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Review

An Analysis of the Transfer Lengths of Different Types of Prestressed Fiber-Reinforced Polymer Reinforcement

by
Aidas Jokūbaitis
* and
Juozas Valivonis
Department of Reinforced Concrete Structures and Geotechnics, Faculty of Civil Engineering, Vilnius Gediminas Technical University, Sauletekio av. 11, LT-10223 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
Polymers 2022, 14(19), 3931; https://doi.org/10.3390/polym14193931
Submission received: 21 August 2022 / Revised: 6 September 2022 / Accepted: 15 September 2022 / Published: 20 September 2022
(This article belongs to the Section Polymer Composites and Nanocomposites)

Abstract

:
The main aim of this paper is to provide a broader analysis of the transfer lengths of different types of fiber-reinforced polymers (FRPs) and to provide corrections to the existing theoretical models. Therefore, this paper presents a description of the main factors that influence the transfer lengths of different types of FRPs based on experimental results found in the literature. A database of more than 300 specimens was compiled with the results of the transfer lengths of different FRPs and the main influencing parameters. The analysis of the database results showed that the transfer length of the carbon fiber composite cable (CFCC) strands depends on the type of prestressed reinforcement release. Therefore, in this article, the new coefficient αt = 2.4 is proposed for the transfer length of suddenly released CFCC strands. Additionally, the transfer length of the aramid fiber reinforced polymer (AFRP) depends on its surface conditions. Therefore, new coefficients αt = 1.5 and αt = 4.0 are also proposed for the transfer lengths of smooth braided and sanded and rough AFRP bars, respectively. Furthermore, the proposed coefficients αt = 2.6, αt = 1.9, and αt = 4.8 found in the literature were validated with the analysis of a larger database of the transfer lengths of glass fiber-reinforced polymer (GFRP) bars, carbon fiber-reinforced polymer (CFRP) bars, and gradually released CFCC strands, respectively. Moreover, the main existing theoretical models are presented, and the comparison of theoretical and experimental transfer length results is discussed. However, the low number of specimens prestressed with basalt fiber-reinforced polymer (BFRP) bars prevented the deeper analysis of the results. the analysis of the transfer length and the proposed new values of the coefficient αt provides possibilities for adapting it to design codes for engineering applications and performing additional research that fills the missing gaps in the field.

1. Introduction

There has been increasing concern about the durability of prestressed concrete structures due to the corrosion of prestressed steel strands, especially in corrosive environments such as parking garages, bridges, marine structures, and railway sleepers [1,2,3]. Steel corrosion is accelerated in these structures as a result of the influence of a chloride-rich environment (deicing salts, etc.). Therefore, there is increasing interest in the use of FRP materials, namely, CFRP, AFRP, GFRP, and the relatively new BFRP [4,5] as replacements for steel reinforcements. BFRP was developed for applications in civil infrastructure as a structural reinforcement material. It has similar tensile strength, modulus of elasticity, and cost to GFRP. BFRP is more chemically stable, has a wider range of working temperatures, and is much cheaper than CFRP. Additionally, it is durable, resistant to high temperatures, corrosion, acid, radiation, ultraviolet (UV), and vibration; it also has excellent electromagnetic characteristics. Furthermore, BFRP is resistant to alkalis and is distinct from GFRP. AR–glass fibers are suggested for application in alkaline environments. However, it has a much higher cost. AFRP has good resistance to impact, high strength, high modulus of elasticity, the lowest density, and sufficient stiffness. AFRP can be utilized for impact-resistant structures. Additionally, AFRP is sufficient for application for strands and cables; however, it has low compressive strength perpendicular to the fiber direction and low long-term strength, as well as higher cost. CFRP has the highest strength of FRP materials and the largest range of strengths. CFRP is more resistant to creep rupture and fatigue failure than the other FRPs. Additionally, it has low conductivity and a high modulus of elasticity, is resistant to chemical effects, and does not absorb water as well. Its higher cost is offset by its high strength and high resistance to cyclic and fatigue failures. CFRP with an ultrahigh modulus of elasticity is popular in the aerospace industry because its strength-to-weight ratio is among the highest of all FRPs. CFRP with a normal modulus of elasticity is used in the infrastructure industry.
FRP consists of strong glass, carbon, aramid, and basalt fibers embedded in a resin matrix. Hybrid fiber reinforced polymer (HFRP) combines CFRP and GFRP [6,7]. The quality of the composite material depends on the surface roughness and the adhesion between the filler and the matrices, which can be enhanced with additional treatment [8,9]. FRP is an anisotropic material (contrary to steel), resulting in better mechanical properties in the longitudinal direction (Table 1). FRP has a lighter weight and higher strength. However, its mechanical properties are linear elastic, which leads to a lower failure strain and elongation rate. Additionally, the modulus of elasticity of FRP is lower than that of steel (except for CFRP bars with a high modulus of elasticity). The material properties of FRPs depend on the fibers, matrices, and fiber–volume ratios. FRP is resistant to corrosion, which can significantly increase the service life of the structure.
FRPs have additional important properties that make them particularly attractive for prestressed concrete applications: high strength, which is similar to or greater than that of steel and low modulus of elasticity, which results in lower concrete prestress losses due to concrete creep and shrinkage as well as the relaxation of the prestressing element.
The major difficulty in using FRP reinforcement for prestressing is that anchorage systems require greater attention than those for steel strands. Therefore, three types of anchorage systems are developed for FRP reinforcement: mechanical, bonded, and composite [9].
The mechanical anchorage of reinforcement consisting of a steel barrel and wedges is ensured by friction between the reinforcement surface and the inner conical anchorage surface. Therefore, compressive stresses appear perpendicular to the reinforcement. However, FRP is an anisotropic material that has weak material properties perpendicular to the fibers. Therefore, practitioners suggest enhancing the mechanical anchorage of the FRP reinforcement using a small slope angle between the inner surface of the barrel and the outer surface of the wedges, the rounded edges of the wedges, and a soft metal sleeve (aluminum or copper) around the FRP. Other mechanical anchorages were described in [9,15] such as the curved wedge anchorage system [16], the nonmetallic wedge anchorage system [17], the integrated sleeve-wedge anchorage system [18], the spike anchorage system, and the clamping anchorage system. The mechanical anchors are usually of small size. However, this type of anchorage lacks stability and reliability.
The bonded-type anchorage consists of a steel barrel with a bonding material (cementitious or resin) surrounding the FRP bar. The inner part of the barrel can have three different shapes: straight; conical with decreased length but larger diameter; or straight and conical with increased length and similar diameter with the purpose of relieving the stress concentration. The bonded-type anchorage depends on the bonding force between the CFRP cable and the bonding material to balance the tension of the cable. The performance of the bonded-type anchorage is mainly influenced by the dimensions and configuration of the steel barrel, the material type and surface condition of the FRP, and the properties of the bonding material. The main drawbacks are a large size, long curing time, creep of the bonding material, sensitivity to moisture, and high temperature.
The composite anchorage takes advantage of mechanical and bonded-type anchorage. In [19], the straight steel pipe filled with resin was directly clamped with a split-wedge anchor that improved the anchorage of the FRP. Additionally, [20] proposed a compound-type anchorage system that adapted load transfer through wedge extrusion and epoxy bonding. The composite anchorage is smaller than the bonded anchorage but larger than the mechanical anchorage and presents good anchoring performance. At the same time, it has complicated construction and installation processes. Mechanical and bond anchorage systems are simpler than the composite anchorage system. Therefore, the mechanical and bond anchorage systems are still under investigation.
The use of FRP reinforcement in prestressed concrete structures is highly dependent on the reliability of the reinforcement anchorage zone. That is, the behavior of concrete members is mainly dependent on the bond between reinforcement and concrete [21,22,23]. In pretensioned concrete structures, the prestressing force is transferred to the concrete by the bond between reinforcement and concrete, which depends on three mechanisms: adhesion, Hoyer effect (wedge action), and mechanical interlocking. The bond of prestressed FRP is mainly influenced by the large Poisson ratio related to the Hoyer effect and the high axial strain capacity of the FRP materials [24]. Furthermore, if the effect of Poisson’s ratio is dominant, the surface conditions of the FRP will have little influence on the bond [25]. In the case of FRP materials, the chemical bond (adhesion) is particularly weak [24]. Lastly, mechanical interlock and friction are quite dependent on the surface characteristics of the reinforcement.
In pretensioned members, the length from the end of the member where the tendon stress is zero to the point along the tendon where the prestress is fully effective is called the transfer length [12]. Ref. [11] defined the transfer length as the length required to transfer the prestressing force to the concrete after the release of a prestressing reinforcement. In other words, it is the distance along the member in which the effective prestressing force is developed.
One of the most important factors that affect the transfer length of prestressed reinforcement is the Hoyer effect, which is caused by the swelling of the strand in the transfer zone after release as a result of the Poisson ratio. During the transfer, the induced confining stresses normal to the tendon enhance the bond strength at the interface, as the lateral deformation is resisted by the surrounding concrete. Enhancement of the bond caused by the Hoyer effect is directly related to the strength of the concrete and the coefficient of friction between the two materials. Additionally, according to [26], the distribution of the bond stress over the transfer length is not linear due to the changing values of transverse strain (Hoyer effect) and slip over the transmission length.
Knowledge of the transfer length is essential to maintaining the integrity of the structure and to preventing the bond slip failure of the member. Additionally, an accurate estimate of the transfer length is important for checking the stress limit at the serviceability limit state, determining the actual bond stress in the anchorage zone of the pretensioned reinforcement, and designing the shear of the prestressed members. The underestimation of the transfer length leads to unconservative shear calculations, while overestimation leads to unconservative stress calculations at the serviceability limit state.
The simulation of the anchorage zone of FRP reinforcement introducing the finite element method (FEM) allows for performing a deeper analysis of the transfer length results that are difficult to measure in real experimental research. The simulation of the transfer lengths of BFRP [27], CFCC, and AFRP [28] showed that the optimization of the transfer length prediction of the FRP can be performed, eliminating unnecessary and expensive future experimental research.
In the last 30 years, numerous experimental researchers have investigated the transfer lengths of prestressed FRP. The transfer length is a function of several factors that depend on the properties of both the prestressing reinforcement and the concrete. Therefore, many studies were performed to investigate the influence of concrete compressive strength [29,30,31,32,33,34,35,36,37,38,39], prestress level [29,30,31,32,33,36,37,39,40,41,42,43,44,45,46,47], reinforcement diameter [24,26,29,30,31,32,35,36,37,38,48], concrete cover [26,29,30,31,32,35,48,49,50], reinforcement surface conditions [24,35,36,37,38,47,48,50], and modulus of elasticity [33,36,47,51,52,53,54] etc. on the transfer length of prestressed FRP reinforcement. However, the large variation in FRP bars in terms of shape, surface conditions, strength, and modulus of elasticity indicates that a deeper understanding of the transfer length of FRPs with different properties remains necessary. Therefore, this article presents a database of transfer length results for pretensioned FRP and provides a comparative analysis of the anchorage zones of different types of FRP.

2. Parameters That Influence the Transfer Length

The transfer length is an important parameter for the anchorage zone of prestressed reinforcement. In addition, it depends on various mechanical and geometric properties of the material. Therefore, this section presents an overview of the influence of different parameters on the transfer length of different prestressed FRP reinforcements (GFRP, CFRP, AFRP, CFCC and BFRP). Unfortunately, only a few studies on the transfer length of BFRP bars were found in the literature [27,55,56]. The lack of results and similar experimental parameters do not allow for qualitatively determining the influence of different parameters on the transfer length of BFRP bars.

2.1. Effect of Concrete Compressive Strength

Many authors investigated the influence of concrete compressive strength at the time of reinforcement release on the transfer length of concrete specimens pretensioned with different types of FRP reinforcement. Table 2 provides a summary of the average transfer length results, showing the influence of concrete compressive strength. The lower (fci.min) and higher (fci.max) concrete strength correspond to higher (Lt.max) and lower (Lt.min) transfer length, respectively.
Zou [33] concluded that compared with the effect of the level of prestressing, the concrete strength at transfer is a more significant factor that affects the transfer length of the spirally indented CFRP Leadline bar. Additionally, [33] stated that all tested beams prestressed with AFRP bars had similar transfer lengths but different concrete strains with respect to concrete strength. Therefore, it was concluded that the transfer length of the AFRP bars is not significantly affected by the concrete strength.
The authors of [36,37] concluded that the transfer length of the prestressed GFRP bars decreased by about 32% when the concrete strength at the time of reinforcement release increased by 2.3 times. Additionally, Crossett et al. [55] showed that the transfer length of the BFRP bar decreased by 10% with an increase in concrete strength by 43%.
The FEM model of Motwani and Laskar [28] showed that peak elastic strain of concrete at the level of prestressed CFCC and AFRP Arapree reinforcement decreases with an increase in concrete strength.
Based on [33,38,39], it was stated in [36,37] that the concrete strength had a minimum effect on the transfer length of the AFRP reinforcement due to its small diameter (normally ≤9.5 mm) and shorter transfer length. Additionally, the authors of [36,37] stated that the larger diameter of the GFRP bars (Ø12–Ø16 mm), the longer the transfer length, allowing the effect of concrete strength on the transfer length to be apparent. However, in [38,39], a higher diameter of AFRP bars was also used (Ø12–Ø16 mm), and it resulted in transfer lengths almost twice as long as in [36,37] for GFRP bars with similar prestress levels and concrete strengths. Although the modulus of elasticity of AFRP and GFRP bars is similar, the surface of AFRP bars is braided (almost plain), and it is ribbed for GFRP bars. Therefore, the different surface conditions of AFRP and GFRP reinforcement may be the deciding factor for the difference in transfer length.
According to Table 2, it can be stated that with the increase i concrete compressive strength, the FRP transfer length decreases. However, the rate of decrease of the transfer length is lower for AFRP and GFRP reinforcement compared with that for CFCC and CFRP reinforcement. Therefore, the concrete strength is more significant for CFCC and CFRP reinforcement.

2.2. Effect of Prestress Level

The FRP reinforcements for prestressed concrete members can have different tensile strengths and initial stresses. Therefore, it is better to compare the ratios between initial stresses and tensile strength (fpi/fpu) of different types of FRPs with the transfer length instead of the initial stresses (fpi). Table 3 provides a summary of average transfer length results showing the influence of prestress level on the FRP reinforcement. The lower (fpi/fpu (min)) and higher (fpi/fpu (max)) prestress levels correspond to the lower (Lt.min) and higher (Lt.max) transfer lengths, respectively.
Research by other authors revealed that the influence of prestress level gives contradictory results depending on the type of FRP. For CFRP Leadline bars [33,40,41,42] and CFRP sanded bars [43,44], the transfer length increases with the increase in prestress level (Table 3). However, other authors [31,32,39,45,46] determined that the transfer length of CFRP sanded bar [45] and the CFRP Leadline bar [31,32,39,46] is not significantly influenced by the prestress level (Table 3).
For the Ø12.5 mm CFCC strand and the concrete strength of 28–30 MPa, the average transfer length increased by 26% with an increase in the prestress level of 25%. For the Ø15.2 mm CFCC strand and the concrete strength of 22–24 MPa, the transfer length increased by 25% with an increase in prestress level of 19%. Therefore, the authors [31,32] stated that the prestress level can have a greater influence on the transfer length of the CFCC strand than the concrete compressive strength due to similar concrete strengths and a greater reduction of the transfer length at a higher prestress level. However, the results from [29,30,39] showed that the transfer length of CFCC strands is not significantly influenced by the prestress level.
Ehsani et al. [47] calculated that the transfer length of the AFRP Arapree bars (Ø9.9 mm) with a smooth surface increased by 81% with an increase in the prestress level of 43% to 59% with concrete strength of 29–31 MPa.
The authors of [36,37] tested concrete beams prestressed with GFRP bars with ribbed surfaces and calculated that for Ø16 mm GFRP bar and concrete strength of 29–31 MPa, the increase in prestress level from 26% to 41% induced a 32% increase in transfer length.
It is evident that in most cases for CFRP Leadline bars, CFCC strands, AFRP, and GFRP bars, the transfer length is proportional to the prestress level (Table 3).

