Carbon Fiber Reinforced Polymer Bars Research Articles

Shear and flexure of FRP-reinforced concrete beams and slabs – A review

The article reviews structural response of flexural members reinforced with fiber-reinforced polymer (FRP) as a sustainable alternative to conventional carbon steel. It overviews experimental studies and code-based models that characterize shear and flexural response of concrete beams and slabs reinforced with FRP bars. Discussion on lower resistance to fire being key limitation of FRP bars is also included. The most commonly used fibers to manufacture FRP bars include carbon, glass, basalt, aramid, or combinations of these materials. Consequently, each material plays its role in contributing to shear and flexure differently. Basalt FRP are characterized by higher tensile capacity and resistance to corrosion, carbon FRP bars can withstand exposure to harsh environments; glass FRP bars possess lower modulus of elasticity that may cause large deflection and wider cracks. FRP bars are generally preferred over carbon steel for use in concrete elements where exposure to chlorides or chemicals is expected, or places where non-magnetic properties are essential. Beams and slabs reinforced with FRP bars are likely to undergo larger deflections due to lower stiffness of FRP bars. The dominant failure mode of FRP-reinforced concrete flexural members is discussed in comparison to conventional steel-reinforced members. The article identifies increasing interest and research in using green concrete reinforced with FRP bars that helps to make construction serviceable and sustainable. However, premature de-bonding of bars remains a concern with more research needed to avoid deterioration of mechanical properties by underutilization of materials. Although concrete is practically fire-resistant, FRP is likely to undergo damage of resin due to the presence of combustible organic polymers. The bulk of research implies that the thermal instability of the resin in FRP reinforcing bars is not a disadvantage that outweighs the possible benefits of its usage in the construction industry.

Numerical investigation on the flexural behavior of geopolymer concrete beam reinforced with different types of fiber-reinforced polymer bars

Concrete is a highly versatile and durable building material. The risk of greenhouse gas emissions and the subsequent environmental deterioration associated with the use of concrete has prompted research on concrete substitutes. Geopolymer concrete (GPC) reinforced with fiber-reinforced polymer (FRP) rebars has gained acceptance as FRP rebars typically possess more tensile strength and are corrosion-resistant compared to steel. The commonly used FRP rebars are Carbon FRP (CFRP), Glass FRP (GFRP), Aramid FRP (AFRP), and Basalt FRP (BFRP). Though research has been done on GPC reinforced with CFRP, GFRP, and BFRP rebars; work has yet to be explicitly reported on GPC reinforced with AFRP. Furthermore, comparative studies on the flexural strength of GPC beams reinforced with different FRP rebars are not available, which calls for additional research on GPC reinforced with various FRPs. This paper compares the flexural behavior of GPC beams reinforced with various FRP bars by performing a nonlinear finite element analysis using Abaqus. The different material constitutive models and parameters of concrete and FRP rebars are analyzed to model their complex nature in Abaqus. The load-deflection behavior and the failure modes of these beams are studied by simulating a four-point bending test in Abaqus. Different parametric studies are conducted on GPC with FRP rebars by varying the parameters of concrete and reinforcements. The results indicate that among the four FRPs considered in this study, CFRP bars performed better for tensile reinforcement, while steel stirrups showed better results for shear reinforcement. As there are no specific design standards for FRP-reinforced GPC beams, these results may be successfully applied to modifying the existing standards.

Shaking table experimental investigations on dynamic characteristics of CFRP cable dome

Carbon fiber reinforced polymer (CFRP) bars have the feature of lower density, higher strength and better anti-fatigue performance compared with steel bars. Therefore, CFRP is a kind of ideal material for a long-span spatial structure. To explore the dynamic performance of spatial structures and take full advantages of CFRP bars in long span cable dome structures, a CFRP cable dome scale model with a diameter of 5.4 m was designed for a shaking table test. In this model, struts and cables were made of CFRP material except that the internal ring beams were fabricated with steel. In the test, new types of joint forms and anchoring configurations for CFRP cable dome structures were proposed because the existing forms for steel domes cannot be applied to CFRP dome structures. In addition, three kinds of seismic waves including Elcentro wave, Kobe wave and Pasadena wave were selected to generate 12 load cases and the maximum acceleration was 900 Gal. The acceleration and strain response of the model under different types of seismic waves was researched. It is demonstrated that middle-ring upper joints have the largest acceleration response because the control vibration modes of the CFRP cable dome structure are anti-symmetric mode. In addition, a CFRP dome numerical model was established to carry out modal analysis by program ANSYS. By comparing the results of finite element modal analysis with the measured frequencies, the natural vibration modes of the structure are analyzed. Based on the results of seismic wave spectrum analysis and structural modal analysis, the Pasadena wave, which has a wide low frequency region for high Fourier amplitude, can excite the greatest acceleration response.

