Assessment of the existing models to evaluate the shear strength contribution of externally bonded frp shear reinforcements
Introduction
Nowadays, there is still a lack of worldwide consensus on the evaluation of the shear strength contribution of the externally bonded (EB) fibre reinforced polymer (FRP) reinforcement, in elements strengthened in shear through this technique. This is due to the confluence of many different reasons: a) the complexity of the shear phenomenon; b) the debonding of the external reinforcement for some configurations and its prediction, c) the linear elastic behaviour of the FRP material (the EB FRP stirrups do not yield); and d) the interaction between concrete, internal steel transverse reinforcement if it exists, the longitudinal reinforcement, and the EB FRP reinforcement.
The EB FRP shear strengthening can be performed in different configurations: a) sheets fully wrapping the section (wrapped); b) sheets or L-shaped laminates bonded on the lateral sides and the bottom surface of the beam (U-shaped); and c) sheets or laminates bonded in the lateral sides of the section (side-bonded). The sheets and laminates can be bonded in a continuous or discontinuous configuration. Both U-shaped and side-bonded configurations are susceptible of debonding once a critical shear crack opens and widens. Then, if the bonded length of each strip at the upper side of the crack (for the U-shaped) or at both sides of the crack (for the side-bonded case) is not long enough to anchor the tensile force of the FRP, the laminate debonds suddenly before reaching its ultimate capacity. This debonding failure mode can be delayed or can be avoided by using appropriate anchorage devices.
The ultimate shear strength of beams externally strengthened in shear by FRP laminates can be calculated as the sum of the contribution of the different components: concrete, transverse steel and FRP external reinforcement.
Some of the existing guidelines (fib Bulletin 90 [1] ACI440.2R-17 [2] CNR-DT-200/2013-R1 [3] Concrete Society TR-55 [4] DAfStb Heft 595 [5] fib Bulletin 14 [6]) add the contribution of the externally bonded (EB) FRP reinforcement to the shear strength of the unstrengthened element. This approach has been previously discussed by [7], [8], [9], [10], [11] observing that the presence of the FRP could influence the effective stress in the internal steel, sometimes leading to non-conservative results. This might be due to possible changes in the strut orientation or additional cracking that may change the contribution of the concrete or existing transverse reinforcement to the shear strength. The interaction of the FRP shear reinforcement with the transversal steel or the concrete is only considered in a few number of the existing formulations [12], [13], [14], [15], [16], [17]. Bousselham and Chaallal in [8] concluded that the contribution of concrete remains more or less unchanged after the formation of diagonal cracking for small and medium size beams. In addition, according to Bousselham and Chaallal [8] the FRP has a significant influence on the behaviour of the transverse steel. In the case of beams with transverse stirrups, the transverse steel contribution is higher than that of FRP, due to better bonding at the stirrup-concrete interface. According to Pellegrino and Modena [18] Deniaud and Cheng [19] Monti and Liotta [13] and Ali et al. [16] the interaction between transverse steel and FRP is important since there is not always full interaction between the shear capacity of the steel stirrups and the FRP, that is, the system is not ductile enough to allow that the maximum contribution of each material occurs at the same instant. Ali et al. [16] developed a partial-interaction mathematical model which was not considered in the following study due to its complexity to be applied in a large database. Mofidi and Chaallal [20] performed a study of the major factors affecting the shear contribution of the FRP, concluding that even though none of the existing guidelines explicitly consider the transverse internal steel contribution when calculating the FRP shear strength, it has a significant influence. In addition, Mofidi and Chaallal in [21] concluded that a lower contribution of existing steel stirrups (due to non-yielding) instead of the full contribution considered in the existing recommendations depends on the stirrup spacing. For this reason, some of the existing recommendations are very strict in detailing to take this fact into account. Colotti et al. [22] developed a closed-form analytical solution for quantifying the contribution of steel stirrups and FRP strips by integrating the stress distributions along the beam height as the critical crack widens. This formulation provides a peak value of the combined contribution of both materials steel and FRP. The FRP contribution follows the same treatment to that used by Chen and Teng [23] but with another bond strength model.