2.3. Effect of Reinforcement Diameter

Several authors have investigated the influence of reinforcement diameter on the transfer length of pretensioned FRP reinforcement. Table 4 provides a summary of average transfer length results showing the influence of reinforcement diameter. The lower (Ømin) and higher (Ømax) reinforcement diameters correspond to the lower (Lt.min) and higher (Lt.max) transfer lengths, respectively.
Domenico and colleagues [29,30] and Mahmoud and colleagues [31,32] calculated that the transfer length of CFCC strands increased by 9–34% and 32%, respectively, with an increase in reinforcement diameter from 12.5 mm to 15.2 mm. Stark and Hegger [26] tested UHPFRC (ultra-high-performance fiber-reinforced concrete) beams prestressed with CFCC 7-wire helical indented strands (Ø7.5 mm) and CFRP spirally indented bars (Ø5 mm). The test results showed that the transfer length of the CFCC strand was 73% higher than the CFRP bar. As both reinforcements had indented surfaces, the helical form of the CFCC 7-wire strand may have an additional positive influence on bond conditions.
Nanni and colleagues [24,38] calculated that at a low prestress level (24%), the transfer length increased by 38% with an increase in the diameter of the AFRP bar (with a smooth braided surface) from 8 mm to 12 mm. For a higher prestress level (about 50%), the transfer length increased to 42% with an increasing diameter of the AFRP bar from 8 mm to 16 mm. Furthermore, Taerwe and Pallemans [35,48] showed that the transfer length increased by 53% with an increasing diameter of the AFRP Arapree bar (with sanded surface) from 5.3 mm to 7.5 mm (the cross-sectional area of reinforcement increased twice).
In [36,37], it was calculated that with the increase in GFRP bar diameter from 12 mm to 16 mm, the average transfer length increased by 19%.
The FEM model of Motwani and Laskar [28] showed that the peak elastic strain of concrete at the level of prestressed CFCC and AFRP Arapree reinforcement increases with an increase in reinforcement diameter.
The results for the influence of reinforcement diameter on the transfer length of pretensioned CFRP, CFCC, AFRP, and GFRP reinforcement showed that it is generally consistent with the literature and that the transfer length is directly proportional to the diameter of the prestressed FRP reinforcement. However, expressing the transfer length in terms of the bar diameter only can result in inaccurate results, as it also depends on the prestressing level and the concrete compressive strength.

2.4. Effect of Concrete Cover

The effect of concrete cover is important for the durability of prestressed concrete structures. However, the FRP reinforcement covers this aspect. Therefore, a sufficient concrete cover is more relevant to controlling concrete splitting during the release of pretensioned reinforcement. Additionally, it is more relevant to analyze the influence of concrete cover on the cracking of the anchorage zone and the transfer length of the FRP reinforcement through the ratio between the concrete cover and the reinforcement diameter (c/Ø).
In [29,30], it was concluded that concrete cover c/Ø of 4 and 5 had no significant influence on the transfer length results for the CFCC strand sizes of Ø12.5 mm and Ø15.2 mm, respectively, for concrete strength of 30–56 MPa and prestress level of 50–75% for a given range of concrete cover (from 50 mm to 75 mm). According to [31,32], a concrete cover of 4·Ø is sufficient to prevent concrete splitting of the anchorage zone of the CFCC strand and the CFRP Leadline bar during reinforcement release for concrete strength between 22 MPa and 42 MPa, reinforcement diameter of 8–15.2 mm, and prestressing level of 60–80%. Therefore, with sufficient concrete confinement, all prestress force can be transferred to the concrete. However, all tested beams had a debonded length of 50 or 100 mm at the end of the beam. Therefore, the radial pressure moved deeper into the beam and could increase the splitting resistance of the transfer zone. Additionally, Stark and Hegger [26,49] calculated that a concrete cover c/Ø of at least 3.0 (absolute concrete cover 22.5 mm) is required for CFCC strand (Ø7.5 mm) and a CFRP bar (Ø5 mm) c/Ø of at least 4.0 (absolute concrete cover 20 mm) is required to ensure the crack-free introduction of the prestressing force for UHPFRC concrete beams.
Taerwe and Pallemans [35] calculated that for sand-coated AFRP bars (Ø5.3 mm and Ø7.5 mm), the critical concrete cover to be used to avoid concrete splitting is approximately equal to 2.8 times the bar diameter (2.8·Ø) for concrete strength of 54 MPa and prestress level of 50%. Additionally, the test results showed that the transfer length decreased with an increase in c/Ø up to approximately 3.5. The further increase in concrete cover did not have a significant influence on the transfer length of the AFRP bars.
Khin et al. [50] performed tested the minimum concrete cover (5 mm, 10 mm, and 15 mm) of concrete prisms (100 × 100 × 600 mm) pretensioned with CFRP, AFRP (prestress level of 60%), and GFRP (prestress level of 50%) bars (Ø8 mm). Based on the experimental test results, the recommended minimum concrete cover was 15 mm (c/Ø = 1.9) for the CFRP bar, but for the GFRP and AFRP bars, the concrete cover could be greater than 15 mm (c/Ø > 1.9). This could be related to the lower modulus of elasticity of the GFRP and AFRP reinforcement, which induces higher splitting stresses in the anchorage zone due to the Hoyer effect.
Motwani and Laskar [28] performed simulation tests for the anchorage zone of the prestressed CFCC strand and AFRP Arapree bar. They established that significant amounts of plastic strain appeared near the prestressing reinforcement, indicating concrete cracking at transfer for Ø12.7 mm, c = 30 mm, and c/Ø = 2.4. Additionally, they determined that the peak elastic strain of concrete at the level of prestressed CFCC and AFRP Arapree reinforcement decreases with an increase in concrete cover.
The small concrete cover could lead to the splitting of the concrete at transfer due to the insufficient confinement of the concrete. Therefore, the additional confinement of the concrete can reduce the risk of splitting the concrete during reinforcement release.

2.5. Effect of Shear Reinforcement

As stated in the previous section, additional concrete confinement can reduce the risk of concrete splitting during the release of pretensioned FRP reinforcement and therefore have a positive effect on the transfer length. Several authors have investigated the different types of concrete confinement at the anchorage zone of pretensioned FRP reinforcement. Table 5 provides a summary of the average transfer length results showing the influence of shear reinforcement.
Saeed [45] tested concrete beams prestressed with Ø12.7 mm CFRP sand-coated and helically wrapped bars. The distance between shear reinforcement of 75 mm and 50 mm for the level of prestressing of 50% and 55% for beams B2-4-55 and B3-4-60, respectively, was analyzed. The shorter distance between the shear reinforcements increased the confinement and decreased the transfer length (495 mm) in beam B3-4-60 compared with the transfer length (533 mm) in beam B2-4-55 despite the higher prestress level in beam B3-4-60. Finally, it was concluded that confinement, represented by the number of stirrups, played a significant role in the bond behavior between the concrete and CFRP bars [45]. Mahmoud and colleagues [31,32] calculated that for the Ø12.5 mm CFCC strands, the addition of shear reinforcement reduced the average transfer length by 21%. For the Ø8 mm CFRP Leadline bar, the addition of shear reinforcement reduced the transfer length by 6%.
Nanni et al. [57] investigated the influence of different levels of concrete confinement on the splitting of concrete during the release of smooth braided AFRP bars. It was calculated that cracking of the anchorage zone can be avoided by using a small-pitch (25 mm) CFRP coil (length 225 mm) that confines the concrete immediately surrounding the AFRP bar or partially blanketing the AFRP bar, intermittently applying the tape for lengths of one and two tendon diameters (16 and 32 mm) at a spacing of one tendon diameter over total lengths of 240 and 272 mm, respectively. However, shear reinforcement (Ø6 mm) (distance between stirrups 20 mm and 25 mm) does not prevent cracking. The transfer lengths of the specimens with shear reinforcement, CFRP coil, and partial blanketing were 625, 600, and 700 mm, respectively. Partial blanketing was determined to be very effective due to the reduction in tensile stress field despite an increase in transfer length of up to 17%.
Despite the low difference between prestress level and concrete compressive strength, it can be stated that specimens with shear reinforcement can induce a reduction in the transfer length of CFCC strands and the CFRP Leadline bar [31,32] (Table 5). Additionally, it was concluded in [31,32] that the absence of shear reinforcement in specimens pretensioned with CFRP Leadline and CFCC strand increases the transfer length with an averages of 10% and 17%, respectively, more than the values predicted by the proposed theoretical models.

2.6. Effect of Reinforcement Surface Conditions

The bond properties between the reinforcement and concrete are influenced by different surface roughnesses of the reinforcement. Furthermore, reinforcement surface conditions can enhance the anchorage zone behavior of pretensioned reinforcement. Table 6 provides a summary of average transfer length results that shows the influence of reinforcement surface conditions.
Ehsani et al. [47] investigated three different types of AFRP bars. The lowest transfer length (327 mm) was calculated for the AFRP Technora bar with a rough (ribbed) surface. For the AFRP Fibra bar with a smooth braided surface, the transfer length was longer (339 mm), and the transfer length of the AFRP Arapree bar with a smooth (plain) surface was the longest (385 mm). Despite the differences in reinforcement diameter (Ø7.4–10.4 mm), it can be concluded that with increasing surface roughness of AFRP reinforcement, the transfer length decreases.
Additionally, in [35,48], three different types of surface finishing (sanded, “expancel” and expancel sanded) for a Ø5.3 mm AFRP Arapree bar were investigated. The expancel coating was applied as a thin compressible layer around the bar to absorb part of the radial expansion of the bar due to thermal expansion and the Hoyer effect [35,48]. The test results revealed that the transfer length of the AFRP bars with the expancel coating (smooth surface) was greater by about 60–80% compared with the transfer length of the AFRP bars with the sanded and expancel-sanded surfaces. Additionally, the reduction of the consequences of the Hoyer effect by applying an expancel coating to the AFRP bar reduces the c/Ø up to approximately 2.33·Ø [35,48]. This indicates that the sand coating of the AFRP bars can significantly decrease the transfer length. However, it can increase the risk of concrete splitting during reinforcement release; additional concrete confinement can reduce the risk of splitting concrete.
Nanni and colleagues [24,38] calculated that the transfer length (225 mm) of sand-coated AFRP bars (Ø12 mm) was more than half the transfer length (450 mm) of smooth braided AFRP bars (Ø12 mm) when the prestress level was 48%. Although the concrete strength of sand-coated AFRP bars (39 MPa) was higher compared with the braided AFRP bars (34 MPa), the silica sand on the AFRP bars with respect to that of smooth bar increased the bond characteristics and significantly reduced the transfer length of the AFRP bar.
The test results revealed that the ribbed surface of the GFRP bar [36,37] and the sand-coated surface of the AFRP bar [24,38] give similar transfer length results (221 mm and 225 mm, respectively) despite different material properties (modulus of elasticity of 60 GPa and 68 GPa, concrete strength of 31 MPa and 39 MPa, and prestress level of 36% and 48%, respectively).
The test results of Khin et al. [50] showed that CFRP reinforcement with increased surface roughness (spirally indented, sanded, and cross-wounded) had a shorter transfer length (300 mm) than CFRP reinforcement with a helical plain surface (400 mm). Additionally, AFRP and GFRP spirally indented bars had similar moduli of elasticity (54 GPa and 47 GPa respectively) and the same transfer length (500 mm).

2.7. Effect of Modulus of Elasticity of Reinforcement

The difference in the bond characteristics in the anchorage zone of reinforcement can be attributed to the different moduli of elasticity of different FRP reinforcements. A lower modulus of elasticity causes more longitudinal deformation during prestressing and consequently more transverse deformation due to the Poisson ratio during the release of reinforcement for the same prestress level. Higher transverse deformations of FRP reinforcement with a lower modulus of elasticity improve bond strength at the transfer zone due to the lateral expansion of the bar, creating a wedge action known as the Hoyer effect. Table 7 provides a summary of the average transfer length results showing the influence of modulus of elasticity of reinforcement.
According to [51,52], the bond characteristic of the GFRP reinforcement is superior to that of steel. This can be attributed to the lower modulus of elasticity of the GFRP reinforcement. It could also be due to the better adhesion and interlock between the GFRP reinforcement and the concrete. Thus, for the same force, the transfer length for the GFRP reinforcement is smaller. Additionally, Zawam and Soudki [36] stated that the lower modulus of elasticity of the GFRP bar will induce more radial expansion compared with CFRP, resulting in an increase in the confining stresses normal to the tendon during the prestress transfer process. This characteristic improved the bond strength at the interface between the bar and the surrounding concrete upon release, resulting in a shorter transfer length compared with CFRP bars [36].
Zou [33] calculated that the transfer length of CFRP Leadline bars (Ø8 mm) was 2–3.8 times higher compared with the transfer length of the AFRP Arapree sanded bar (Ø7.8 mm). The large difference in transfer length can be attributed to the significantly lower modulus of elasticity of the AFRP bar (54 GPa) compared with the CFRP Leadline bar (172 GPa). Additionally, the sanded surface of the AFRP bar can enhance bonding conditions, in contrast with the spirally indented CFRP Leadline bar.
Ehsani et al. [47] calculated that the transfer length of the CFCC (helical plain surface) and CFRP Leadline (spirally indented surface) reinforcement was similar (432 mm). However, the transfer length of the AFRP Technora bar (rough surface) was shorter (327 mm) and may be related to the higher surface roughness and lower modulus of elasticity (69 GPa) of the AFRP bar compared to the CFCC strand and CFRP bar.
Lu et al. [53,54] calculated that the transfer length of the AFRP Technora bar (rough surface) was 13% shorter compared with the CFRP Leadline bar (spirally indented surface). It can be related to a higher surface roughness and a lower modulus of elasticity (45 GPa) of the AFRP bar compared to the CFRP Leadline bar (171 GPa).
Since the modulus of elasticity of FRPs is generally less than that of steel, the transfer length of most FRPs is less than that of steel [11].