Mechanical properties of axially and eccentrically loaded CFRP–coral concrete columns

Bearing capacity tests were carried out on axially and eccentrically loaded coral concrete short columns reinforced with carbon-fibre-reinforced polymer (CFRP) bars. Parameters such as the ultimate bearing capacities and the stress in the CFRP bars and surface concrete were measured and analysed. All the columns failed due to the crushing of concrete in the compression zone. An increase in eccentricity not only decreased the ultimate bearing capacity, but also resulted in the shear fracture of CFRP longitudinal bars in the compression zone. In general, the stress of the longitudinal CFRP reinforcements in all specimens was quite low. The maximum stress of the CFRP bars in the columns was 105.78 MPa, just 23.5% of the ultimate compressive strength of the CFRP reinforcement. The superior bond between the CFRP bars and coral concrete conformed to the deformation coordination. A calculation method for the bearing capacity of CFRP-reinforced coral concrete short columns was developed and the calculated results were found to agree well with the test results.

Influence of elevated temperature on the microhardness and microstructure of carbon fiber reinforced polymers

Carbon fiber-reinforced polymer (CFRP) has attracted attention for the reinforcement and retrofitting of concrete structures. Thus, their degradation in elevated temperatures is important feature to investigate. Herein, influence of elevated temperatures on microstructure and microhardness properties of different types of CFRP was investigated. A series of CFRP plate-, sheet-, and bar-type samples were fired at 150, 250, 350, and 450°C. Crystal structural properties of epoxy resin matrices and carbon fibers in the CFRP composites were examined using X-ray diffraction analysis. An increase in surface defects was observed for the fired CFRP plates and bars; however, there was no significant difference between the microstructures of the fired CFRP sheets. Hardness of CFRP plates fired at 150 and 250°C substantially decreased from 0.67 to 0.62 and 0.47 GPa, respectively, compared to that of unfired CFRP plate. Similarly, hardness of CFRP bars fired at 150, 250, and 350°C decreased from 2.09 to 1.73, 1.63, and 0.62 GPa, which is reduced by 17, 22, and 70%, respectively, compared to that of unfired CFRP bar. Decrease in hardness is attributed to several factors, such as mechanical degradation in the resin matrix, fiber/matrix debonding, and an increase in microcracks on the surface.

Performance of composite stone beams with prestressed NSM longitudinal CFRP reinforcement subjected to bending

This paper presents an investigation on the performance of stone beams reinforced with prestressed near-surface mounted (NSM) longitudinal carbon fiber reinforced polymer (CFRP) bars subjected to bending. Seven composite stone beams and four bare ones were tested. The test variables included the reinforcement ratio and prestressing level of CFRP bars, and the shear span to depth ratio of the tested beams. Test results showed that, the composite stone beams with either prestressed or non-prestressed reinforcement exhibited a ductile failure with visible deflection and multiple cracks. As the level of prestressing force increased, the cracking load and the shear capacity of composite stone beams increased but the deformation capacity decreased. The increase in reinforcement ratio could suppress the crack propagation and increase the flexural capacity of composite stone beams. As the shear span to depth ratio decreased, the cracking load, the shear capacity, and the peak load corresponding to flexural capacity of composite stone beams increased accordingly. Theoretical models for predicting the cracking and peak moments of composite stone beams were developed based on sectional mechanical analysis, and a good agreement with the experimental results was obtained.

