bars were investigated. The beams were reinforced with four different sizes of BFRP (10, 13, 16, and 25 mm). The flexural reinforcement ratios ρf ranged from 1.43 to 10.70 times the balanced ratio ρfb. The beams were divided into three categories with low, moderate, and high ρf. As expected, all the beams failed by crushing of the concrete in the top compression fiber. Higher ρf/ρfb, to some extent, has a better effect on reducing the deflection than increasing the beam's ultimate strength. The strain compatibility equation per ACI 440.1R-06 was conservative in predicting the ultimate flexural strain in the BFRP bars and the ultimate moment capacity. The effective moment of inertia (Ie) prediction model recommended by ACI 440.1R was the least conservative among other models when compared with the experimental Ie.
By employing the concept of reliability index, an interim index of "comparative reliability" is proposed that bypasses the loading variables and weighs the resistances of two structural elements with the same ultimate limit state directly against each other. The comparative reliability index is then related to the conventional target reliability to allow a simple calculation method of the strength reduction factor for elements whose safety factor is yet to be calibrated. This is achieved by comparing a pair of elements that experience the same failure mode and yet only one holds a validated level of safety (that is, strength reduction factor and reliability index). This concept is put into practice by calculating flexural and shear-strength reduction factors for fiber-reinforced polymer (FRP) reinforced concrete (RC) members by comparison with conventional steel-reinforced concrete beams possessing the same ultimate capacity. As a result, a revised set of strength reduction factors and deign provisions are proposed for use in FRP design guidelines for shear and flexure.
This paper presents an experimental study of the flexural defections of concrete beam reinforced with basalt FRP bars. Six concrete beams with different BFRP reinforcement ratio and one comparative beam reinforced with steel rebar are tested in laboratory. Numerical simulations using sectional analysis method and spatial FEM are performed. The experimental results can fit well with numerical simulation results. Analysis and experimental results in the literature collected indicate that the ACI-440.1R-06 equations underestimate the deflection of FRP-RC beams. Based on the experimental and numerical simulation results, a modified equation of the flexural rigidity is proposed to calculate the deflection of the FRP-RC beams. The proposed equation can fit better with the experimental results than the ACI-440.1R-06 equations.
This paper investigated the flexural behavior and serviceability performance of glass fiber-reinforced polymer (GFRP)-reinforced concrete (GFRP-RC) beams fabricated with normal- and high-strength concretes (NSCs and HSCs). The beam specimens measured 4250 mm long x 200 mm wide x 400 mm deep (167.0 x 7.9 x 15.6 in.). Three GFRP products with moduli of elasticity ranging from 48.7 to 69.0 GPa (7063 to 10,008 ksi) with sand-coated and helically grooved surface textures were employed. A total of 12 full-scale beams reinforced with GFRP bars and two reinforced with steel bars, serving as control specimens, were tested to failure in four-point bending over a clear span of 3750 mm (147.6 in.). The test parameters were: 1) type and ratio of the GFRP reinforcement; 2) surface configuration of the GFRP bars; 3) concrete strength; and 4) bar diameter. The test results were reported in terms of deflection, crack width, strains in concrete and reinforcement, flexural capacity, and mode of failure; they were also employed to assess the accuracy of the current deflection and crack-width prediction equations in the FRP-RC codes. The test results revealed that the crack widths were affected by the bar diameter and surface configuration while the deflections were not significantly affected. In addition, the bond coefficient kb value of 1.4 was very conservative for both of the sand-coated and helically grooved GFRP bars in NSC and HSC.
This paper presents the results of an experimental study to investigate the behaviour of structurally damaged full-scale reinforced concrete beams retrofitted with CFRP laminates in shear or in flexure. The main variables considered were the internal reinforcement ratio, position of retrofitting and the length of CFRP. The experimental results, generally, indicate that beams retrofitted in shear and flexure by using CFRP laminates are structurally efficient and are restored to stiffness and strength values nearly equal to or greater than those of the control beams. It was found that the efficiency of the strengthening technique by CFRP in flexure varied depending on the length. The main failure mode in the experimental work was plate debonding in retrofitted beams.