2.8. Dead End versus Live End for Transfer Length Results

Different transfer lengths may appear at two ends of the pretensioned concrete member. This can be attributed to more than one specimen prestressed with the same reinforcement. In this case, one end of the reinforcement is prestressed (Live end), while the other at the same time is fixed to the rigid support (Dead end). During the release of prestressed reinforcement, differences can appear in the transfer lengths of different FRP reinforcements.
In [58], the measured transfer lengths at the live and dead ends of the box beams were in close agreement with the sudden release of the CFCC strands and CFRP Leadline bars. The same trend was identified for the gradual release of CFRP Leadline bars [45], AFRP bars [24], and GFRP ribbed bars [36,37].
The experimental results provided in [59,60,61] showed that the transfer lengths of the CFCC strands at the live ends are higher than the transfer lengths at the dead ends for the sudden release. As explained by [62], this could be influenced by factors such as concrete casting location, cutting location, and the use of multiple batches of concrete. However, the average dead end to live end ratios of transfer lengths ranged from 0.74 for pile 3 to 0.86 for piles 4 and 5. This shows that the casting location had minimal to no effect on the transfer length. Additionally, Krem [43] calculated that the transfer length at the live end was slightly greater than at the dead end for the same beam. The increase in transfer length at the live end could be a result of the dynamic impact of the sudden release of the CFRP bar.
The results of Crossett et al. [55] showed that the transfer length of the BFRP bars is 16–48% higher at the live end than at the dead end. Additionally, it was explained that the release of stress is more gradual at the dead (anchoraged) end, and therefore, shorter transfer lengths were calculated [53].

2.9. Long-Term Effect

The transfer of the prestressing force to the concrete during the release of reinforcement is a short-term effect. However, the prestressed concrete member is intended for long-term operation. After the release of the prestressed reinforcement, the concrete members are affected by many long-term effects (shrinkage and creep of the concrete, relaxation of the reinforcement, etc.) that can influence the anchorage zone and transfer length of the prestressed concrete member.
Zou [33] stated that the transfer length of AFRP Arapree sanded bars is not affected by time (up to 238 days), although the average concrete strain beyond the transfer length increases significantly. Nanni et al. [24] have also drawn the same conclusion for smooth braided AFRP bars for up to three weeks.
According to Zou [33], there is no apparent deterioration of the bond between the CFRP Leadline bar and the concrete with time, and the measured transfer length did not change with time for normal and high strength concrete beams. Furthermore, the application of two-point loads in the midspan did not affect the transfer length up to 390 days.
Grace [39] showed that the increase in the transfer length of CFRP Leadline bar after 300 days and the CFCC strands after 391 days is only about 7.8% and 7%, respectively, and there is no significant effect of time on the transfer length. Approximately the same result (6%) is for steel strands [63].
Soudki et al. [46] calculated that 200 days after CFRP Leadline bar (prestress level of 50%) release for the T-beam specimen, no significant change in the measured transfer length was observed.
Lu et al. [54] also determined that there are little changes in transfer length with time for CFRP Leadline and CFRP (both spirally indented) and bars after 28 days and for AFRP Teachnora (rough) bars after 90 days.
Mahmoud et al. [31,32] determined that the helical shape of the CFCC and steel strands enhanced the mechanical component of the bond and did not result in an increase in the transfer length over time. The 22% increase in the transfer length of CFRP Leadline bar over time could be due to its relatively smooth surface compared to CFCC and steel strands.
In [51,52], it was calculated that the transfer length increased by 40% and 20% with time (after 600 days) for the GFRP and steel strands, respectively. However, the rate of increase was almost double for GFRP reinforcement compared with steel.
According to [55], the transfer length of the BFRP bars increased after 5 days of reinforcement release by 4–39%.
It is suggested that at the ends of the member, the concrete strain increased with an increase in time, mainly due to the shrinkage of the concrete [46]. Away from the ends, the increase in strain includes the combined effects of creep, shrinkage, and the relaxation of the prestressing reinforcement [24,33,46].

3. Theoretical Models

Table 8 presents a summary of the recommended expressions for the transfer length of the FRP reinforcement (Equation (1)–(3)) and steel strands (Equations (4)–(6)). The nomenclature in this table is presented.
Equation (5) provided in [64] is evaluating the fewest different parameters (fpi and Ø) influencing the transfer length. Additionally, with an empirical coefficient (20.7) which is based on the large database of transfer length results, Equation (5) was developed for steel strands. Mitchell et al. [63] suggested supplementing the ACI-318 [64] equation with the compressive strength at transfer. As concrete strength enhances the bond of reinforcement, it becomes a good additional parameter for increasing the accuracy of the transfer length prediction. Additionally, Equation (6) with the empirical coefficient (20.7) is proposed for the steel strands. Equation (3) proposed by Domenico [30] replaces the reinforcement diameter (Ø) with a cross-sectional area (Ap) of the reinforcement and proposes an empirical coefficient CT = 80 for the CFCC strand. Additionally, it calculates f c i 1 / 2 as also in Equations (2) and (6). However, Zou [33] stated that the influence of prestress on the transfer length of CFRP reinforcement is significantly lower than the concrete strength at transfer. Therefore, it can be neglected, and the transfer length can be calculated according to Equation (2) with an empirical coefficient κ = 480 (in N·mm units) for the prestressed CFRP Leadline bar. According to [58,65], the theoretical results of the transfer length of the CFRP bar predicted by Equations (1) and (5) were up to 10% and 6% higher compared with the experimental ones, respectively. For CFCC strands [58,66], the theoretical values predicted by Equations (1) and (5) were up to 15% higher and up to 12% lower compared with the experimental results, respectively. Furthermore, Equation (2) provided the least inaccurate prediction and the theoretical values of the transfer length of the CFRP and CFCC reinforcement were up to 2.8 and 2.9 times higher than the experimental ones, respectively. Therefore, these results contradict the concluding remarks of Zou [33], who states that for all practical purposes, the effect of prestress on the transfer length of the tendons can be neglected. Based on the measured data in [31,32], the transfer length of CFRP reinforcement is proportional to the reinforcement diameter, the initial prestress level, and the concrete compressive strength at transfer, and Equation (1) was proposed for the transfer length of CFRP reinforcement. Equation (1) was adopted in design codes [10,12]. The main difference from other theoretical models is that Equation (1) proposes an empirical coefficient αt dependent on the type of FRP reinforcement. Therefore, the coefficient αt can be calibrated for different types of FRP reinforcement (GFRP, CFCC, CFRP, AFRP, BFRP) with different surface conditions. Additionally, it presents the concrete strength as f c i 2 / 3 instead of f c i 1 / 2 (Equations (2), (3) and (6)). The presentation of concrete strength as f c i 2 / 3 can be explained by the correlation of concrete compressive strength with concrete tensile strength f c t m = 0.3 · f c i 2 / 3 provided in [67,68,69]. Additionally, Marti-Vargas et al. [70] proposed Equation (4) for prestressed seven-wire steel strands, which is similar to Equation (1). The only differences are in the empirical coefficient (2.5) and that the reinforcement diameter (Ø) is replaced with an area of cross-section of reinforcement (Ap).
Table 8 presents a summary of the recommended expressions for the transfer length of the FRP reinforcement (Equation (1)–(3)) and steel strands (Equations (4)–(6)). Up until now, Equation (1) is still the main equation to calculate the transfer length of CFRP and CFCC reinforcements. There are different types of FRP reinforcement (CFRP, CFCC, GFRP, AFRP, BFRP) with different surface conditions and material properties. Therefore, other researchers proposed values of the empirical coefficient αt for different types of FRP reinforcement (Table 9). The values proposed by [31,32] and adopted in [10,12] are αt = 1.9 and αt = 4.8 for CFRP Leadline bars and CFCC strands respectively. The authors of [39] proposed αt = 1.95 and αt = 2.12 for CFRP Leadline bars and CFCC strands, respectively. In [36,37], αt = 2.6 was proposed for GFRP ribbed bars. Additionally, [43,44] investigated specimens made of self-compacting concrete (SCC) and prestressed with CFRP bars and proposed αt = 2.84 − fpi/800.

4. Results

4.1. Database of Transfer Length Results

A literature review of the experimental results of the transfer lengths of different types of pretensioned FRP reinforcement was performed. In total, 318 specimens were found. Table 10 provides a summary of the initial parameters of the database (Table A1, Table A2, Table A3, Table A4 and Table A5 in Appendix A) of the transfer length of FRP reinforcement. Specifically, 26 of 26, 62 of 99, 73 of 99, 70 of 88, and 6 of 6 specimens prestressed with GFRP (Table A1), CFCC (Table A2), CFRP (Table A3), AFRP (Table A4), and BFRP (Table A5) reinforcement were found with the transfer length results, respectively. Table A1, Table A2, Table A3, Table A4 and Table A5 present the original specimen number from the experimental research, type of FRP reinforcement, surface conditions of FRP reinforcement, specimen type and dimensions (b × h × l—width and height of the cross-section and length of the specimen), release type of prestressed reinforcement, information about the existence of shear reinforcement in the cross-section of the specimen, protective concrete cover (c), reinforcement diameter (Ø), cross-sectional area of one prestressed bar (Ap), modulus of elasticity (Ep), tensile strength (fpu), initial stresses (fpi) of reinforcement, the ratio between initial stresses and tensile strength of reinforcement (fpi/fpu), concrete compressive strength at transfer (fci), average transfer length (Lt) of pretensioned reinforcement.

4.2. Analysis of Experimental Results

The experimental results for the transfer length sof different types of FRP reinforcement (GFRP, CFCC, CFRP, AFRP, and BFRP) found in the literature are analyzed in this chapter. Figure 1 shows the distribution of the experimental transfer lengths (Lt) of different types of pretensioned FRP reinforcement under the influence of different experimental parameters: concrete compressive strength at transfer (fci), the ratio between initial stress in pretensioned reinforcement, and tensile strength (fpi/fpu), reinforcement diameter (Ø), concrete protective cover (c), the ratio between the concrete cover and reinforcement diameter (c/Ø) and modulus of elasticity of FRP reinforcement (Ep). The ranges of influential parameters (fci, fpi/fpu, Ø, c, c/Ø and Ep) presented in Figure 1 are presented in Table 10.
The results show that the transfer lengths of different types of pretensioned FRP reinforcement decrease with increasing concrete compressive strength at the time of pretensioned reinforcement release (Figure 1a). In general, the increased compressive strength of concrete enhances the bond between the reinforcement and the concrete. Therefore, it provides better anchorage properties for the pretensioned reinforcement. Research by other authors confirms the trend that the transfer length decreases with the increase of concrete strength. However, according to the results of Zou [25] and Zawam with colleagues [26,27], the rate of decrease in transfer length is lower for the AFRP and GFRP bars. Therefore, the concrete strength is more significant for CFCC and CFRP reinforcement.
The transfer length of different types of pretensioned FRP reinforcement tends to increase with an increase in the fpi/fpu ratio (Figure 1b). The higher prestress level transfers a higher prestress force to the concrete, which induces greater damage to the bond between the reinforcement and the concrete. Therefore, the transfer length is usually higher for a higher level of prestress. Some results in the literature can be found that show little influence of prestress level on the transfer length. It can be attributed to CFCC [29,30,39] and CFRP [31,32,39,45,46] reinforcement (Table 3). On the other hand, in [31,32] it is stated that the prestress level may have a greater effect on the transfer length of CFCC strands compared with the concrete strength. Despite some discrepancies between the results of the transfer length of CFCC and the CFRP reinforcement of different authors, the main trend of increasing the transfer length with an increase in prestress level remains for different types of FRP reinforcement (GFRP, CFCC, CFRP, AFRP) (Figure 1b).
The transfer lengths of different types of pretensioned FRP reinforcement (CFCC, CFRP, and AFRP) increase with increasing diameter of reinforcement (Figure 1c). For the larger reinforcement diameter, the prestress force will be higher than for the lower reinforcement diameter for the same prestress level. Therefore, higher prestress force transferred to the concrete will cause more damage to the surface between the reinforcement and the concrete. Additionally, this damage will be distributed in a larger contact area with a larger reinforcement diameter. Therefore, the damage to the bond of a larger reinforcement diameter will be larger and will cause a longer transfer length. However, the results of GFRP reinforcement are the opposite (Figure 1c). Therefore, it is evident that reinforcement diameter alone cannot be assessed as the main factor influencing the transfer length.
The transfer lengths of different types of pretensioned FRP reinforcement (CFCC, CFRP, and AFRP) increase with an increase in concrete protective cover (Figure 1d). The release of pretensioned reinforcement induces splitting tensile stresses in concrete due to the Hoyer (wedge) effect, which is the result of the swelling of the reinforcement at transfer. Therefore, the concrete protective cover plays an important role in restricting the splitting of concrete and maintaining sufficient reinforcement bond conditions at transfer. Additional confinement may be introduced in the form of shear stirrups or spiral reinforcement to take over splitting tensile stresses. As in the case of reinforcement diameter (Figure 1c), the transfer length of the GFRP reinforcement decreases with increasing concrete cover (Figure 1d). Therefore, it shows that the transfer length should be compared by evaluating the combination of several influencing factors. Additionally, the concrete cover is more important in the case of durability and splitting of the concrete anchorage zone at transfer.
As in the case of reinforcement diameter (Figure 1c) and concrete cover (Figure 1d), the transfer lengths of different types of pretensioned FRP reinforcement increase with increasing ratio c/Ø (Figure 1e). It should be noted that the increase in the ratio c/Ø with an increase in transfer length is significantly reduced compared to the results presented in Figure 1c,d. Therefore, the evaluation of these two parameters (c and Ø) provides a more uniform distribution of the relationship between the transfer length and c/Ø. Additionally, Taerwe and Pallemans [35] determined that for sand-coated AFRP bars the transfer length decreased with an increase of c/Ø up to approximately 3.5. The further increase in concrete cover did not have a significant influence on the transfer length of the AFRP bars. Therefore, it shows the importance of choosing the appropriate value of the concrete cover (c) for a certain reinforcement diameter (Ø). Additionally, it is again proven that the transfer length should be evaluated in a combination of several influencing factors. The ratio c/Ø is important to ensure the crack-free introduction of the prestressing force into the concrete, while the absolute concrete protective cover is important for the durability of the member.
A comparison of the transfer length and modulus of elasticity of different types of FRP reinforcement shows that in most cases, the transfer length of FRP reinforcement (GFRP, CFCC, and CFRP) increases with increasing modulus of elasticity (Figure 1f). In [36,51,52], it was stated that a lower modulus of elasticity will cause a greater swelling of the reinforcement, resulting in an increase in the confining stresses at transfer. It improves the bond strength of the reinforcement, resulting in a shorter transfer length [36]. The results of [33,47,53,54] showed that the transfer length of AFRP bars was lower than that of the CFRP Leadline bar due to the lower modulus of elasticity of the AFRP reinforcement. However, Figure 1f shows that the transfer length of AFRP bars is slightly decreasing with increasing modulus of elasticity. This may be related to the higher range of modulus of elasticity of AFRP reinforcement (Table 10) and the additional variation of other parameters (nonidentical).
The transfer length of the BFRP bar also decreases with an increase in concrete strength (Figure 1a). However, the trends of other parameters (fpi/fpu, Ø, c, c/Ø, and Ep) with respect to the transfer length are opposite compared to GFRP, CFCC, CFRP, and AFRP reinforcements. The results of only six specimens pretensioned with BFRP reinforcement are presented in the database of transfer length (Table A5). The number of specimens and the variation of the parameters are too small. Therefore, it is difficult to distinguish a clear influence of different parameters on the transfer length of BFRP bars. Therefore, broader experimental research needs to be performed for a better understanding the behavior of anchorage zone of prestressed BFRP bar.
The prestress force can be transferred to the concrete in two ways: gradually or suddenly. Therefore, the influence of the type of release of CFCC reinforcement (sudden or gradual) on the transfer length and parameters (fci, fpi/fpu, Ø, c, c/Ø and Ep) influencing the transfer length is presented in Figure 2. It can be seen that there is a clear difference between the results, and in most cases, a sudden release gives higher transfer length results compared to a gradual release of CFCC strands. The same tendency is observed with pretensioned steel strands. The influence of reinforcement release type on the transfer length of CFCC strand can be affected by the the similar shape of the the CFCC and steel strand (seven helically wounded wires).