The existing guidelines provide formulations to evaluate the shear strength contribution of the FRP laminates (Vf) which are similar to the contribution of the internal transverse steel reinforcement to the shear strength (Eq. (1)), since most of them are based on the truss analogy.where Af/sf is the area per unit length of FRP reinforcement, zf is the inner lever arm of the FRP reinforcement, ffd is the FRP design tensile strength when failure occurs, θ is the angle between the concrete compression strut and the longitudinal axis of the member, α is the angle between principal fibre orientation of the FRP and the longitudinal axis of the member.
The definition of the stress level at the FRP and the θ angle are the main difference between the existing formulations and guidelines. The effective stress or strain of the FRP is substantially lower than the FRP ultimate strength or strain, this is due to the variable tensile stress developed along the crack profile [13]. Some of the formulations adopt 45° for the θ angle [2], [7] or alternatively a variable angle approach [3], [6] as that of Eurocode 2 [24].
The main difference with the transverse internal steel formulations is that the FRP reinforcement does not yield at failure. The different existing models define the stresses at the EB reinforcement depending on its configuration, taking into account debonding for the U-shaped and side-bonded configurations and assuming failure in the laminate in the rounded corner of the sections for the wrapped configuration. In other words, they consider different scenarios related to failure. To consider debonding, the anchorage of the FRP laminate in relation to the critical shear crack should be defined. Therefore, some formulations consider a mean value for the bonded length that crosses the critical shear crack. For the wrapped configuration, to consider failure at the rounded corner, most of the formulations are semiempirical and come from an adjustment of a formula obtained from confinement tests performed in columns strengthened with FRP sheets.
Sas et al. [25], Pellegrino and Vasic [11], Rousakis et al. [26], D’Antino and Triantafillou [27] performed an assessment of the existing formulations to evaluate the FRP shear strength contribution. Sas et al. [25] compared the performance of the formulations of Chaallal [28], Triantafillou [29] and Triantafillou and Antanopoulos [30], Khalifa et al. [31], Khalifa and Nanni [32], Chen and Teng [23], [33], [34], Deniaud and Cheng [35], [36], Adhikary et al. [37], Ye et al. [38], Cao et al. [39], Zhang and Hsu [40], Carolin [41], Carolin and Täljsten [42], and Monti and Liotta [13]. They concluded that the different predictive performance of the models can partially be explained by the fact that some of them were calibrated from a reduced amount of experimental results. According to Sas et al. [25] the shear models for FRP strengthening in the present form do not predict the shear failure very well, and the T-sections were treated as a special case of a rectangular beam. Pellegrino and Vasic [11] analysed the overall shear strength of FRP strenghenend elements, by applying different fomulations to evaluate the FRP shear strength (fib Bulletin 14 [6], CNR-DT-200/2004 [43], ACI440.2R-08 [44], Chen and Teng [23], [34], Carolin and Täljsten [42], Pellegrino and Modena [18], Bukhari et al. [45] and Mofidi and Chaallal [12]) combined with the estimation of the concrete, steel and compressive strength of concrete according to basic model codes for unstrengthened RC structures (Eurocode 2 [24], ACI 318 [46] and Model Code 2010 [47]). In their study, Pellegrino and Vasic [11] focused special attention to the θ angle, which has a significant influence on the prediction of the results. In general, according to Pellegrino and Vasic [11] the CNR-DT-200/2004 [43] and Pellegrino and Modena [18] gave good results in terms of mean value (MV) and coefficient of variation (COV) of the ratio between the experimental and theoretical ultimate shear force. When combining the model of Pellegrino and Modena [18] with the Eurocode 2 [24] the best predictions were obtained for a variable crack shear angle. Rousakis et al. [26] also performed an assessment and improvement of existing recommendations for shear design of RC beams strengthened with composite materials. In [26] a straightforward comparison of the total shear strength not only the FRP contribution is analysed, observing that the trend line of predictions without safety factors is conservative for most of the existing guidelines. Finally, D’Antino and Triantafillou in [27] performed an assessment of five design guidelines (EN 1998-3 [48], ACI 440.2R-08 [44], DafStb [5], TR-55 [4], CNR-DT/200-R1. 2013[49]) and a new proposed model. They concluded that all models tend to underestimate the FRP shear strength for the completely wrapped configuration. However, models were more accurate for the U-shaped configuration. Their proposal is an extension of the German guideline [5] and gave conservative results (MV = 1.77 COV = 2.21 for U-shaped and MV = 3.51 and COV = 4.32 for wrapped).