The use of fibre reinforced polymer (FRP) reinforcements in concrete structures has increased rapidly in the last 10 years due to their excellent corrosion resistance, high tensile strength, and good non-magnetization properties. However, the low modulus of elasticity of the FRP materials and their non-yielding characteristics results in large deflection and wide cracks in FRP reinforced concrete members. Consequently, in many cases, serviceability requirements may govern the design of such members. This paper describes the development of simple approaches in estimating the deflection of FRP reinforced concrete members subjected to flexural stresses. The predictions of these approaches are compared with the experimental results obtained by testing seven prototype concrete beams reinforced with glass fibre reinforced polymer, GFRP, and carbon fibre reinforced polymer, CFRP, bars. The proposed analytical methods are also substantiated by test results available in the literature from eight concrete slabs reinforced with conventional steel, GFRP, and CFRP bars. Good agreement was shown between the theoretical and the experimental results.
This paper proposed to use high-strength grout and corrugated sleeves to hold FRP bars in tension zone of concrete beams, aimed at reducing crack width and improving serviceability performance. Ten large-scale simply supported beams measuring 200 mm wide, 400 mm depth, and 4000 mm length, were tested under four-point bending. One reference beam was reinforced with steel bars and four beams were reinforced with FRP bars. Other five beams were reinforced with FRP bars grouted in sleeves in the tension zone. Test results are discussed in terms of failure modes, deflection and cracking behavior. FRP-RC beams failed by concrete crushing, achieving higher flexural capacity and larger deflection than the steel-RC beam. The use of FRP bars grouted in corrugated sleeves in tension zone of beams was an effective way to reduce crack widths and improve serviceability performance. The average bond-dependent coefficient (k b ) for grouted FRP bars in sleeves was 38% lower than FRP bars surrounded by concrete. The maximum crack width at service load, which accounted for variability of crack width and long-term effect of sustained load, was less than the crack width limit of 0.7 mm for beams with grouted FRP bars in sleeves but not for beams only with FRP bars.
An experimental study of the behaviour of concrete beams reinforced with fibre reinforced plastic (FRP) bars in three-point bending was undertaken. The load-deflection response was monitored throughout the test. The results from the flexural tests on FRP reinforced concrete beams were compared with those obtained with steel reinforcement. The failure mechanisms and the ultimate loads and displacements for the FRP and steel reinforcement of concrete were analysed and compared.
The structural reliability of concrete flexural members reinforced with fiber reinforced polymer (FRP) reinforcement is investigated. Reliability indices based on the equations for flexure in ACI 440.1R-03, which uses the load factors from ACI 318-99 are presented. Choice of a resistance factor for flexure for ACI 440.1R-06, which uses the load factors from ACI 318-02 is also presented. Flexural designs using either ACI 440.1R-03 or ACI 440.1R-06 provide sufficient reliability, with reliability indices between 3.5 and 4.8, with the older versions of ACI 440.1R yielding higher reliability. An analysis of curvature of the beams at failure showed that flexural members that fail by FRP reinforcement rupture have ductilities similar to those that fail by concrete crushing, indicating that FRP reinforcement fracture is not necessarily a more brittle failure mode than concrete crushing.
The ACI Building Code requires the control of flexural cracking in reinforced concrete structures. Because of durability concerns, the use of thicker concrete covers is rapidly increasing. However, currently used crack control methods that are based strictly on statistical reasoning become unworkable with the use of thick covers. This study investigates the development of the crack control provisions and the crack width equation on which those provisions are based, explores the use of the crack width equation for the calculation of large covers, and presents a new formulation of the equation for calculating crack width that is based on the physical phenomenon. Use of that equation is supported by an evaluation of existing test data; based on that equation, a design recommendation is presented for the control of cracking that addresses the use of both coated and uncoated reinforcement.
In this study the efficiency of the use of Ultra High Performance Fibre Reinforced Concrete (UHPFRC) for the strengthening of existing Reinforced Concrete (RC) beams has been investigated. Experimental work has been conducted to determine UHPFRC material properties. Dog-bone shaped specimens have been tested under direct tensile loading, and standard cubes have been tested in compression. These results have been used for the development of a numerical model using Finite Element Method. The reliability of the numerical model has been validated using further experimental results of UHPFRC layers tested under flexural loading. Further numerical study has been conducted on full-scale beams strengthened with UHPFRC layers and jackets, and these results were compared to respective results of beams strengthened with conventional RC layers and with combination of UHPFRC and steel reinforcing bars. Superior performance was observed for strengthened beams with UHPFRC three side jackets, and the efficiency of this technique was highlighted by comparisons with other strengthening techniques.