4.3. Derivation of the Coefficient αt

Previous analysis of the results (Figure 1 and Figure 2) showed that the influence of separate factors on the transfer length of prestressed FRP reinforcement does not always provide a qualitative comparison. Equation (1) provided in Table 8 is proposed for prestressed FRP reinforcement and takes into account initial prestress (fpi), reinforcement diameter (Ø), and concrete compressive strength at transfer (fci). Therefore, for a better analysis of the results based on Equation (1), a graphical comparison of the transfer length of different FRP reinforcements (GFRP, CFCC, CFRP, and AFRP) and f p i · Ø / f c i 2 / 3 is presented in Figure 3, Figure 4, Figure 5 and Figure 6. Additionally, these graphs represent a distribution of the results with the proposed average values for the coefficient αt.
It was calculated that for the database of GFRP reinforcement, the average coefficient αt is 2.58 with the standard deviation (STD) of 0.33 and the coefficient of variation (COV) of 12.8% (Table 8) (for the concrete strength 29–71 MPa, the level of prestressing 26–47% and the diameter of the reinforcement 9.5–16 mm). The graphical representation is presented in Figure 3a with a very strong correlation coefficient R2 = 0.98. Almost all GFRP bars had ribbed surfaces, and the influence of the reinforcement surface conditions could not be determined. Additionally, Figure 3b shows that the influence of shear reinforcement and the type of prestressed reinforcement release (sudden or gradual) has an almost negligible effect on the transfer length of the GFRP reinforcement. However, it should be mentioned that the database of transfer length results of GFRP reinforcement is quite small (Table A1) compared with other FRP types (Table A2, Table A3 and Table A4): only five specimens reinforced with shear reinforcement and prestressed with GFRP reinforcement affected by a sudden transfer of prestressing were found in the literature. Therefore, more research is needed to investigate the effect of shear reinforcement and the type of release of prestressed GFRP reinforcement on the transfer length.
The type of CFCC strand release has already been shown to affect the transfer length even when the influence of separate factors was analyzed (Figure 2). Furthermore, the effect is more obvious when comparing the transfer length with f p i · Ø / f c i 2 / 3 (Figure 4a). Figure 4a represents the distribution of the results corresponding to an average αt = 4.99 with STD = 0.62, COV = 12.5%, and R2 = 0.99 for the gradual transfer of prestress (for concrete strength of 22–56 MPa, level of prestress 31–81% and diameter of reinforcement 8.3–15.2 mm) and αt = 2.42 with STD = 0.67, COV = 27.7%, and R2 = 0.94 for sudden transfer of prestress (Table 11) (for concrete strength of 37–48 MPa, level of prestressing 30–65% and diameter of reinforcement 12.5–15.2 mm). Additionally, the higher variation of the results (27.7% and 12.5% for sudden and gradual release, respectively) of the sudden type of reinforcement release shows that this type of release is more dangerous and can cause more damage to the anchorage zone of prestressed CFCC strands and, therefore, increase the transfer length. According to Figure 4b, there is no clear influence of shear reinforcement on the transfer length of the CFCC strand. All CFCC seven-wire strands in the collected database have helical plain or almost plain surfaces, and therefore, their effect on the transfer length could not be determined.
Figure 5a presents the transfer length distribution of CFRP bars with respect to f p i · Ø / f c i 2 / 3 with an average αt = 1.92 with STD = 0.48, COV = 24.8%, and R2 = 0.94 (Table 11) (for concrete strength of 26–101 Mpa, prestress level 26–86%, and reinforcement diameter 5.3–12.7 mm). According to Figure 5b,c, there is no influence of the type of transfer of prestressing and shear reinforcement on the transfer length of CFRP bars. Most CFRP bars were Leadline bars with a spirally indented surface (Table A3), and a few studies were performed on spirally indented, sanded, and spirally indented and sanded CFRP bars. Khin et al. [50] determined that CFRP reinforcement with spirally indented or sanded surface had up to 25% lower transfer length compared with CFRP reinforcement with a helical plain surface. The trend lines show that the higher the roughness of the CFRP bar surface, the lower the transfer length (Figure 5d). However, the scatter of the bigger database results is too large to qualitatively confirm this trend.
Figure 6a presents the transfer length distribution of AFRP bars with respect to f p i · Ø / f c i 2 / 3 with an average αt = 2.9 with STD = 1.8, COV = 62.1%, and R2 = 0.84 (Table 11) (for concrete strength of 27–81 MPa, prestressing level 23–82% and reinforcement diameter 5.3–16 mm). The variation in the results is very high (62%). Therefore, the additional influence of other variables was investigated on the transfer length of the AFRP bars. According to Figure 6b, shear reinforcement may have some influence on the transfer length of AFRP bars. However, since the transfer length is shown to be higher for specimens with shear reinforcement, it contradicts the results for GFRP (Figure 3b) and CFCC (Figure 4b) reinforcement. Therefore, it was decided that the influence of shear reinforcement will be neglected in determining the coefficient αt. Additionally, Figure 6c shows that two reinforcement surface conditions can be distinguished for the AFRP bars. Therefore, the transfer length is higher for smooth braided AFRP bars compared to sanded and rough FRP bars. The same trend of decrease in transfer length with an increase in reinforcement surface roughness was observed by [24,35,38,47,48]. Additionally, the ribbed surface of the GFRP bar [36,37] and the sand-coated surface of the AFRP bar [24,38] gave similar transfer length results; the increased roughness of reinforcement increases the bond between reinforcement and concrete and therefore the transfer length. Furthermore, reinforcement classification according to surface roughness gives different results of αt = 1.53 with STD = 0.55, COV = 35.8%, and R2 = 0.93 for smooth braided AFRP bars (for concrete strength of 29–39 MPa, prestressing level 23–58%, and reinforcement diameter 8–16 mm) and αt = 3.99 with STD = 1.70, COV = 42.7%, and R2 = 0.86 for sanded and rough AFRP bars (Table 11) (for concrete strength of 27–81 MPa, prestressing level 37–82%, and reinforcement diameter 5.3–13.5 mm). These results show that an additional classification of AFRP bars according to surface conditions reduces the variation of the results from 62% to 36%–43%. However, this level of variation in the results is still high compared with GFRP, CFCC, and CFRP reinforcement. Therefore, the surface condition of AFRP bars should be evaluated in additional comprehensive research.
Figure 7a presents the transfer length distribution of the BFRP bars with respect to f p i · Ø / f c i 2 / 3 with an average αt = 2.1 with STD = 1.7, COV = 79.2%, and R2 = 0.68 (Table 11) (for concrete strength of 27–52.4 MPa, prestressing level 34–48%, and reinforcement diameter 8–12 mm). The low number of results gives high variation in αt. Therefore, it cannot be applied to calculate the transfer length of BFRP bars. Additionally, Figure 7b shows a preliminary comparison of the transfer length and f p i · Ø / f c i 2 / 3 with the influence of release type of reinforcement. The results show that sudden transfer of prestress induces a longer transfer length of the BFRP bar compared to gradual transfer of prestress (Figure 7b). This confirms the results of the CFCC strands influenced by different types of reinforcement release (sudden or gradual) (Figure 4a). Therefore, the influence of the type of BFRP reinforcement release and other important factors (fci, fpi/fpu, c) on the transfer length could be the topic of future research.

4.4. Comparison of Experimental and Theoretical Results

In this section, theoretical models for the calculation of transfer length (Table 8, Section 3) are compared with experimental results from the literature (Table A1, Table A2, Table A3 and Table A4). In particular, models are presented by [10,12,31,32] (Equation (1)), [63] Equation (6), [64] Equation (5), and [30] Equation (3). Equation (2) proposed by Zou [33] is not analyzed due to the lack of correlation with the experimental results found in the literature. Furthermore, Equation (4) is not taken into account because it is proposed for steel strands [70] and is very similar to Equation (1) proposed for FRP reinforcement. The results presented in Figure 8, Figure 9 and Figure 10 show the relationships between the experimental and theoretical results of the transfer length of different FRP reinforcements. In addition, they show the differences between different theoretical models for calculating the transfer length. The theoretical model proposed by [31,32] is presented in Figure 8, Figure 9 and Figure 10 with the αt coefficients proposed in this article (Table 8).
From Figure 8a, it is clear that the theoretical models presented by [30,64] are less accurate than the models presented by [31,32,63]. Furthermore, the [64] model overestimates experimental results on average by 47% (Lt,teor/Lt.exp = 1.47) with STD = 0.32 and COV = 21.7% and [30] underestimates experimental results of the transfer length of prestressed GFRP reinforcement on average by 38% (Lt,teor/Lt.exp = 0.62) with STD = 0.19 and COV = 31.2%. The models of Mitchell [63] and Mahmoud [31,32] (αt = 2.6) show similar results with Lt,teor/Lt.exp = 1.05, STD = 0.13, COV = 12.1% and with Lt,teor/Lt.exp = 1.0 STD = 0.13, COV = 12.6%, respectively. The models presented by [31,32,63] are in the best agreement with the experimental results (difference up to 5%) and the variation of the results is the lowest (COV = 12%). Therefore, it shows the best agreement between theoretical and experimental results.
In the case of CFRP reinforcement (Figure 8b), Equation (3) gives the most inappropriate results with an underestimation of the experimental results by 70% (Lt,teor/Lt.exp = 0.30) with STD = 0.12, COV = 40.2%. Equation (6) also underestimates the experimental results with Lt,teor/Lt.exp = 0.82, STD = 0.28, COV = 34%, but Equation (5) overestimates the results with Lt,teor/Lt.exp = 1.17, STD = 0.55, COV = 47.2%. Despite the relatively high variation of the results the most accurate prediction of experimental results was received by Equation (1) (αt = 1.9) with Lt,teor/Lt.exp = 1.01, STD = 0.33, COV = 32.5%.
Figure 9 distinguishes the comparison of experimental and theoretical results of the transfer length of CFCC strands for the gradual (Figure 9a) and sudden (Figure 9b) types of prestressing release. Equation (5) significantly overestimates the experimental results for gradual transfer of prestress with Lt,teor/Lt.exp = 2.31, STD = 0.81, COV = 35% (Figure 9a). Additionally, Equation (5) gives the same trend of the results for sudden transfer of prestressing with Lt,teor/Lt.exp = 1.41, STD = 0.30, COV = 21.3% (Figure 9b). However, Equation (3) significantly underestimates the experimental results for both gradual (Figure 9a) and sudden (Figure 9b) prestress transfer with Lt,teor/Lt.exp = 0.69, STD = 0.19, COV = 27.2% and Lt,teor/Lt.exp = 0.38, STD = 0.14, COV = 37%, respectively. Despite the low precision (Lt,teor/Lt.exp = 1.84, STD = 0.48, COV = 25.9%) in predicting the transfer length for the gradual transfer of prestress (Figure 9a), Equation (6) presents a very accurate prediction of the experimental results for the sudden transfer of prestress (Figure 9b) with Lt,teor/Lt.exp = 0.99, STD = 0.26, COV = 26%. Additionally, Equation (1) provides a very accurate prediction of the transfer length for gradual (αt = 5.0) (Figure 9a) and sudden (αt = 2.4) (Figure 9b) types of release with Lt,teor/Lt.exp = 1.0, STD = 0.12, COV = 12.5% and Lt,teor/Lt.exp = 1.02, STD = 0.27, COV = 26.6%, respectively. The higher variation in the results for sudden prestress transfer shows that it has more damage to the bond of reinforcement and results in a longer transfer length. Part of the results of Equation (6) coincide with the results of Equation (1) for sudden transfer of prestress. It shows that the combination of empirical coefficient (20.7) and f c i 1 / 2 in Equation (6) is similar to the combination of coefficient αt = 2.4 and f c i 2 / 3 in Equation (1) in case of sudden transfer of prestress. However, Equation (1) provides more consistent results for both gradual and sudden transfer of prestress.
Figure 10 presents the comparison of the experimental and theoretical results of the transfer length of AFRP reinforcement with smooth braided (Figure 10a) and sanded and rough (Figure 10b) surfaces. Theoretical results calculated according to Equations (3), (5), and (6) give lower transfer lengths of AFRP reinforcement with a smooth braided surface compared to the experimental results with Lt,teor/Lt.exp = 0.3, STD = 0.15, COV = 51.8%; Lt,teor/Lt.exp = 0.8, STD = 0.23, COV = 30.1%; and Lt,teor/Lt.exp = 0.6, STD = 0.21, COV = 34.3%, respectively (Figure 10a). However, the prediction of Equation (1) (with αt = 1.5) is closer to the experimental results with Lt,teor/Lt.exp = 1.02, STD = 0.36, COV = 35.8%, and more values are on the safe side (Figure 10a). The prediction of the transfer length of AFRP reinforcement with sanded and rough surfaces (Figure 10b) was also significantly underestimated according to Equation (3) with Lt,teor/Lt.exp = 0.3, STD = 0.12, COV = 36.6%. However, in this case, Equations (5) and (6) significantly overestimate the transfer length with Lt,teor/Lt.exp = 2.9, STD = 1.4, COV = 48.9% and Lt,teor/Lt.exp = 1.8, STD = 0.77, COV = 42.3%, respectively. A similar trend can be observed for all results from the database (without grouping according to surface conditions) (Figure 10c) calculated according to Equations (3), (5) and (6) with Lt,teor/Lt.exp = 0.3, STD = 0.14, COV = 42.6%; Lt,teor/Lt.exp = 1.8, STD = 1.41, COV = 78.6%; and Lt,teor/Lt.exp = 1.2, STD = 0.79, COV = 66%, respectively. The most accurate prediction of the results was obtained according to Equation (1) for AFRP reinforcement with sanded and rough surfaces (αt = 4.0) (Figure 10b) and all types of AFRP reinforcement (αt = 2.9) (Figure 10c) with Lt,teor/Lt.exp = 1.0, STD = 0.43, COV = 42.7% and Lt,teor/Lt.exp = 1.0, STD = 0.62, COV = 62.1%, respectively. However, the variation in the results is still very high for AFRP reinforcement.
Different values of coefficient αt (used in Equation (1)) were proposed by other authors (Table 9) and calculated in this article (see Section 4.3 and Table 11). The results in this article confirm the αt = 2.6 proposed by [36,37] for calculating the transfer length of the GFRP bars. Additionally, the αt = 1.92 calculated in this article is in close agreement with the proposals of other authors [10,12,31,32] αt = 1.90 and [39] αt = 1.95 for CFRP bars. The proposed αt = 5.0 for gradually released CFRP bars is slightly higher than αt = 4.8 [10,12,31,32] and significantly higher than αt = 2.12 [36,37]. The suggested αt = 2.4 is new, as there is no proposal of this coefficient for the sudden release of pretensioned CFCC reinforcement in the literature. This value is between the αt = 4.8 [10,12,31,32] and αt = 2.12 [36,37] suggested in the literature for the gradual release of pretensioned CFCC reinforcement. Furthermore, the literature review does not provide any proposal of αt for the AFRP reinforcement. Therefore, three possible values of αt were proposed in this article: αt = 2.9 for all different types of AFRP reinforcement, αt = 1.5 for smooth braided AFRP bars, and αt = 4.0 for sanded and rough AFRP bars. However, the high variation in the transfer length results of AFRP reinforcement suggests additional research and analysis for better understanding its behavior.
The comparison of the ratio between theoretical and experimental results of the transfer length (Lt.teor/Lt.exp) of different types of FRP reinforcement for different values of αt is presented in Figure 11. Table 12 presents an additional statistical analysis.
The results for the GFRP bars with αt = 2.6 (Table 12 and Figure 11a) show a low COV = 12.6% and a high inbound value (between the upper and lower bounds) of 80%. Therefore, the proposed coefficient is suitable for GFRP bars.
The αt = 2.12 proposed by [39] for the gradual release of CFCC strands is not suitable due to a very high overestimation of the experimental transfer length with a mean Lt.teor/Lt.exp = 2.35, and all 41 specimens are on the safe side (Table 12 and Figure 11b). Furthermore, more CFCC strands with αt = 4.8 are on the safe side compared with αt = 5.0 (Table 12), and considering that all other statistical parameters are almost identical, αt = 4.8 may be a more appropriate choice for gradual transfer. For sudden CFCC strand release, the proposed αt = 2.4 gives better agreement with the experimental results for transfer length with theoretical values higher by 1% compared with results higher by 14% with αt = 2.12 (Table 12). Additionally, the linear trend line presented in Figure 11c shows that the theoretical results with αt = 2.4 are in closer agreement with the experimental transfer length.
The results for the relationship between the theoretical and experimental transfer lengths are almost identical for CFRP bars, with αt ranging from 1.90 to 1.95 (Table 12 and Figure 11d). For αt = 1.95, the theoretical results on average are 2% lower than the experimental ones. Therefore, it is better to use αt = 1.9 for determining the transfer length of the CFRP bars.
The proposed αt = 2.9 for the AFRP bars provides 65% inbound values (Table 12 and Figure 11e). However, the 62% variation in the results is too large. Additionally, a separate αt = 1.5 for FRP bars with the smooth braided surface was proposed and provided a lower variation of the results (35%) and a similar inbound 61%. The αt = 4.0 proposed for the FRP reinforcement with sanded and rough surface shows a higher variation in the theoretical results (42%) compared with the results of the smooth braided AFRP bars (35%), but less than the results for all AFRP reinforcement with αt = 2.9. As the results of the sanded and rough AFRP bars provide about 49% inbound values, the amount of overestimated (OV = 20) and underestimated (UV = 19) values is similar.