In this paper, a comparative analysis of the existing formulations to evaluate the FRP contribution (given in Appendix A) is performed and presented through the use of a wide database of experimental tests distinguishing those cases with and without internal steel transverse reinforcement and the different FRP strengthening configurations.
Section snippets
Description of the database
A database of 555 RC beams FRP-strengthened, tested and failing in shear has been assembled as seen in Appendix B (355 with rectangular section and 200 with T-section). The database gathers the results of more than 80 experimental programs. This database includes tests of other existing available databases such as Dabasum (University of Minho) and the database published in [10], [21], [22], [25]. Despite some of the data belong to existing databases, all data included in this database have
Existing models to evaluate the frp contribution to the shear strength of eb frp shear strengthened beams
The models considered in the comparative analysis of the following section are those included in the existing guidelines (JSCE [51], fib Bulletin 14 [6], CIDAR (2006) [52], TR-55 [4], CNR-DT 200.R1 2013 [49], Dafstb [5], ACI 440.2R-17 [2], fib Bulletin 90 [1]) and also some other approaches such as Rousakis et al. [26], Kotynia [14], Mofidi and Chaallal [20], Pellegrino and Modena [10], [18], [53], Monti and Liotta [13], Carolin and Täljsten [42] and Chen and Teng [23], [34]. In relation to the
Assessment of the existing formulations to evaluate the frp contribution to the shear strength of eb frp shear strengthened beams
The reliability of the existing formulations to evaluate the shear strength contribution of the EB FRP of a shear-strengthened RC beam is evaluated in this section through the comparison of the experimental (Vf,exp) and theoretical (Vf,th) EB FRP shear contribution at failure. The experimental value of the FRP contribution, Vf,exp, is calculated as the difference between the ultimate shear force of the strengthened beam and the ultimate shear force of the unstrengthened control beam. Therefore,
Analysis of the influence of the angle of inclination of struts in the theoretical predictions
From the experimental results compiled on the database, some parameters have a significant influence in the calculation of the FRP contribution to the shear strength as observed by Kotynia et al. [50]. In addition, Mofidi and Chaallal [12] identified several major parameters: bond model, effective strain, anchorage length, width-to-spacing ratio for discontinuous configurations, crack angle, crack pattern, effect of transverse steel. Some of them have already been considered in the existing
Conclusions
A database of 555 tests strengthened in shear by EB FRP sheets was assembled from the existing experimental programs distinguishing between the EB FRP configuration and the existence of internal transverse reinforcement. A comparative analysis of the experimental-to-theoretical ratio of the FRP contribution to the ultimate shear strength has been performed by means of the database. From this analysis, the following conclusions can be drawn:
For rectangular beams without transverse reinforcement
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This paper has been developed under the framework of the Research Projects “BIA2015-64672-C4-1-R” and “RTI2018-097314-B-C21” funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and co-funded by the European Regional Development Funds (ERDF). The authors would also like to thank the Cost Action TU1207 which funded a short term scientific mission of the first author in Lodz University of Technology.
References (129)
- et al.
Assessment of design procedures for the use of externally bonded FRP composites in shear strengthening of reinforced concrete beams
Compos Part B Eng
(2013) - et al.
Tests and design equations for FRP-strengthening in shear
Constr Build Mater
(2007) Shear interaction effect between transverse reinforcements in FRP-strengthened RC beams
Compos Part B Eng
(2013)- et al.
Vertical shear interaction model between external FRP transverse plates and internal steel stirrups
Eng Struct
(2006) - et al.
Unified analytical approach for determining shear capacity of RC beams strengthened with FRP
Eng Struct
(2011) - et al.