Experimental assessment of the thermo-mechanical bond behavior of NSM CFRP with cement-based adhesives

Cement-based materials, which are incombustible and show low thermal diffusivity, show great potential as a valid alternative to polymeric matrices for bonding near surface mounted (NSM) carbon fiber reinforced polymer (CFRP) systems for the strengthening of reinforced concrete (RC) structures. The performance of these materials in different loading conditions, including high temperature exposure, still needs to be better explored. This paper presents a study on the characterization of the bond behavior using cement-based adhesives and CFRP strips with innovative surface treatment. The CFRP strips used in this study were manufactured specifically with sand-treated surfaces to improve the bonding performance between CFRP and cement-based adhesive by taking advantage of the better grip of increased roughness surfaces. The results of the pull-out tests in ambient conditions, as well as exposed to elevated temperatures, are presented and discussed. The effect of using sand particles of different sizes, adhered with two different resins on the CFRP strips surface embedded in different cement-based matrices, was compared. The obtained results showed that by applying a sand treatment on the surface of CFRP strips, the maximum pull-out force was up to 12 times higher than when using smooth surfaced strips. Pull-out tests showed that, by using the NSM sand treated CFRP strips and CFRP bars with cement-based adhesive, an average bond strength up to about 9 MPa and 11 MPa, respectively, could be achieved. Thermo-mechanical pull-out tests showed the proposed strengthening system is able to withstand up to 30 min of heat exposure before bond failure.

Shear behavior of composite stone beams reinforced with NSM longitudinal CFRP bars

Employing near-surface mounted (NSM) carbon fiber reinforced polymer (CFRP) bars in the tensile zone of bare stone beams can effectively improve their flexural performance. Meanwhile, shear failure could occur when excessive amount of flexural reinforcement is adopted. Seven composite stone beams were tested to study the shear behavior of composite stone beams reinforced with NSM CFRP bars. The test variables included the shear span to depth ratio and the reinforcement ratio. Digital Image Correlation (DIC) technology was used to capture the full-field strain of the beams. The results indicated that the composite stone beam exhibited ductile failure mode with visible deflection and multiple cracks formed in both constant bending zone and flexural-shear zone. With the decrease of shear span to depth ratio, the cracking load and shear capacity increased linearly but the deformation capacity decreased. For the same shear span to depth ratio of 2.5, the composite beam with a higher CFRP reinforcement ratio observed higher shear load-carrying capacity. DIC results demonstrated the shear force was mainly provided by the arch action before failure. A shear-resistance theoretical model based on Rankine's failure criteria, sectional mechanical analysis and experimental observations was proposed and verified with the current and previous test results.

Ultra high performance concrete and C-FRP tension Re-bars: A unique combinations of materials for slabs subjected to low-velocity drop impact loading

In this research work, different combinations of normal strength concrete (NSC), ultra-high-performance concrete (UHPC), and steel fiber-reinforced UHPC (SFR-UHPC) concrete with re-bars of conventional steel and of carbon fiber-reinforced polymer (C-FRP) are used in a two-way square slab of size 1000mm x 1000mm x 75mm subjected to 2500 mm free-fall impact loading. Experimental arrangement consisting of 105 kg dropping weight with the circular flat impacting face of 40 mm diameter used for carrying out impact test is modeled using a high-fidelity physics-based finite element computer code, ABAQUS/Explicit-v.6.15. After validating the experimental results of the NSC slab with steel bars, analyses are extended by replacing NSC and steel bars with UHPC/SFR-UHPC and C-FRP bars, respectively, under the same dropping weight. Only the remote face (tension face) of the slabs is provided with the re-bars. Widely employed and available with the ABAQUS, the Concrete Damage Plasticity model with strain-rate effects has been entrusted for simulating the concrete plastic response. Re-bars of steel are idealized with the Johnson-Cook plasticity damage model. C-FRP re-bars are defined with the classical plasticity model following the elastic-plastic constitutive laws. The impact responses of the slabs consisting of NSC/UHPC/SFR-UHPC concrete with re-bars of steel, and C-FRP combinations considered are discussed and compared. Slabs made of UHPC/SFR-UHPC concrete with the C-FRP re-bars are found to offer a promising combination of materials to withstand low-velocity impact load with little damage and extraordinary impact performance.