5. Conclusions

A large database of the transfer lengths of different FRP reinforcements was collected, and the analysis of experimental results, description of theoretical models, and comparison of experimental and theoretical results led to the following conclusions and proposals:
  • The analysis of the literature showed that the concrete compressive strength has a greater influence on the transfer lengths of CFRP and CFCC reinforcement, and the prestress level has a greater effect on the transfer lengths of AFRP and GFRP reinforcement. Additionally, most transfer lengths of FRP reinforcements (GFRP, CFCC, CFRP, and AFRP) are directly proportional to prestress level, reinforcement diameter, and modulus of elasticity of reinforcement and inversely proportional to concrete strength.
  • The minimum concrete cover to avoid concrete splitting in the anchorage zone of the FRP reinforcement is 1.9·Ø for the CFRP bar and 2.8·Ø for the AFRP and GFRP bars. Additional research is needed for the CFCC strand, but the sufficient concrete cover for the CFCC strand is 4·Ø. Therefore, the concrete cover of 3.5·Ø and above does not have a significant influence on the transfer length of FRP reinforcement.
  • Equation (1) was determined to give the most accurate prediction of the transfer length by applying different values of coefficient αt for different types of FRP reinforcement. The results of this article confirmed that the coefficients αt = 2.6, αt = 1.9, and αt = 4.8 proposed by other authors are suitable for predicting the transfer length of the GFRP bars, CFRP bars, and CFCC strands (only gradual type of release), respectively.
  • The analysis of the database revealed that the transfer length of CFCC strands is highly dependent on the type of prestress transfer. Therefore, a new coefficient αt = 2.4 was proposed to determine the transfer length of the suddenly released CFCC strand based on a collected database of the transfer length results. The proposed value is valid for a concrete strength of 37–48 MPa, prestress level 30–65%, and reinforcement diameter of 12.5–15.2 mm.
  • It was determined that there is a correlation between the surface conditions and the transfer length of AFRP bars. Despite the relatively high variation in the results, in this article, new values are proposed: αt = 1.5 for smooth braided AFRP bars (for concrete strength 29–39 MPa, prestress level 23–58%, and reinforcement diameter 8–16 mm) and αt = 4.0 for sanded and rough AFRP bars (for concrete strength of 27–81 MPa, prestress level 37–82%, and reinforcement diameter 5.3–13.5 mm).
  • The analysis of the transfer length and the new values proposed for the coefficient αt provides possibilities for adapting it to design codes for engineering applications and performing additional research that fills the missing gaps in the field. In particular, additional research is needed on the effects of shear reinforcement, release type of the prestressed GFRP and AFRP reinforcements, and the surface conditions of the AFRP and CFRP bars. Furthermore, the influence of prestressing transfer method and other important parameters (fci, fpi/fpu, Ø, c) on the transfer length of the BFRP reinforcement could be a subject of future research.

Author Contributions

Conceptualization, A.J. and J.V.; methodology, A.J.; validation, A.J. and J.V.; formal analysis, A.J. and J.V.; data curation, A.J.; writing—original draft preparation, A.J.; writing—review and editing, A.J. and J.V.; visualization, A.J.; supervision, J.V.; project administration, A.J. and J.V. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the European Social Fund (project No 09.3.3-LMT-K-712-23-0161) under a grant agreement with the Research Council of Lithuania (LMTLT).

Institutional Review Board Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Appendix A