Concrete members reinforced with glass fiber-reinforced polymer (GFRP) bars exhibit large deflections and crack widths compared with concrete members reinforced with steel. This is due to the low modulus of elasticity of GFRP. Current design methods for predicting deflections at service load and crack widths developed for concrete structures reinforced with steel may not be used for concrete structures reinforced with GFRP. This paper presents methods for predicting deflections and crack widths in beams reinforced with GFRP. To use the effective moment of inertia for concrete beams reinforced with GFRP bars, the effect of the fiber-reinforced polymer (FRP) reinforcement ratios and elastic modulus of FRP were incorporated in the exponent m of Branson 's equation. In addition, an equation based on flexural stiffness of GFRP reinforced concrete was developed to predict deflections. Based on this investigation and those conducted by others, a theoretical correlation for predicting crack width was proposed. Six concrete beams reinforced with different GFRP reinforcement ratios were tested- Their measured deflections and crack widths were compared with the proposed models. The experimental results compared favorably with those predicted by the models.
This paper presents the evaluation of parameters describing bond action between fiber-reinforced polymer (FRP) and concrete in RC structures strengthened in flexure. The parameters were evaluated on the basis of fitting nonlinear finite-element results to experimental results from literature. Three-dimensional (3D) finite-element simulations were used to account for transversal effects without introducing any geometry-related correction coefficients in the material model. The parameters defining the material model, describing bond action, were initial stiffness, shear strength, and fracture energy of the FRP-concrete interface. Bilinear, trilinear, and exponential curve shapes were evaluated. The parameters were related to concrete tensile strength and shear stiffness of the adhesive. According to the analysis, the models provide a good estimation of ultimate load and strain distribution in FRP compared with test results. The results showed that whether the bond-slip curve was assumed to be bilinear, trilinear, or exponential has a minor effect.
The flexural and shear performances are evaluated for concrete beams reinforced with basalt fiber-reinforced polymer (BFRP) rebar and stirrups. Nine 150 x 300 x 3, 100-mm beams were tested in four-point bending to examine the effect of BFRP flexural reinforcement ratios varying from 0.28 to 1.60 the balanced ratio on the structural performance. The beams were reinforced by either BFRP or steel stirrups, and some had no shear reinforcement. It was shown that ultimate and service loads increased with flexural reinforcement ratio for all shear reinforcement types while the service load levels were not affected by stirrup type. Beams without stirrups and those with BFRP stirrups failed in shear, with the former reaching 55-58% of ultimate flexural capacity and the latter failing by stirrup rupture at 90-96% of flexural capacity. Beams with steel stirrups failed in flexure. Deformability values show that methods that combine strength and curvature digress more from those based on midspan strain energy as shear-related deformation increases. Standard provisions predicted well the capacity of beams failing in flexure. For beams failing in shear, standards were both conservative and nonconservative. The modified compression field theory predicted well the shear capacity for members with and without stirrups. Designated methods gave reasonable predictions for service loads at deflections of span/360 and span/180. (C) 2014 American Society of Civil Engineers.
Corrosion is the primary limit state in steel reinforced concrete (RC) beams in severe environments. Corrosion of steel bars causes a decrease in steel bar section, loss of bond, and delamination of concrete cover Very limited models have been developed for estimating the residual flexural strength of corroded RC beam. These models do not differentiate between the decrease in flexural strength due to loss of steel section, or due to loss of bond between the steel bars and the surrounding concrete. This paper presents an analytical model for estimating the residual flexural strength of RC beams with unbonded bars. In this research, the "neutral axis depth" approach, which is widely used to obtain the ultimate stress in prestressed concrete, was adopted and modified to estimate the residual ultimate capacity of concrete beams reinforced with unbonded steel bars. A finite element analysis (FEA) model was developed, and the results were verified against experimental data by others. The experimental data of a total of 109 RC beams covered many variables: span-depth ratio, reinforcement ratio, concrete compressive strength, length of unbonded zone, and type of applied load. Using the aforementioned data and FEA model, an analytical model was developed to calculate the ultimate strength of concrete beams reinforced with unbonded steel bars. The results of this investigation suggest that the reinforcement ratio and the unbonded length have a major effect on the residual flexural strength of RC beams with unbonded reinforcement, whereas the other variables have limited impact.