Bond behavior of an ultra-high performance concrete-filled anchorage for carbon fiber-reinforced polymer tendons under static and impact loads

To investigate the bond behavior of an ultra-high performance concrete (UHPC)-filled bond-type anchorage for carbon fiber-reinforced polymer (CFRP) tendons, both static tensile tests and impact tests were performed on 20 groups of specimens. The anchorages with embedded lengths of 50, 100, 150 and 200 mm were subjected to the static tension and longitudinal impact loads with drop heights of 150, 300, 600 and 900 mm. During the tests, the longitudinal tension and slip of the anchorage were obtained, and the effect of anchorage length and loading rate on the bond behavior was discussed. The results show that in the static tests, slip failure occurred for the anchorages with lengths from 50 to 150 mm, and CFRP bar ruptured as the length raised to 200 mm. When subjected to impact loads, slip failure was observed for all specimens. The damages on the CFRP bar to UHPC interface under impact loads were slighter than those under static tension, and correspondingly the dynamic bond strength was approximately half of the static one owing to the weakened mechanical interlocking. With increasing the embedded length, the bond strength and slip increased due to the radial constraining effect of outside steel tube. Based on the experimental results, a strain rate-dependent function was proposed to quantify the retention of bond strength under impact loads, and prediction formulas were established for determining the dynamic bond strength and critical embedded length of the bond-type anchorage.

Numerical and Statistical Evaluation of the Performance of Carbon Fiber-Reinforced Polymers as Tunnel Lining Reinforcement during Subway Operation

Ground vibrations during train operations have become a serious problem in recent years. Local residents often feel disturbed by the vibrations emanating from the railroad line. This inconvenience is particularly pronounced in loose areas traversed by subways. However, improving the mechanical properties of tunnels has been the subject of several studies. Among these works, the widely discussed fiber-reinforced polymer (FRP) is considered as a material that can be incorporated into the tunnel structure to increase stiffness, durability, and corrosion resistance. However, the function of FRP in the interaction between the soil and the tunnel during operation has scarcely been studied. In this study, the effectiveness of carbon fiber-reinforced polymers (CFRP) as reinforcement of tunnel lining on ground vibration is investigated. For this purpose, a nonlinear 3D finite element model was developed based on a subway section in Shanghai to simulate the dynamic behavior of the system. The moving subway load was modeled as a transient dynamic load via a DLOAD subroutine, in which the rail irregularities are taken into account. The numerical model was efficiently validated by field tests. Then, the efficiency of using CFRP as concrete reinforcement of the tunnel lining during the subway operation was investigated. In addition, a statistical analysis of the ground dynamic response depending on the CFRP bars properties is presented, evaluated, and discussed.

Prediction of Structural Behavior of Continuous Reinforced Concrete Beams with Hybrid CFRP-Steel Bars.

The present investigation aims to identify the flexural performance of two-span concrete beams reinforced with hybrid carbon fiber reinforced polymer (CFRP) and steel bars. By applying a finite element analysis, a comprehensive numerical assessment is performed. The investigated variables are Af/Ar (Af = area of CFRP bars; Ar = total area of CFRP/steel bars), load pattern (symmetrical and unsymmetrical loading) and load type (center-point, third-point and uniform loading). The results show that beams with Af/Ar of 0.25 show 16.0% and 11.3% higher ultimate load at symmetrical and unsymmetrical loading, respectively, than beams with Af/Ar of 0.0 (i.e., beams with steel bars), but the change in ultimate load is not apparent when varying Af/Ar between 0.25 and 1.0. Unsymmetrical loading causes 6.0-15.0% greater deflection capacities than the symmetrical one. When Af/Ar increases from 0.0 to 1.0, moment redistribution at symmetrical loading is decreased significantly by 62%, while the redistribution variation is marginal at unsymmetrical loading. In addition, the applicability of two equations based on the ultimate strain in tensile bars for predicting moment redistribution is evaluated. It is generally shown that these equations can account for the influence of Af/Ar and load type.

Flexural Behavior of Reinforced Concrete Beams with FRP Bars Exposed to Elevated Temperature

The present study aims to evaluate the performance of concrete beams with different Fiber Reinforced Polymer (FRP) and steel bars exposed to elevated temperatures through a detailed experimental investigation. Flexural behavior of beams is analyzed with Carbon Fiber Reinforced Polymer bars (CFRP), Basalt Fiber Reinforced Polymer bars (BFRP), Glass Fiber Reinforced Polymer bars (GFRP), and steel bars tests. Beams were exposed to elevated temperature 925 °C (1 hr) following standard fire curve, and subsequently cooled by either natural or forced water spraying. After the cooling, beam specimens were tested under four-point loading up to the failure load. Ultimate load and deflection profile of heated and unheated beams are evaluated. At higher temperatures (925 °C), the steel and GFRP specimens show a higher strength loss of about 60–80% with higher deformation values. The load carrying capacity of CFRP beams is found to be higher as compared to other types of beams. Specimens cooled by water shows higher strength loss of about 7–12% than air cooled specimens. The failure pattern of beams with FRP and steel beams are different, and it is based on heating cooling regime.