Table A1. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned GFRP reinforcement.
Table A1. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned GFRP reinforcement.
ReferenceSpecimen No.FRP TypeFRP SurfaceSpecimen TypeRelease TypeShear ReinforcementSpecimen Dimensions
(b × h × l, mm)
c, mmØ, mmAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPaLt, mm
[36,37]N40-16-1GFRP
Bar
RibbedBeamGradualYes150 × 255 × 360055.016.0201.06012004900.4131.0287.5
N40-16-2BeamGradualYes150 × 255 × 360055.016.0201.06012004900.4131.0285.0
N40-16-3BeamGradualYes150 × 255 × 360055.016.0201.06012004900.4131.0270.0
N40-16-4BeamGradualYes150 × 255 × 360055.016.0201.06012004900.4131.0270.0
N40-12-1BeamGradualYes150 × 255 × 360055.012.0113.06013504900.3631.0225.0
N40-12-2BeamGradualYes150 × 255 × 360055.012.0113.06013504900.3631.0220.0
N40-12-3BeamGradualYes150 × 255 × 360055.012.0113.06013504900.3631.0210.0
N40-12-4BeamGradualYes150 × 255 × 360055.012.0113.06013504900.3631.0227.5
H40-16-1BeamGradualYes150 × 255 × 360055.016.0201.06012005000.4271.0177.5
H40-16-2BeamGradualYes150 × 255 × 360055.016.0201.06012005000.4271.0200.0
H40-16-3BeamGradualYes150 × 255 × 360055.016.0201.06012005000.4271.0187.5
H40-16-4BeamGradualYes150 × 255 × 360055.016.0201.06012005000.4271.0187.5
H25-16-1BeamGradualYes150 × 255 × 360055.016.0201.06012003130.2629.0215.0
H25-16-2BeamGradualYes150 × 255 × 360055.016.0201.06012003130.2629.0207.5
H25-16-3BeamGradualYes150 × 255 × 360055.016.0201.06012003130.2629.0212.5
H25-16-4BeamGradualYes150 × 255 × 360055.016.0201.06012003130.2629.0210.0
[71]SC-12-1.5GFRP
Bar
SandedBeamGradualYes200 × 235 × 200025.012.0138.05514345360.3746.3300.0
R-12-1.5RibbedBeamGradualYes201 × 235 × 200025.012.0113.05513505200.3947.2300.0
SC-16-1.5SandedBeamGradualYes202 × 235 × 200025.016.0196.06111804520.3846.3200.0
SC-16-3SandedBeamGradualYes203 × 240 × 200045.016.0196.06111804530.3847.8200.0
R-16-1.5RibbedBeamGradualYes204 × 235 × 200025.016.0201.06011004260.3947.2200.0
[51]FG-W4GFRP
7-wire Strand
Helical plainPrismSuddenNo152 × 102 × 259046.39.545.36919418990.4640.1279.4
FG-M4PrismSuddenNo153 × 102 × 259046.39.545.36919418990.4640.1254.0
FG-E4PrismSuddenNo154 × 102 × 259046.39.545.36919418990.4640.1279.4
FG-E5PrismSuddenNo155 × 102 × 259046.39.545.36919419040.4740.1254.0
FG-M7PrismSuddenNo156 × 102 × 259046.39.545.36919418250.4332.6254.0
Table A2. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned CFCC reinforcement.
Table A2. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned CFCC reinforcement.
ReferenceSpecimen NoFRP TypeFRP SurfaceSpecimen TypeRelease TypeShear ReinforcementSpecimen Dimensions
(b × h × l, mm)
c, mmØ, mmAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPaLt, mm
[29,30,58,66]BBC-I-1CFCC
7-wire Strand
Helical
plain
Box beamSuddenYes230 × 970 × 610050.012.777.414218695650.3042.6266.7
BBC-I-2Box beamSuddenYes231 × 970 × 610050.012.777.414218695610.3042.6292.1
BBC-II-1Box beamSuddenYes232 × 970 × 610050.012.777.414218695640.3043.3330.2
BBC-II-2Box beamSuddenYes233 × 970 × 610050.012.777.414218695870.3143.3304.8
BBC-III-1Box beamSuddenYes234 × 970 × 610050.012.777.414218695960.3244.0317.5
BBC-III-2Box beamSuddenYes235 × 970 × 610050.012.777.414218695970.3244.0368.3
[29,30]A type-B6CFCC
7-wire Strand
Helical
plain
T BeamGradualYesT50.012.576.013718709330.5056.3126.5
A type-B7T BeamGradualYesT50.012.576.013718709550.5156.3148.5
A type-B8T BeamGradualYesT50.012.576.013718708950.4841.4149.5
B type-D10T BeamGradualYesT75.012.576.013718709090.4941.4167.5
A type-C9T BeamGradualYesT50.012.576.0137187010240.5550.0147.5
D type-BT7BeamGradualYes100 × 25050.012.576.0137187014030.7530.0400.0
D type-BT8BeamGradualYes100 × 25050.012.576.0137187014030.7530.0375.0
D type-BT9BeamGradualYes100 × 25050.012.576.0137187014030.7530.0350.0
D type-BT10BeamGradualYes100 × 25050.012.576.0137187014030.7530.0350.0
A type-A1T BeamGradualYesT50.015.2113.613717508380.4835.8-
A type-A2T BeamGradualYesT50.015.2113.613717508510.4935.8-
A type-A3T BeamGradualYesT50.015.2113.613717508510.4940.2223.0
B type-D5T BeamGradualYesT75.015.2113.613717508770.5040.2200.5
C type-BT1BeamGradualYes120 × 30060.015.2113.6137175010500.6030.0370.0
C type-BT2BeamGradualYes120 × 30060.015.2113.6137175010500.6030.0370.0
A type-C4T BeamGradualYesT50.015.2113.6137175012120.6945.1232.0
C type-BT3BeamGradualYes120 × 30060.015.2113.6137175013130.7530.0400.0
C type-BT4BeamGradualYes120 × 30060.015.2113.6137175013130.7530.0387.5
C type-BT5BeamGradualYes120 × 30060.015.2113.6137175013130.7530.0412.5
C type-BT6BeamGradualYes120 × 30060.015.2113.6137175013130.7530.0412.5
[31,32]BT11CFCC
7-wire Strand
Helical
plain
A1 BeamGradualYes80 × 250 × 138045.010.555.7140172514000.8129.0305.0
BT12A2 BeamGradualYes80 × 250 × 138145.010.555.7140172514000.8129.0312.5
BT13A1 BeamGradualYes80 × 250 × 138245.010.555.7140172514000.8129.0312.5
BT14A2 BeamGradualYes80 × 250 × 138345.010.555.7140172514000.8129.0312.5
BT7A1 BeamGradualYes100 × 250 × 138050.012.576.0141186814080.7528.0400.0
BT8B BeamGradualYes100 × 250 × 138150.012.576.0141186814080.7528.0375.0
BT9B BeamGradualYes100 × 250 × 138250.012.576.0141186814080.7528.0360.0
BT10B BeamGradualYes100 × 250 × 138350.012.576.0141186814080.7528.0360.0
BT15C1, C2 BeamGradualYes100 × 250 × 275050.012.576.0141186811250.6030.0300.0
BT16C1, C2 BeamGradualYes100 × 250 × 275150.012.576.0141186811250.6030.0295.0
BT19C5 BeamGradualNo175 × 250 × 275050.012.576.0141186813550.7323.0500.0
BT20C5 BeamGradualNo175 × 250 × 275050.012.576.0141186813550.7323.0450.0
BT1A1 BeamGradualYes120 × 300 × 172060.015.2113.6138175010740.6135.0365.0
BT2A1 BeamGradualYes120 × 300 × 172060.015.2113.6138175010740.6135.0355.0
BT3A1 BeamGradualYes120 × 300 × 172060.015.2113.6138175013120.7531.0392.5
BT4B BeamGradualYes120 × 300 × 172160.015.2113.6138175013120.7531.0387.5
BT5A2 BeamGradualYes120 × 300 × 172260.015.2113.6138175013120.7531.0400.0
BT6A3 BeamGradualYes120 × 300 × 172360.015.2113.6138175013120.7531.0400.0
BT17C3, C4 BeamGradualNo200 × 300 × 350060.015.2113.6138175012940.7422.0650.0
BT18C5 BeamGradualNo200 × 300 × 350060.015.2113.6138175012940.7422.0600.0
BT21C5 BeamGradualNo175 × 300 × 350060.015.2113.6138175010830.6224.0510.0
BT22C3, C4 BeamGradualNo175 × 300 × 350060.015.2113.6138175010830.6224.0490.0
[59,60,61]5SCFCC
7-wire Strand
Helical
plain
PileSuddenYes610 × 610 × 1220043.415.2115.0155234815260.6537.0647.7
3NPileSuddenYes610 × 61076.215.2115.6155233615180.6537.0736.6
3SPileSuddenYes611 × 61076.215.2115.6155233615180.6537.0546.1
4NPileSuddenYes612 × 61076.215.2115.6155233615180.6537.0647.7
4SPileSuddenYes613 × 61076.215.2115.6155233615180.6537.0558.8
5NPileSuddenYes614 × 61076.215.2115.6155233615180.6537.0711.2
5SPileSuddenYes615 × 61076.215.2115.6155233615180.6537.0622.3
[47]CT-2CFCC
7-wire Strand
Helical
plain
PrismGradualNo106 × 102 × 300046.98.354.2137222013050.5928.1279.4
CT-1 (J)BeamGradualNo143 × 203 × 600064.58.354.2137222011740.5330.6457.2
CT-1 (D)BeamGradualNo144 × 203 × 600064.58.354.2137222011740.5330.6558.8
2CT-1 (J)BeamGradualNo145 × 203 × 600064.58.354.213722206810.3130.8558.8
2CT-1 (D)BeamGradualNo146 × 203 × 600064.58.354.213722206810.3130.8330.2
[39]CDT2-1-WA-A1CFCC
7-wire Strand
Helical
plain
GirderSuddenYesDouble T38.212.576.013818689250.5048.0501.5
CDT2-1-WA-A2GirderSuddenYesDouble T38.212.576.013818699010.4848.0-
CDT2-1-WA-A3GirderSuddenYesDouble T38.212.576.013818708780.4748.0-
CDT2-1-WA-B1GirderSuddenYesDouble T38.212.576.013818719540.5148.0419.0
CDT2-1-WA-B2GirderSuddenYesDouble T38.212.576.013818729540.5148.0-
CDT2-1-WA-B3GirderSuddenYesDouble T38.212.576.013818739130.4948.0-
CDT2-2-WA-A1GirderSuddenYesDouble T38.212.576.013818749540.5148.0482.5
CDT2-2-WA-A2GirderSuddenYesDouble T38.212.576.013818759590.5148.0-
CDT2-2-WA-A3GirderSuddenYesDouble T38.212.576.013818769420.5048.0-
CDT2-2-WA-B1GirderSuddenYesDouble T38.212.576.013818779130.4948.0468.5
CDT2-2-WA-B2GirderSuddenYesDouble T38.212.576.013818789240.4948.0-
CDT2-2-WA-B3GirderSuddenYesDouble T38.212.576.013818799770.5248.0-
CDT2-3-WA-A1GirderSuddenYesDouble T38.212.576.0138188010180.5448.0520.5
CDT2-3-WA-A2GirderSuddenYesDouble T38.212.576.013818819660.5148.0-
CDT2-3-WA-A3GirderSuddenYesDouble T38.212.576.013818829830.5248.0-
CDT2-3-WA-B1GirderSuddenYesDouble T38.212.576.013818839720.5248.0412.5
CDT2-3-WA-B2GirderSuddenYesDouble T38.212.576.0138188410010.5348.0-
CDT2-3-WA-B3GirderSuddenYesDouble T38.212.576.0138188510360.5548.0-
CDT2-4-WA-A1GirderSuddenYesDouble T38.212.576.013818869830.5248.0443.0
CDT2-4-WA-A2GirderSuddenYesDouble T38.212.576.0138188710950.5848.0-
CDT2-4-WA-A3GirderSuddenYesDouble T38.212.576.013818889950.5348.0-
CDT2-4-WA-B1GirderSuddenYesDouble T38.212.576.0138188910590.5648.0400.0
CDT2-4-WA-B2GirderSuddenYesDouble T38.212.576.0138189010240.5448.0-
CDT2-4-WA-B3GirderSuddenYesDouble T38.212.576.0138189112400.6648.0266.7
Table A3. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned CFRP reinforcement.
Table A3. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned CFRP reinforcement.
ReferenceSpecimen NoFRP TypeFRP SurfaceSpecimen TypeRelease TypeShear ReinforcementSpecimen Dimensions
(b × h × l, mm)
c, mmØ, mmAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPaLt, mm
[53,54]CLCFRP LeadlineSpirally
Indented
Beam-No89 × 178 × 300040.67.947.1171225513650.6140.0421.6
CSCFRP CustomBeam-No89 × 178 × 300040.67.950.3161183411720.6435.5408.9
[58,65]BBD-I_BP-1CFRP-DCITendonSpirally
Indented
Box beamSuddenYes-50.09.570.913119306350.3333.8241.5
BBD-I_BP-2Box beamSuddenYes-50.09.570.913119306350.3333.8279.5
BBD-II_B0-1Box beamSuddenYes-50.09.570.913119306350.3434.8266.5
BBD-II_B0-2Box beamSuddenYes-50.09.570.913119306350.3334.8279.5
BBD-III_BN-1Box beamSuddenYes-50.09.570.913119306350.3335.2304.5
BBD-III_BN-2Box beamSuddenYes-50.09.570.913119306350.3235.2279.0
[72]-CFRP LeadlineSpirally
Indented
Double T BeamSuddenYes-100.010.071.6147226211800.5245.9381.0
[45]B1-4-65CFRP LeadlineSpirally
indented sanded
BeamGradualYes139.7 × 247.7 × 400031.812.7126.5124227513450.5945.4607.1
B2-4-55BeamGradualYes139.7 × 247.7 × 400131.812.7126.5124227511380.5047.9533.4
B3-4-60BeamGradualYes139.7 × 247.7 × 400231.812.7126.5124227512410.5546.8495.3
B4-4-60BeamGradualYes139.7 × 247.7 × 400331.812.7126.5124227512820.5650.7342.9
[31,32]BL1CFRP LeadlineSpirally
Indented
BeamGradualYes80 × 200 × 170035.08.046.1147197011930.6134.0452.5
BL2BeamGradualYes80 × 200 × 170135.08.046.1147197011930.6134.0462.5
BL3BeamGradualYes80 × 200 × 170235.08.046.1147197014100.7235.0480.0
BL4BeamGradualYes80 × 200 × 170335.08.046.1147197014100.7235.0480.0
BL5BeamGradualYes80 × 250 × 250035.08.046.1147197014970.7628.0620.0
BL6BeamGradualYes80 × 250 × 170035.08.046.1147197014970.7628.0625.0
BL7BeamGradualYes80 × 250 × 210035.08.046.1147197014970.7628.0610.0
BL8BeamGradualYes80 × 250 × 210035.08.046.1147197014970.7628.0625.0
BL9BeamGradualNo150 × 250 × 400036.08.046.1147197012580.6426.0700.0
BL10BeamGradualNo150 × 250 × 400036.08.046.1147197012580.6426.0700.0
BL11BeamGradualNo150 × 250 × 390036.08.046.1147197015180.7742.0600.0
BL12BeamGradualNo150 × 250 × 390036.08.046.1147197015180.7742.0500.0
PL1PrismGradualNo70 × 95 × 188435.08.046.1147197011930.6134.0490.0
PL2PrismGradualNo70 × 95 × 188435.08.046.1147197011930.6134.0480.0
PL3PrismGradualNo80 × 80 × 188440.08.046.1147197014100.7231.0540.0
PL4PrismGradualNo80 × 80 × 188440.08.046.1147197014100.7231.0525.0
[33]C40-80-L-CCFRP LeadlineSpirally
Indented
BeamGradualYes150 × 300 × 600061.08.050.217228457890.2826.0750.0
C40-120-L-CBeamGradualYes151 × 300 × 600061.08.050.2172284512130.4326.0825.0
C40-80-S-SBeamGradualYes152 × 300 × 600061.08.050.217228458340.2935.0480.0
C40-80-L-UBeamGradualYes153 × 300 × 600061.08.050.217228458190.2935.0530.0
C40-120-L-UBeamGradualYes154 × 300 × 600061.08.050.2172284512250.4337.0675.0
C80-120-L-UBeamGradualYes156 × 300 × 600061.08.050.2172284512170.4355.0655.0
C80-120-S-SBeamGradualYes158 × 300 × 600061.08.050.2172284511410.4063.0355.0
C80-80-L-CBeamGradualYes159 × 300 × 600061.08.050.217228457450.2663.0305.0
[40,41,42]1CFRP LeadlineSpirally
Indented
T BeamGradualYesT46.17.847.314719709800.5047.0360.0
2T BeamGradualYesT46.17.847.3147197013800.7050.0500.0
[47]CL-2CFRP LeadlineSpirally