FRP reinforcement for concrete has been developed to replace steel in several applications, particularly in corrosion-prone RC structures. FRP rebars, generally, have a lower modulus of elasticity compared to steel, which leads to wider cracks and larger deflections. Furthermore, the FRP rebars have a low transverse stiffness and strength which are usually neglected. Consequently, the effectiveness of concrete contribution to shear capacity in terms of aggregate interlock and dowel action of the longitudinal rebars is lower for FRP-RC members respect to steel. Eurocode-like design equations for predicting the shear strength of FRP-RC members are herein suggested. Based on a database containing 129 flexural tests on RC beams strengthened with FRP stirrups performed in different research institutions across the world, a statistical calibration of Eurocode-like design equations for the shear capacity of RC beams with FRP shear reinforcement has been performed according to two alternative regression-based proposals and the EN 1990-procedure that is used as a benchmark.
This paper presents a comparative analysis of experimental and theoretical deflections of simply supported beams reinforced with BFRP rebar (Basalt Fiber Reinforced Polymers). The tested BFRC model beams have been made of concrete class C30/37 and reinforced with flexural basalt bars of 8 mm in diameter with the characteristic identified in strength tests in tension. During the investigation of model beams there were registered beam deflection, concrete strains and width cracks, as well as critical forces. It has been shown that much lesser cross-sectional stiffness of basalt BFRP bars produces higher deflections and crack widths compared to the beams reinforced with steel bars of the same cross-section. The results of theoretical analysis of BFRC beam deflections on the basis of the known formulas showed some significant discrepancies compared to experimentally obtained deflections, especially for lower level of loading forces. The results clearly show that basalt rebar having full resistance against corrosion may be good alternative for the reinforcement of concrete structures, like RC bridge girders subjected to environmental attack.
Flexural behavior and serviceability performance of 24 full-scale concrete beams reinforced with carbon-, glass-, and aramid-fiber-reinforced-polymer (FRP) bars are investigated. The beams were 3,300 mm long with a rectangular cross section of 200 mm in width and 300 mm in depth. Sixteen beams were reinforced with carbon-FRP bars, four beams were reinforced with glass-FRP bars, two beams were reinforced with aramid-FRP bars, and two were reinforced with steel, serving as control specimens. Two types of FRP bars with different surface textures were considered: sand-coated bars and ribbed-deformed bars. The beams were tested to failure in four-point bending over a clear span of 2,750 mm. The test results are reported in terms of deflection, crack-width, strains in concrete and reinforcement, flexural capacity, and mode of failure. The experimental results were compared to the available design codes.
The flexural response of FRP RC elements is investigated through load–deflection tests on 24 RC beams and slabs with glass FRP (GFRP) and carbon FRP (CFRP) reinforcement covering a wide range of reinforcement ratios. Rebar and concrete strains around a crack inducer are used to establish moment–curvature relationships and evaluate the shear and flexural components of mid-span deflections. It is concluded that the contribution of shear and bond induced deformations can be of major significance in FRP RC elements having moderate to high reinforcement ratios. Existing equations to calculate short-term deflection of FRP RC elements are discussed and compared to experimental values.
The paper presents some of the results from a large experimental program undertaken at the Department of Civil Engineering of Salerno University. The static behaviour under service conditions of concrete beams reinforced with GFRP (Glass Fibre-Reinforced Polymer) as well as CFRP (Carbon Fibre-Reinforced Polymer) bars and stirrups is examined. Within the whole experimental program concerning forty beams, two different concrete strengths and two different percentages of reinforcement are taken into consideration. The final aim is to investigate both deflections at midspan and crack widths. Moreover, the ultimate behaviour up to failure is also investigated. A part of this experimental program, concerning ten prototypes reinforced with GFRP bars, is here presented and discussed. Finally, comparisons with analytical predictions given by CNR-DT 203/2006 are also shown.
Guide for the design and construction of concrete reinforced with FRP bars
American Concrete Institute (ACI). Guide for the design
and construction of concrete reinforced with FRP bars.
ACI 440.1R-06 2006, Farmington Hills, MI.