Nonlinear finite element investigation on shear behaviour of simply supported and continuous RC T-beams retrofitted with deep embedded CFRP/steel bars

The shear performances of simply supported (SS) and continuous (CN) reinforced concrete T-beams strengthened with deep embedded (DE) steel or carbon fibre-reinforced polymer bars are compared in this investigation. A nonlinear finite element (NLFE) analysis is performed for this purpose by modelling these beams with the FEM software by validating with the experimental data from the published studies. The experimental and NLFE shear strength values are then compared with those of the available design models to examine the efficacy of these models. Thereafter, the parametric study is conducted to obtain the impact of beam types (SS and CN) on the structural performances. It shows that the DE-strengthened CN beam provides higher shear capacity in comparison to the corresponding SS beam. However, the enhancements of the shear strength of SS beam due to strengthening with DE bars are significantly higher than that of the corresponding CN beam.

The behavior of alkali-silica reaction-damaged full-scale concrete bridge deck slabs reinforced with CFRP bars

Steel material is susceptible to corrosion after being in an aggressive environment and chemical attacks causing major deficiencies and failure; in some cases, maintenance or repair is necessary. Consequently, carbon fiber-reinforced polymers (CFRP) materials have been innovated to replace the usage of conventional steel reinforcement. In this study, the behavior of reinforced concrete bridge deck slab has been investigated under the effect of ASR damage and internal reinforcement with CFRP bars. However, the effect of the reinforcement type (CFRP and steel), reinforcement ratio (0.38, 0.46, and 0.57) %, and ASR damage stage (without, first, second, and third) has been carried out using the NLFEA technique after a well-calibration process against available experimental data. Generally, it has been noticed that the utilization of CFRP bars significantly improved the slab's strength in compression and tension, stiffness, and modulus of elasticity. Moreover, an innovative and cost-effective reinforcing technique, using CFRP bars with a 0.38% ratio or 0.46% reinforcement ratio, represents an ideal solution to improve the ultimate load-carrying capacity, serviceability, and durability. In addition, CFRP exhibited more strain values in concrete and steel materials and decreased under exposure to ASR damage action. Under exposure to ASR damage action, both the elastic and post-cracking stiffnesses are reduced regardless of the reinforcement type. Generally, it has been observed that the resulting degradation could be approximated by a parabolic shape having a slower decreasing rate at ASR levels of 2 and 3 where the material's losing most of its mechanical properties. Finally, a linearly decreasing relationship was found between the slab's energy capability and ASR level.

Bond-behavior improvement of carbon fiber reinforced polymer bars: an experimental study

Bond-behavior improvement of carbon fiber reinforced polymer bars: an experimental study

Flexural performance of RC beams strengthened with inorganic adhesive bonded NSM CFRP bar

Organic adhesives (e.g. epoxy) have been widely utilized in near-surface mounted (NSM) carbon fibre reinforced polymer (CFRP) strengthening technique for reinforced concrete (RC) structural members. Their inevitable shortcomings, such as poor fire resistance, emission of toxic fumes, and incompatibility with concrete substrate, necessitate the advancement of eco-friendly inorganic adhesives. In this study, two types of inorganic adhesives, including ordinary Portland cement mortar (OPCM) and alkali-activated slag mortar (AASM), were adopted in the NSM CFRP bar strengthening method for RC beams. The inorganic adhesive type, bonding length, and additional anchorage device on CFRP bar were considered as parameters in the strengthening scheme. One control beam and four strengthened beams were fabricated and tested, followed by comparison of their failure modes, loading behaviour, and reinforcement strains. The results show that all the strengthened beams exhibit higher ultimate loads than the control beam. Comparing to the OPCM, the AASM is more effective in mitigating debonding of CFRP bar and enhancing the ultimate load of beams. Furthermore, it is essential to provide a sufficient bonding length for AASM bonded NSM CFRP bars to guarantee their strengthening effectiveness. The addition of anchorage device for CFRP bars can further enhance the synergistic action between CFRP bar and adhesive, leading to a further enhancement in flexural strength and CFRP bar strain. In addition, the flexural strengths of OPCM or AASM bonded NSM CFRP bar-strengthened beams can be accurately predicted by the equations provisioned in ACI 440.2R-2017.