Indented
PrismGradualNo105 × 102 × 300047.17.946.5150197911000.5628.1939.8
CL-1 (J)BeamGradualNo137 × 203 × 600064.77.946.5150197913020.6628.3-
CL-1 (D)BeamGradualNo138 × 203 × 600064.77.946.5150197913020.6628.3-
2CL-1 (J)BeamGradualNo139 × 203 × 600064.77.946.5150197911690.5929.0304.8
2CL-1 (D)BeamGradualNo140 × 203 × 600064.77.946.5150197911690.5929.0381.0
CL-3 (J)BeamGradualNo141 × 203 × 600064.77.946.5150197911390.5828.3431.8
CL-3 (D)BeamGradualNo142 × 203 × 600064.77.946.5150197911390.5828.3609.6
[46]T1CFRP LeadlineSpirally
Indented
T BeamGradualYesT46.17.946.1150230011280.4930.0650.0
T2T BeamGradualYesT46.17.946.1150230015780.6930.0725.0
T3-1T BeamGradualYesT46.17.946.1150230011500.5030.0675.0
T3-2T BeamGradualYesT46.17.946.1150230016100.7030.0675.0
R1-R4BeamGradualYes150 × 30046.17.946.1150230013560.5930.0625.0
[39]CDT1-1-WA-A1CFRP LeadlineSpirally
Indented
GirderGradualYesDouble T40.57.946.1147225617400.7748.0557.5
CDT1-1-WA-A2GirderGradualYesDouble T40.57.946.1147225618300.8148.0-
CDT1-1-WA-A3GirderGradualYesDouble T40.57.946.1147225613000.5848.0-
CDT1-1-WA-B1GirderGradualYesDouble T40.57.946.1147225615400.6848.0507.5
CDT1-1-WA-B2GirderGradualYesDouble T40.57.946.1147225615400.6848.0-
CDT1-1-WA-B3GirderGradualYesDouble T40.57.946.1147225613600.6048.0-
CDT1-2-WA-A1GirderSuddenYesDouble T40.57.946.1147225616400.7348.0470.0
CDT1-2-WA-A2GirderSuddenYesDouble T40.57.946.1147225617400.7748.0-
CDT1-2-WA-A3GirderSuddenYesDouble T40.57.946.1147225611200.5048.0-
CDT1-2-WA-B1GirderSuddenYesDouble T40.57.946.1147225615400.6848.0-
CDT1-2-WA-B2GirderSuddenYesDouble T40.57.946.1147225616400.7348.0-
CDT1-2-WA-B3GirderSuddenYesDouble T40.57.946.1147225611200.5048.0-
CDT1-3-WA-A1GirderSuddenYesDouble T40.57.946.1147225616400.7348.0502.5
CDT1-3-WA-A2GirderSuddenYesDouble T40.57.946.1147225616400.7348.0-
CDT1-3-WA-A3GirderSuddenYesDouble T40.57.946.1147225610500.4748.0-
CDT1-3-WA-B1GirderSuddenYesDouble T40.57.946.1147225619300.8648.0415.0
CDT1-3-WA-B2GirderSuddenYesDouble T40.57.946.1147225615400.6848.0-
CDT1-3-WA-B3GirderSuddenYesDouble T40.57.946.114722569300.4148.0-
CDT1-4-WA-A1GirderSuddenYesDouble T40.57.946.1147225616400.7348.0487.5
CDT1-4-WA-A2GirderSuddenYesDouble T40.57.946.1147225616400.7348.0-
CDT1-4-WA-A3GirderSuddenYesDouble T40.57.946.1147225612400.5548.0-
CDT1-4-WA-B1GirderSuddenYesDouble T40.57.946.1147225617400.7748.0502.5
CDT1-4-WA-B2GirderSuddenYesDouble T40.57.946.1147225613500.6048.0-
CDT1-4-WA-B3GirderSuddenYesDouble T40.57.946.1147225612400.5548.0-
[73]1CFRP LeadlineSpirally
Indented
BeamGradualYes150 × 300 × 300046.08.050.2-207012420.641.0662.5
3BeamGradualYes151 × 300 × 300046.08.050.2-207012420.641.0650.0
4BeamGradualYes152 × 300 × 300046.08.050.2-207012420.641.8625.0
6BeamGradualYes153 × 300 × 300046.08.050.2-207012420.641.0561.5
[43,44]I-SCC30-1CFRP BarSandedBeamGradualYes150 × 250 × 360038.112.7126.714417656130.3230.4-
I-SCC30-2BeamGradualYes150 × 250 × 360138.112.7126.714417656010.3130.4355.0
I-SCC30-3BeamGradualYes150 × 250 × 360238.112.7126.714417657260.3741.0-
I-SCC30-4BeamGradualYes150 × 250 × 360338.112.7126.714417656470.3541.0-
II-SCC45-1BeamGradualYes150 × 250 × 360438.112.7126.714417658070.4335.0-
II-SCC45-2BeamGradualYes150 × 250 × 360538.112.7126.714417658840.4635.0505.0
II-SCC45-3BeamGradualYes150 × 250 × 360638.112.7126.714417658410.4535.0530.0
II-SCC45-4BeamGradualYes150 × 250 × 360738.112.7126.714417658050.4335.0-
III-SCC60-1BeamGradualYes150 × 250 × 360838.112.7126.714417659800.5430.4665.0
III-SCC60-2BeamGradualYes150 × 250 × 360938.112.7126.7144176510970.5830.4-
III-SCC60-3BeamGradualYes150 × 250 × 361038.112.7126.7144176510080.5441.0695.0
III-SCC60-4BeamGradualYes150 × 250 × 361138.112.7126.7144176510520.5741.0680.0
IV-N30-1BeamGradualYes150 × 250 × 361238.112.7126.714417656350.3337.0300.0
IV-N60-2BeamGradualYes150 × 250 × 361338.112.7126.7144176511680.6337.0-
IV-N60-3BeamGradualYes150 × 250 × 361438.112.7126.7144176511210.6037.0580.0
IV-N60-4BeamGradualYes150 × 250 × 361538.112.7126.7144176511530.6237.0590.0
[74]Slab 3CFRP BarSandedSlab-No200 × 45 × 336019.85.422.9150200012000.6101.2160.0
[34])C1-UHMCFRP BarSandedBeamGradualYes90 × 157.5 × 300022.55.322.150915268000.5262.8158.0
C1-UTSBeamGradualYes91 × 157.5 × 300022.55.322.114520318000.3961.886.0
C4-UHMBeamGradualYes92 × 157.5 × 300022.55.322.150915268000.5232.9194.0
Table A4. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned AFRP reinforcement.
Table A4. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned AFRP reinforcement.
ReferenceSpecimen NoFRP TypeFRP SurfaceSpecimen TypeRelease TypeShear ReinforcementSpecimen Dimensions
(b × h × l, mm)
c, mmØ, mmAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPaLt, mm
[57]Beam1AFRP TendonSmooth braidedBeamGradualNo120 × 21062.016.0180.06313926980.5029.1-
Beam2BeamGradualNo121 × 21062.016.0180.06313926980.5029.1-
Beam3BeamGradualYes122 × 21062.016.0180.06313926980.5029.1625.0
Beam4BeamGradualYes123 × 21062.016.0180.06313926980.5029.1-
Beam5BeamGradualYes124 × 21062.016.0180.06313926980.5029.1575.0
Beam6BeamGradualYes125 × 21062.016.0180.06313926980.5029.1-
Beam7BeamGradualNo126 × 21062.016.0180.06313926980.5029.1700.0
Beam8BeamGradualNo127 × 21062.016.0180.06313926980.5029.1-
[24,38]A2-1AFRP Tendon Smooth braidedBeamGradualYes120 × 210 × 400066.08.042.07616393740.2337.4300.0
A2-2(J)BeamGradualYes121 × 210 × 400066.08.042.07616393740.2337.5300.0
A2-2(F)BeamGradualYes122 × 210 × 400066.08.042.07616393740.2338.4300.0
A2-S3(J)BeamGradualYes123 × 210 × 400066.08.042.07616393740.2338.6200.0
A2-S3(F)BeamGradualYes124 × 210 × 400066.08.042.07616393740.2338.7200.0
A2-S4(F)BeamGradualYes125 × 210 × 400066.08.042.07616397480.4633.1400.0
A2-S4(J)BeamGradualYes126 × 210 × 400066.08.042.07616397480.4633.4400.0
B1-1(F)BeamGradualYes127 × 210 × 400064.012.090.06814613490.2437.8400.0
B1-1(J)BeamGradualYes128 × 210 ×400064.012.090.06814613490.2437.9400.0
B1-2(F)BeamGradualYes129 × 210 × 400064.012.090.06814613490.2435.8400.0
B1-2(J)BeamGradualYes130 × 210 × 400064.012.090.06814613490.2438.6400.0
B1-S3(J)BeamGradualYes131 × 210 × 400064.012.090.06814613490.2437.6300.0
B1-S3(F)BeamGradualYes132 × 210 × 400064.012.090.06814613490.2437.8300.0
B1-S6(J)BeamGradualYes133 × 210 × 400064.012.090.06814613490.2438.0300.0
B1-S6(F)BeamGradualYes134 × 210 × 400064.012.090.06814613490.2438.1300.0
B1-S7(F)BeamGradualYes135 × 210 × 400064.012.090.06814616980.4833.7450.0
B1-S7(J)BeamGradualYes136 × 210 ×400064.012.090.06814616980.4834.0450.0
B2-S1(J)BeamGradualYes137 × 210 × 400064.012.090.06814613490.2438.9400.0
B2-S1(F)BeamGradualYes138 × 210 × 400064.012.090.06814613490.2439.0400.0
C1-S4(F)BeamGradualYes139 × 210 × 400062.016.0180.06313926980.5034.3550.0
C1-S4(J)BeamGradualYes140 × 210 × 400062.016.0180.06313926980.5034.6550.0
C1-S6/1BeamGradualYes141 × 210 × 400062.016.0180.06313926980.5031.3600.0
C1-S6/2BeamGradualYes142 × 210 × 400062.016.0180.06313926980.5031.9600.0
C1-S7/1BeamGradualYes143 × 210 × 400062.016.0180.06313926980.5031.6550.0
C1-S7/2BeamGradualYes144 × 210 × 400062.016.0180.06313926980.5032.2550.0
D1-1(J)SandedBeamGradualYes145 × 210 × 400063.313.590.06814616980.4839.0250.0
D1-1(F)SandedBeamGradualYes146 × 210 ×400063.313.590.06814616980.4839.1250.0
D1-S3(J)SandedBeamGradualYes147 × 210 × 400063.313.590.06814616980.4839.2200.0
D1-S3(F)SandedBeamGradualYes148 × 210 × 400063.313.590.06814616980.4839.4200.0
[33]A40-80-SAFRP Arapee TendonSandedBeamGradualYes160 × 300 × 600061.17.847.85411344190.3727.0220.0
A40-80-LBeamGradualYes161 × 300 × 600061.17.847.85411344190.3727.0220.0
A80-80-SBeamGradualYes164 × 300 × 600061.17.847.85411344190.3764.0170.0
A80-80-LBeamGradualYes165 × 300 × 600061.17.847.85411344190.3764.0170.0
[35]7.5S-N-50-1AFRP Arapee TendonSandedPrismGradualNo50 × 50 × 100021.37.522.291300014870.5054.6-
7.5S-N-60-1PrismGradualNo60 × 60 × 100026.37.522.291300014870.5054.6135.0
7.5S-N-70-1PrismGradualNo70 × 70 × 100031.37.522.291300014870.5054.6135.0
7.5S-N-50-2PrismGradualNo50 × 50 × 100021.37.522.291300014870.5054.6220.0
7.5S-N-60-2PrismGradualNo60 × 60 × 100026.37.522.291300014870.5054.6110.0
7.5S-N-70-2PrismGradualNo70 × 70 × 100031.37.522.291300014870.5054.6135.0
7.5S-N-50-3PrismGradualFibres50 × 50 × 100021.37.522.291300014870.5054.6135.0
7.5-S-N-50-4PrismGradualFibres50 × 50 × 100021.37.522.291300014870.5054.6160.0
7.5S-N-50-5PrismGradualFibres50 × 50 × 100021.37.522.291300014870.5054.6160.0
7.5S-H-45-1PrismGradualNo45 × 45 × 100018.87.522.291300014870.5081.5110.0
7.5S-H-50-1PrismGradualNo50 × 50 × 100021.37.522.291300014870.5081.5135.0
7.5S-H-50-2PrismGradualNo50 × 50 × 100021.37.522.291300014870.5081.5135.0
5.3S-N-45-1PrismGradualNo45 × 45 × 100019.95.311.191300014870.5054.685.0
5.3E-N-45-1ExpancelPrismGradualNo45 × 45 × 100019.95.311.191300014870.5054.6225.0
5.3ES-N-45-1SandedPrismGradualNo45 × 45 × 100019.95.311.191300014870.5054.685.0
5.3S-N-40-1SandedPrismGradualNo40 × 40 × 100017.45.311.191300014870.5054.685.0
5.3E-N-40-1ExpancelPrismGradualNo40 × 40 × 100017.45.311.191300014870.5054.6200.0
5.3S-N-35-1SandedPrismGradualNo35 × 35 × 100014.95.311.191300014870.5054.685.0
5.3S-N-30-1SandedPrismGradualNo30 × 30 × 100012.45.311.191300014870.5054.6-
5.3E-N-35-1ExpancelPrismGradualNo35 × 35 × 100014.95.311.191300014870.5054.6185.0
5.3E-N-30-1ExpancelPrismGradualNo30 × 30 × 100012.45.311.191300014870.5054.6-
5.3ES-N-35-1SandedPrismGradualNo35 × 35 × 100014.95.311.191300014870.5054.6110.0
5.3ES-N-30-1PrismGradualNo30 × 30 × 100012.45.311.191300014870.5054.6-
5.3S-N-40-2PrismGradualNo40 × 40 × 100017.45.311.191300014870.5054.6-
5.3S-N-35-2PrismGradualNo35 × 35 × 100014.95.311.191300014870.5054.685.0
5.3-ES-N-40-1PrismGradualNo40 × 40 × 100017.45.311.191300014870.5054.6135.0
5.3ES-N-40-2PrismGradualNo40 × 40 × 100017.45.311.191300014870.5054.6-
5.3ES-N-35-2PrismGradualNo35 × 35 × 100014.95.311.191300014870.5054.6110.0
5.3ES-N-30-2PrismGradualNo30 × 30 × 100012.45.311.191300014870.5054.6-
[47]AA-2AFRP Arapee TendonSmoothPrismGradualNo102 × 102 × 300046.19.938.1128244810270.4231.6482.6
AF-2AFRP FibraSmooth-braidedPrismGradualNo103 × 102 × 300045.810.483.24814348070.5630.8330.2
AT-2AFRP Technora tendonRoughPrismGradualNo104 × 102 × 300047.37.443.26917248840.5130.1345.4
AA-1 (J)AFRP Arapee TendonSmoothBeamGradualNo127 × 203 × 600063.79.938.1128244810400.4331.5406.4
AA-1 (D)BeamGradualNo128 × 203 × 600063.79.938.1128244810400.4331.5266.7
AA-3 (J)BeamGradualNo129 × 203 × 600063.79.938.1128244814370.5929.0685.8
AA-3 (D)BeamGradualNo130 × 203 × 600063.79.938.1128244814370.5929.0711.2
AF-3 (J)AFRP FibraSmooth-braidedBeamGradualNo131 × 203 × 600063.410.483.24814348280.5829.7381.0
AF-3 (D)AFRP FibraSmooth-braidedBeamGradualNo132 × 203 × 600063.410.483.24814348280.5829.7304.8
AT-1 (J)AFRP Technora tendonRoughBeamGradualNo133 × 203 × 600064.97.443.269172414090.8230.1330.2
AT-1 (D)BeamGradualNo134 × 203 × 600064.97.443.269172414090.8230.1279.4
AT-3 (J)BeamGradualNo135 × 203 × 600064.97.443.26917249760.5730.1254.0
AT-3 (D)BeamGradualNo136 × 203 × 600064.97.443.26917249760.5730.1381.0
[75]B1AFRP Technora tendonRoughBeamSuddenYes150 × 300 × 210037.06.028.853176712900.7331.2-
B2BeamSuddenYes151 × 300 × 210037.06.028.853176712050.6832.3-
B3BeamSuddenYes152 × 300 × 210037.06.028.853176712080.6836.5225.0
[53,54]ATAFRP Technora tendonRoughBeamGradualNo89 × 178 × 300040.67.950.345171010550.6243.1368.3
Table A5. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned BFRP reinforcement.
Table A5. Geometrical, mechanical properties of the material and transfer lengths of specimens with pretensioned BFRP reinforcement.
ReferenceSpecimen NoFRP TypeFRP SurfaceSpecimen TypeRelease TypeShear ReinforcementSpecimen Dimensions
(b × h × l, mm)
c, mmØ, mmAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPaLt, mm
[56]B1SBFRP BarSandedBeamSuddenNo100 × 200 × 300046.08.050.24411263810.3427.0350.0
B1NBeamSuddenNo100 × 200 × 300046.08.050.24411263650.3227.0500.0
B2SBeamSuddenNo100 × 200 × 300046.08.050.24411263460.3127.0250.0
B2NBeamSuddenNo100 × 200 × 300046.08.050.24411263500.3127.0400.0
[55]Beam 1BFRP BarSandedBeamGradualYes90 × 200 × 300058.012.0113.1369204420.4836.5100.0
Beam 2 BeamGradualYes90 × 200 × 300058.012.0113.1369204420.4852.493.0