Shear capacity of FRP-strengthened RC beams: FRP debonding
Constr. Build. Mater.
(2003) - et al.
Utilization of hybrid approach towards advanced database of concrete beams strengthened in shear with FRPs
Compos Part B Eng
(2016) - et al.
Improving shear capacity of existing RC T-section beams using CFRP composites
Cem Concr Compos
(2000) - et al.
Predicting the shear–flexural strength of slender reinforced concrete T and I shaped beams
Eng Struct
(2015) - et al.
Strengthening concrete beams for shear using CFRP-materials: evaluation of different application methods
Compos Part B Eng
(2000)
Rehabilitation of rectangular simply supported RC beams with shear deficiencies using CFRP composites
Constr Build Mater
Shear strengthening effectiveness with CFF strips
Eng Struct
Strengthening concrete beams for shear with CFRP sheets
Constr Build Mater
Behavior and capacity of RC beams strengthened in shear with NSM FRP reinforcement
Constr Build Mater
Near surface mounted CFRP laminates for shear strengthening of concrete beams
Cem Concr Compos
Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates
Compos Part B Eng
Shear capacity of precracked and non-precracked reinforced concrete shear beams with externally bonded bi-directional CFRP strips
Constr Build Mater
Behavior of reinforced concrete t-beams strengthened in shear with carbon fiber-reinforced polymer-an experimental study
ACI Struct J
Mechanisms of shear resistance of concrete beams strengthened in shear with externally bonded FRP
J Compos Constr
Interaction between steel stirrups and shear-strengthening FRP strips in RC beams
J Compos Constr
Fiber reinforced polymer shear strengthening of reinforced concrete beams with transverse steel reinforcement
J Compos Constr
Shear strengthening of RC beams with externally bonded FRP composites: effect of strip-width-to-strip-spacing ratio
J Compos Constr
Shear strengthening of RC beams with polymer composites
FRP-RC Beam in Shear: Mechanical Model and Assessment Procedure for Pseudo-Ductile Behavior
Polymers (Basel)
An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams
Mech Compos Mater
Review of shear design methods for reinforced concrete beams strengthened with fibre reinforced polymer sheets
Can J Civ Eng
Shear Strengthening of RC Beams with EB FRP: Influencing Factors and Conceptual Debonding Model
J Compos Constr
Tests and Design Provisions for Reinforced-Concrete Beams Strengthened in Shear Using FRP Sheets and Strips
Int J Concr Struct Mater
European Committee for Standardization. Eurocode 2: Design of Concrete Structures: Part 1: General Rules and Rules for Buildings
European Committee for Standardization
Are available models reliable for predicting the FRP contribution to the shear resistance of RC beams?
J Compos Constr
Accuracy of design-oriented formulations for evaluating the flexural and shear capacities of FRP-strengthened RC beams
Struct Concr
Strengthening of reinforced concrete beams with externally bonded fiber-reinforced-plastic plates: Design guidelines for shear and flexure
Can J Civ Eng
Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded FRP Composites
ACI Struct J
Contribution of Externally Bonded FRP to Shear Capacity of RC Flexural Members
J Compos Constr
Anchorage strength models for FRP and steel plates bonded to concrete
J Struct Eng
Shear capacity of fiber-reinforced polymer-strengthened reinforced concrete beams: Fiber reinforced polymer rupture
J Struct Eng
Shear Behavior of Reinforced Concrete T-Beams with Externally Bonded Fiber-Reinforced Polymer Sheets
ACI Struct J
Simplified shear design method for concrete beams strengthened with fiber reinforced polymer sheets
J Compos Constr
Shear strengthening of reinforced concrete beams using fiber-reinforced polymer sheets with bonded anchorage
ACI Struct J
Debonding in RC beams shear strengthened with complete FRP wraps
J Compos Constr
Shear strengthening of reinforced concrete beams using carbon-fiber- reinforced polymer laminates
J Compos Constr
Carbon fiber reinforced polymers for strengthening of structural elements
Carbon Fibre Reinf Polym Strength Struct Elem
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