Study on Bond-Slip Behavior between Seawater Sea-Sand Concrete and Carbon Fiber-Reinforced Polymer (CFRP) Bars with Different Surface Shapes.

The application of CFRP bar and seawater sea-sand concrete (SSSC) in construction can overcome the shortcomings in conventional reinforced concrete, such as corrosion induced by carbonation and chloride ingress. In this study, the bond-slip behavior between an SSSC cube and CFRP bar has been investigated, and different CFRP bar surface shapes have been considered. A total of 27 specimens (9 groups) were fabricated for a pull-out test, where three types of CFRP bar with different surface shapes were used: smooth regular bars, double-wrapped bars and ribbed bars. Bond strength, bond-slip curve, and failure mode have been presented and discussed. FE models have been constructed and validated by experimental results. The effect of concrete compressive strength and relative area of ribs on bond strength has been studied through numerical simulations. It is found that the bond strength increased with concrete compressive strength, and the ribbed bar had significantly higher bond strength than the smooth regular bar. Pull-out failure was observed when the cover-depth-to-bar-diameter ratio was no less than 4 and, otherwise, splitting failure occurred. In addition, a simple formula has been proposed to approximately evaluate the bond strength between an SSSC cube and CFRP bar and validated by experimental results, and analytical expressions for different bond-slip curves have also been developed.

Bond performance of FRP bars in plain and fiber-reinforced geopolymer under pull-out loading

Geopolymer-bonded fiber-reinforced polymer (FRP) bar is an emerging strengthening system for concrete structures, owing to the excellent geopolymer/concrete bond and the superior moisture and fire resistance of geopolymer matrix (compared to organic bonding adhesives). To apply this strengthening system, the bond performance between FRP bars and geopolymer should be properly understood. In this study, pull-out tests on 81 specimens with a carbon FRP (CFRP) bar embedded in plain and fiber-reinforced geopolymer were conducted. Key factors including the strength of geopolymer (different mass ratios of fly ash and slag), bar embedded length (5, 10, and 15 times the bar diameter), fiber volume fraction in geopolymer (0, 1%, and 2%), and bar diameters (3 mm, 6 mm, and 10 mm) were explored. The results showed that (1) an increase in geopolymer strength improves the bond strength; (2) increasing embedded length (from 5db to 15db) would reduce the average bond strength (by 20–30%); and (3) adding steel and PVA fibers in geopolymer had a marginal effect on the bond strength. Furthermore, a modified bond strength model of CFRP bars in the geopolymer mortar is proposed based on the current experimental results. The findings lay the groundwork for understanding the bond behaviour of FRP bars in geopolymer, which is critical for the successful application of geopolymer-bonded FRP bar strengthening system.

Experimental study on lap behavior of CFRP indented bars in UHPC

The lap behavior of Carbon Fiber Reinforced Polymer (CFRP) indented bars in Ultra-High Performance Concrete (UHPC) were investigated based on pullout test under direct tension on 27 specimens in total. The test variables include splice length, UHPC strength and stirrup ratio. The lap failure mechanism of CFRP bar embedded in UHPC and the influence of test parameters on lap performance were analyzed. Test results showed that the failure modes, pull-out and rupture of CFRP bar, in those lap-spliced specimens were governed only by the splice length of the CFRP bar embedded in UHPC. The pullout failure was caused by the shearing off of indented ribs on the surface of the bars and the fracture failure was governed by the tensile strength of the bars. The bond strength of lap-spliced indented CFRP bars in UHPC is mostly dependent on the shear strength of indented ribs on CFRP bars, little on the UHPC strength and stirrup ratio. For CFRP bars with a 2480 MPa tensile strength and a 9.8 mm diameter (d), a splice length of 30d in UHPC can fully develop the tensile strength of the bar. A simplified equation for predicting the critical splice length of CFRP bars in UHPC was proposed. Compared with the results on anchorage of CFRP bars in UHPC, the critical splice length of CFRP bar in UHPC was 1.45 times the corresponding anchorage length.