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Figure 1. Relationship between transfer length and (a) concrete compressive strength at transfer (fci), (b) ratio between initial stress and tensile strength (fpi/fpu), (c) reinforcement diameter (Ø), (d) concrete cover (c), (e) ratio between the concrete cover and reinforcement diameter (c/Ø), (f) modulus of elasticity (Ep) of different types of pretensioned FRP reinforcement.
Figure 1. Relationship between transfer length and (a) concrete compressive strength at transfer (fci), (b) ratio between initial stress and tensile strength (fpi/fpu), (c) reinforcement diameter (Ø), (d) concrete cover (c), (e) ratio between the concrete cover and reinforcement diameter (c/Ø), (f) modulus of elasticity (Ep) of different types of pretensioned FRP reinforcement.
Polymers 14 03931 g001
Figure 2. Relationship between transfer length and (a) concrete compressive strength at transfer (fci), (b) ratio between initial stress and tensile strength (fpi/fpu), (c) reinforcement diameter (Ø), (d) concrete cover (c), (e) ratio between the concrete cover and reinforcement diameter (c/Ø), (f) modulus of elasticity (Ep) of different types of CFCC pretensioned reinforcement under different methods of prestress transfer.
Figure 2. Relationship between transfer length and (a) concrete compressive strength at transfer (fci), (b) ratio between initial stress and tensile strength (fpi/fpu), (c) reinforcement diameter (Ø), (d) concrete cover (c), (e) ratio between the concrete cover and reinforcement diameter (c/Ø), (f) modulus of elasticity (Ep) of different types of CFCC pretensioned reinforcement under different methods of prestress transfer.
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Figure 3. Relationship between the transfer length of GFRP reinforcement and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of the shear reinforcement and the type of transfer of the prestress.
Figure 3. Relationship between the transfer length of GFRP reinforcement and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of the shear reinforcement and the type of transfer of the prestress.
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Figure 4. Relationship between the transfer length of CFCC strands and f p i · Ø / f c i 2 / 3 : (a) effect of types of transfer of prestressing, (b) effect of shear reinforcement.
Figure 4. Relationship between the transfer length of CFCC strands and f p i · Ø / f c i 2 / 3 : (a) effect of types of transfer of prestressing, (b) effect of shear reinforcement.
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Figure 5. Relationship between transfer length of CFRP bars and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of type of prestressing transfer, (c) effect of shear reinforcement, (d) effect of reinforcement surface conditions.
Figure 5. Relationship between transfer length of CFRP bars and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of type of prestressing transfer, (c) effect of shear reinforcement, (d) effect of reinforcement surface conditions.
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Figure 6. Relationship between transfer length of AFRF bars and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of shear reinforcement, (c) effect of reinforcement surface conditions.
Figure 6. Relationship between transfer length of AFRF bars and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of shear reinforcement, (c) effect of reinforcement surface conditions.
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Figure 7. Relationship between the transfer length of BFRP reinforcement and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of the type of transfer of the prestressing.
Figure 7. Relationship between the transfer length of BFRP reinforcement and f p i · Ø / f c i 2 / 3 : (a) all results, (b) effect of the type of transfer of the prestressing.
Polymers 14 03931 g007
Figure 8. Relationship between the experimental and theoretical transfer lengths of (a) GFRP reinforcement and (b) CFRP reinforcement [30,31,63,64].
Figure 8. Relationship between the experimental and theoretical transfer lengths of (a) GFRP reinforcement and (b) CFRP reinforcement [30,31,63,64].
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Figure 9. Relationship between experimental and theoretical transfer lengths of CFCC strands (a) for the gradual transfer of prestress, (b) for sudden transfer of prestress [30,31,63,64].
Figure 9. Relationship between experimental and theoretical transfer lengths of CFCC strands (a) for the gradual transfer of prestress, (b) for sudden transfer of prestress [30,31,63,64].
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Figure 10. Relationship between the experimental and theoretical transfer lengths of AFRP reinforcement with different surface conditions: (a) smooth braided, (b) sanded and rough, (c) both (all results) [30,31,63,64].
Figure 10. Relationship between the experimental and theoretical transfer lengths of AFRP reinforcement with different surface conditions: (a) smooth braided, (b) sanded and rough, (c) both (all results) [30,31,63,64].
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Figure 11. Comparison of experimental and theoretical transfer length results: (a) GFRP reinforcement, (b) CFCC strands with gradual transfer, (c) CFCC strands with sudden transfer, (d) CFRP bars, (e) AFRP bars.
Figure 11. Comparison of experimental and theoretical transfer length results: (a) GFRP reinforcement, (b) CFCC strands with gradual transfer, (c) CFCC strands with sudden transfer, (d) CFRP bars, (e) AFRP bars.
Polymers 14 03931 g011
Table 1. Basic physical and mechanical properties of different FRP bars [10,11,12,13,14].
Table 1. Basic physical and mechanical properties of different FRP bars [10,11,12,13,14].
FRP
Type
Density, kg/m3Tensile
Strength, MPa
Modulus of
Elasticity, GPa
Elongation, %Longitudinal Coefficient of
Linear Expansion (10−6/°C)
GFRP1250–2500480–160035–861.2–5.06.0–10.0
CFRP1500–2100600–3920120–7840.5–1.9−9.0–0.0
AFRP1250–14501720–362041–1751.4–4.4−6.0–2.0
BFRP1900–2100600–165045–651.2–3.09.0–12.0
Prestressing steel78501770–2060195–2053.5–4.012.0
Table 2. Summary of transfer length results on the influence of concrete compressive strength at transfer.
Table 2. Summary of transfer length results on the influence of concrete compressive strength at transfer.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ø,
mm
c/ØEp,
GPa
fpi/fpufci.min,
MPa
fci.max,
MPa
Lt.max,
mm
Lt.min,
mm
[31,32]CFCCHelical plain5012.54.01410.752328475374
CFCCHelical plain6015.23.91380.62435500360
CFCCHelical plain6015.23.91380.752231625395
[29,30]CFCCHelical plain5012.54.01370.54156158.5137.5
[31,32]CFRPSpirally indented358.04.41470.752835620480
[33]CFRPSpirally indented618.07.61720.32663750305
CFRPSpirally indented618.07.61720.42663825355
[34]CFRPSpirally indented sanded22.55.34.25090.523363194158
[33]AFRPSanded61.17.87.8540.42764220170
[35,48]AFRPSanded21.37.52.8910.554.581.5169135
[36,37]GFRPRibbed5516.03.4600.43171278188
[55]BFRPSanded5812.04.8360.4836.552.410090
c—concrete cover, Ø—reinforcement diameter, Ep—modulus of elasticity of reinforcement, fpi—initial prestress of reinforcement, fpu—tensile strength of reinforcement, fci.min and fci.max—lower and higher concrete strength, respectively, Lt.min and Lt.max—lower and higher transfer length, respectively.
Table 3. Summary of transfer length results for the influence of prestress level of FRP reinforcement.
Table 3. Summary of transfer length results for the influence of prestress level of FRP reinforcement.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ø,
mm
c/ØEp,
GPa
fci,
MPa
fpi/fpu
(min)
fpi/fpu
(max)
Lt.min,
mm
Lt.max,
mm
[39]CFCCHelical plain38.212.53.1-480.490.56468400
[31,32]CFCCHelical plain5012.54.0141-28–300.60.75298374
CFCCHelical plain6015.23.913822–240.620.74500625
[29,30]CFCCHelical plain6015.23.9137300.60.75370403
[40,41]CFRPSpirally indented46.17.85.9147500.50.7360500
[43,44]CFRPSanded38.112.73.0144370.330.62300585
CFRPSanded38.112.73.0144300.310.56355665
[33]CFRPSpirally indented618.07.6172260.30.4750825
CFRPSpirally indented618.07.6172360.30.4505675
CFRPSpirally indented618.07.6172630.30.4305355
[45]CFRPSpirally indented sanded31.812.72.5124460.50.55533495
CFRPSpirally indented sanded31.812.72.5124460.50.59533607
[46]CFRPSpirally indented46.17.95.8150300.50.6662625
CFRPSpirally indented46.17.95.8150300.50.7662700
[39]CFRPSpirally indented40.57.95.1147480.60.68470507
CFRPSpirally indented40.57.95.1147480.60.75470504
[31,32]CFRPSpirally indented358.04.414734–350.610.72458480
[47]AFRPPlain63.79.96.412829–310.430.59385699
[36,37]GFRPRibbed5516.03.46029–310.260.41211278
c—concrete cover, Ø—reinforcement diameter, Ep modulus of elasticity of reinforcement, fci—concrete compressive strength at transfer, fpi—initial prestress of reinforcement, fpu—tensile strength of reinforcement, fpi/fpu (min) and fpi/fpu (max)—lower and higher prestress levels, respectively, Lt.min and Lt.max—lower and higher transfer lengths, respectively.
Table 4. Summary of the transfer length results for the influence of reinforcement diameter of the FRP reinforcement.
Table 4. Summary of the transfer length results for the influence of reinforcement diameter of the FRP reinforcement.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ep,
GPa
fpi/fpufci,
MPa
Ømin,
mm
Ømaz,
mm
Lt.min,
mm
Lt.max,
mm
[29,30]CFCCHelical plain501370.54012.515.2158212
CFCCHelical plain501370.753012.515.2369403
[31,32]CFCCHelical plain50138–1410.7522–2312.515.2475625
[26]CFCCHelical indented18.8–211550.5563–697.57.5211211
CFRPSpirally indented15–251670.5466–685.05.0122122
[24,38]AFRPSmooth braided6468–760.2436–398.012.0260360
AFRPSmooth braided6263–760.531–348.016.0400567
[35,48]AFRPSanded-910.5545.37.598149
[36,37]GFRPRibbed55600.43112.016.0224276
c—concrete cover, Ep—modulus of elasticity of reinforcement, fci—concrete compressive strength at transfer, fpi initial prestress of reinforcement, fpu— tensile strength of reinforcement, Ømin and Ømax—lower and higher reinforcement diameters, respectively, Lt.min and Lt.max—lower and higher transfer lengths, respectively.
Table 5. Summary of transfer length results under the influence of shear reinforcement.
Table 5. Summary of transfer length results under the influence of shear reinforcement.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ø,
mm
c/ØEp,
GPa
fpi/fpufci,
MPa
Lt., mm
(With Stirrups)
Lt., mm
(Without Stirrups)
[31,32]CFCCHelical plain5012.54.01410.73–0.7523–28374475
CFRPSpirally indented358.04.41470.6134457485
c—concrete cover, Ø—reinforcement diameter, Ep—modulus of elasticity of reinforcement, fpi—initial prestress of reinforcement, fpu—tensile strength of reinforcement, fci—concrete compressive strength at release, Lt (with stirrups)—transfer length of specimen with shear reinforcement, Lt (without stirrups)—transfer length of specimen without shear reinforcement.
Table 6. Summary of transfer length results on the influence of reinforcement surface conditions.
Table 6. Summary of transfer length results on the influence of reinforcement surface conditions.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ø,
mm
c/ØEp,
GPa
fpi/fpufci,
MPa
Lt.,
mm
[47]AFRPRough47.37.46.4690.51–0.5730.1327
AFRPSmooth braided45.810.44.4480.56–0.5830339
AFRPSmooth46.19.94.71280.42–0.4331.5385
[35,48]AFRPSanded14.9–19.95.32.8–3.7910.55585
AFRPExpancel sanded14.9–19.95.32.8–3.7910.555110
AFRPExpancel14.9–19.95.32.8–3.7910.555203
[24,38]AFRPSmooth braided6412.05.368–760.4834450
AFRPSanded63.312.05.3680.4839225
[36,37]GFRPRibbed5512.04.6600.3631221
[50]CFRPSpirally indented, sanded, cross wound468.05.8130–1440.645300
CFRPHelical plain468.05.81470.645400
AFRPSpirally indented468.05.8540.645500
GFRPSpirally indented468.05.8470.645500
c—concrete cover, Ø—reinforcement diameter, Ep—modulus of elasticity of reinforcement, fpi—initial prestress of reinforcement, fpu—tensile strength of reinforcement, fci—concrete compressive strength at release, Lt—transfer length.
Table 7. Summary of transfer length results on the influence of modulus of elasticity of reinforcement.
Table 7. Summary of transfer length results on the influence of modulus of elasticity of reinforcement.
ReferenceFRP
Type
FRP
Surface
c,
mm
Ø,
mm
c/Øfpi/fpufci,
MPa
Ep,
GPa
Lt.,
mm
[33]CFRPSpirally indented618.07.60.426172825
CFRPSpirally indented618.07.60.463172355
AFRPSanded617.87.80.372754220
AFRPSanded617.87.80.376454170
[47]CFRPSpirally indented64.77.98.20.58–0.5928–29150432
CFCCHelical plain46.9–64.58.35.6–7.80.53–0.5928–30137432
AFRPRough47.3–64.97.96.4–8.80.51–0.573069327
[53,54]CFRPSpirally indented40.67.95.10.6140171422
AFRPRough40.67.95.10.624345368
[51,52]GFRPHelical plain46.39.54.90.433269254
GFRPHelical plain46.39.54.90.464069267
[36,37]GFRPRibbed5512.04.60.363160221
GFRPRibbed5516.03.40.413160278
c—concrete cover, Ø—reinforcement diameter, Ep—modulus of elasticity of reinforcement, fpi—initial prestress of reinforcement, fpu—tensile strength of reinforcement, fci—concrete compressive strength at release, Lt—transfer length.
Table 8. Summary of the theoretical models for the transfer length of FRP reinforcement.
Table 8. Summary of the theoretical models for the transfer length of FRP reinforcement.
ReferenceEquationEquation No.Notes
[10,12,31,32] L t = f p i · Ø α t · f c i 2 3 (1)Lt—is the transfer length,
fpi—is the initial prestress level,
Ø—is the reinforcement diameter,
fci—is the concrete compressive strength at the time of transfer,
αt—is a material dependent coefficient.
[33] L t = κ · Ø f c i (2)κ—is a factor equal to 480 in N·mm units (for the CFRP Leadline bar with a spirally indented surface),
Ø—is the reinforcement diameter,
fci—is the concrete compressive strength at the time of transfer.
[30] L t = f p e · A p C T · f c i (3)Ap—cross-sectional area of prestressed reinforcement,
fpe—effective prestressing stress in the CFCC strand,
CT—constant is equal to 80 for CFCC strands,
fci—is the concrete compressive strength at the time of transfer.
[70] L t = 2.5 · A p · f p i f c i 2 3 (4)Ap—cross-sectional area of prestressed reinforcement,
fpi—is the initial prestress level,
fci—is the concrete compressive strength at the time of transfer.
[64] L t = f p i · Ø 20.7 (5)fpi—is the initial prestress level,
Ø—is the reinforcement diameter.
[63] L t = f p i · 20.7 · 20.7 f c i (6)fpi—is the initial prestress level,
Ø—is the reinforcement diameter,
fci—is the concrete compressive strength at the time of transfer.
Table 9. Summary of material dependent coefficient αt.
Table 9. Summary of material dependent coefficient αt.
ReferenceReinforcement Typeαt
[10,12,31,32]CFRP Leadline bar1.9
CFCC strands4.8
[39]CFRP Leadline bar1.95
CFCC strands2.12
[36,37]GFRP bars2.6
[43,44]CFRP bars (SCC concrete) α t = 2.84 f p i 800
Table 10. Summary of initial parameters of the transfer length database.
Table 10. Summary of initial parameters of the transfer length database.
FRP Typec, mmØ, mmc/ØAp, mm2Ep, GPafpu, MPafpi, MPafpi/fpufci, MPa
GFRP25–559.5–161,6–4.945.3–20155–69.21100–1941313–9030.26–0.4729–71
CFCC38.2–76.28.3–15.22.9–7.854.2–115.6137–1551725–2348561–15260.3–0.8122–56.3
CFRP19.8–1005.3–12.72.5–1022.1–126.7124.1–1721526–2845600–19300.26–0.8626–101.2
AFRP12.4–665.3–162.3–8.811.1–18044.8–127.51134–3000349–14860.23–0.8227–81.5
BFRP46–588–124.8–5.850.2–113.136–44920–1126369–4420.31–0.4827–52.4
Table 11. Results for the coefficient αt.
Table 11. Results for the coefficient αt.
αtGFRPCFCCCFRPAFRPBFRP
Gradual
Release
Sudden
Release
AllSmooth
Braided
Sanded and
Rough
Mean2.584.992.421.922.901.533.992.1
Standard deviation0.330.620.670.481.800.551.701.7
Coefficient of variation, %12.812.527.724.862.135.842.779.2
Table 12. Summary of the statistical results for Lt.teor/Lt.exp.
Table 12. Summary of the statistical results for Lt.teor/Lt.exp.
ParametersGFRPCFCCCFRPAFRP
GradualSuddenAllSmooth BraidedSanded and Rough
αt = 2.6αt = 5.0αt = 4.8αt = 2.12αt = 2.4αt = 2.12αt = 1.90αt = 1.92αt = 1.95αt = 2.9αt = 1.5αt = 4.0
M1.001.001.042.351.011.141.011.000.981.001.021.00
STD0.130.120.130.290.280.320.250.250.240.620.360.43
COV, %12.612.512.512.527.727.724.824.824.862.135.842.7
Ntotal264141412121737373703139
OV17212841811404039291420
UV9201301310333334411719
M+STD1.131.121.172.651.291.461.261.251.231.621.381.42
M-STD0.870.880.912.060.730.830.760.750.740.380.650.57
>M+STD36665588815310
<M-STD2888221313139910
Inbound212727271414525252461919
Inbound, %80.865.965.965.966.766.771.271.271.265.761.348.7
M—mean Lt.teor/Lt.exp, STD—standard deviation, COV—coefficient of variation, Ntotal—the total amount of specimens, UV—underestimated values, OV—overestimated values, M+STD—upper bound, M-STD—lower bound.
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Jokūbaitis, A.; Valivonis, J. An Analysis of the Transfer Lengths of Different Types of Prestressed Fiber-Reinforced Polymer Reinforcement. Polymers 2022, 14, 3931. https://doi.org/10.3390/polym14193931

AMA Style

Jokūbaitis A, Valivonis J. An Analysis of the Transfer Lengths of Different Types of Prestressed Fiber-Reinforced Polymer Reinforcement. Polymers. 2022; 14(19):3931. https://doi.org/10.3390/polym14193931

Chicago/Turabian Style

Jokūbaitis, Aidas, and Juozas Valivonis. 2022. "An Analysis of the Transfer Lengths of Different Types of Prestressed Fiber-Reinforced Polymer Reinforcement" Polymers 14, no. 19: 3931. https://doi.org/10.3390/polym14193931

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