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Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique
Engineering Structures 101 (2015) 34–44
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Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique Xin Wang a,b, Jianzhe Shi b, Gang Wu a,b, Long Yang b, Zhishen Wu a,b,⇑ a b
Key Laboratory of C & PC Structures Ministry of Education, Southeast University, Nanjing 210096, China International Institute for Urban Systems Engineering, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 10 June 2014 Revised 26 June 2015 Accepted 29 June 2015
Keywords: BFRP tendon External prestressing Flexural performance Tension control stress Bending angle
a b s t r a c t This paper investigates the feasibility of newly developed basalt fiber reinforced polymer (BFRP) as prestressing material and the structural behavior of reinforced concrete (RC) beams strengthened with externally prestressing BFRP tendons. Three main factors potential controlling structural strengthening effects, including tension stresses, bending angles and anchorages of the tendons, were first discussed based on literature review and finite element (FE) simulation. In the structural experiment, the effects of tension stresses and the tendon profiles on the flexural behavior of RC beams were discussed and the evaluation on the ultimate bearing capacity, cracking moment, crack width and deflection of strengthened beams was conducted by theoretical calculation and experimental results. The results show that the prestressing level of BFRP tendon can be determined to be 0.50fu and 0.38fu (fu is the tensile strength) according to creep rupture limit. The bending angle at the deviator is optimized to be 2° and the bond anchorage with resin epoxy was adopted to maximize strength utilization. For strengthening behavior, the second-order effect of the externally prestressed beam can be effectively relieved by using proper deviators, which is demonstrated by enhanced ultimate capacity. All of the strengthened RC beams are failed by concrete crushing, with satisfactory crack patterns and superior ductility compared to the control beam, which demonstrates the simultaneous working of internal steel reinforcements and external prestressing BFRP tendons during loading. The evaluation on mechanical behavior of strengthened RC beams indicates theoretical calculation according to several existing standards can well predict strengthening effect. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Strengthening of reinforced concrete (RC) beam by external prestressing technology with steel tendons has been developed for strengthening bridge and building structures as well as for use in new construction in recent decades [1,2]. The technology is characterized by several advantages, including the possibility of replacing tendons, reducing web thickness by eliminating internal tendons and the capability of applying precast segmental construction methods. Numerous researches have demonstrated that the behavior of service and ultimate states under static load can be effectively enhanced and the deflection induced by fatigue can be significantly decreased by external prestressing tendons [2–4]. However, the issues of steel corrosion and related fatigue degradation, which can greatly affect the structural durability and result in ⇑ Corresponding author at: International Institute for Urban Systems Engineering, Southeast University, Nanjing 210096, China. Tel.: +86 2583793232. E-mail address: [email protected] (Z. Wu). http://dx.doi.org/10.1016/j.engstruct.2015.06.052 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
catastrophic failure, still restrict their wider applications [5,6]. To overcome the above shortcomings, fiber-reinforced polymer (FRP) composites have been developed in the application of the structural strengthening owing to their high strength, light weight, and corrosion and fatigue resistance [7]. Because of the anisotropic property of unidirectional FRP members, the most efficient application of FRP is considered to be a tension-only element with prestressing technology in the forms of sheets, plates and tendons. For instance, the external-bonded prestressing CFRP sheets, plates and external unbounded prestressing FRP tendons have demonstrated their effectiveness in enhancing service and ultimate behavior of the RC beams [8] and the prestress losses due to FRP material are limited [9–11]. For prestressing materials, conventional carbon FRP (CFRP) and aramid FRP (AFRP) tendons are adopted because of their high creep rupture stress in comparison to glass FRP (GFRP), which is not allowable for prestressing because its creep rupture stress is less than 30% of the tensile strength (fu). However, the constant high cost and brittle behavior of CFRPs and large relaxation and cost issue for AFRPs continue to limit their
X. Wang et al. / Engineering Structures 101 (2015) 34–44
acceptance for replacing steel tendons in external prestressing applications. Basalt FRP (BFRP) is a newly developed composite material that has receiving significant attention in strengthening constructions. Basalt fibers are environmentally friendly inorganic materials produced from volcanic rock by using single-component raw materials and drawing fibers from the molten rock at a temperature of 1400–1500 °C. The greatest attraction of BFRPs lies in their superior integrated properties compared with conventional FRP composites, such as their greater than 25% higher strength and modulus, similar cost, and increased chemical stability compared to GFRPs as well as a wider range of working temperatures and much lower cost compared with CFRPs [12,13]. Recent studies reveal that BFRPs can be tensioned up to approximately 52%fu without creep rupture [14] and perform efficiently as cables for long-span bridges [15–17]. Moreover, BFRPs and their hybrid tendons also show superior performance under marine environment [18]. These advantages allow their potential application as prestressing tendons. Therefore, the combination of external prestressing technology and BFRP tendons should be a promising way to realize a new prestressing method.
2. Review of previous work In previous studies, the CFRPs, AFRPs and GFRPs were all investigated as the external prestressing tendons in RC beams strengthening. Lou et al. [19] focused on the static behavior of RC beams strengthened with CFRP and GFRP tendons and concluded that the structural performance of beams externally prestressed by CFRP tendons was similar to those prestressed by steel tendons, and the ductility of beams externally prestressed by GFRP tendons was even better, although their ultimate strength was lower than external steel tendon-strengthened beams. Similar studies by Pisani [5] also concluded that GFRP cables were reliable when applied to external prestressing and AFRP cables were suitable for bonded prestressing. Although GFRP achieved superior structural behavior by external prestressing strengthening, the low creep rupture limitation of GFRP tendon, usually less than 30%fu, greatly restricts its high efficiency in prestressing application. While, no recommendation on CFRP tendon was proposed because of their high cost and low ductility. Because of the importance of deviators in external prestressing applications, Ghallab et al. [11,20] conducted a comprehensive study on RC beams prestressed by deviated Parafil ropes (AFRP) to explore several factors affecting external prestressing stresses. They concluded that the number of deviators, the effective prestressing stress of tendon and the horizontal distance between deviators had significant effects on the stress distribution in external tendons. Regarding the long-term performance, Saadatmanesh et al. [21] reported that although the fatigue and creep performance of AFRP tendons were good, its relaxation losses were excessively high, especially in alkaline or acidic solutions. Investigations of RC beams strengthened with externally prestressed BFRP tendons have not been found in the existing literature. Based on the above review, it can be concluded that the application of BFRP tendons as external prestressing materials not only provides advantages in the ductility of strengthened structures but also avoids limitations of low creep rupture stress such as that with GFRPs. Thus, a comprehensive study of the mechanical properties of BFRP tendons as prestressing components, the relevant key factors controlling strengthening effects and the strengthening performance of structures should be conducted. In this study, an experiment was conducted on a series of large-sized concrete beams with T-shaped sections prestressed by external BFRP tendons. The tension control stress and bending angle for the BFRP tendons were determined based on the creep
35
rupture behavior and on existing study together with a finite element (FE) analysis, respectively. The effects of the tension control stress and the tendon profile on the flexural performance of the strengthened RC beam were discussed. Finally, the evaluation of design methods for BFRP externally prestressed concrete beams was conducted based on the existing specifications. 3. Key factor determination for BFRP prestressing tendons 3.1. Tensile strength of BFRP tendons BFRP tendons with a diameter of 12 mm were adopted in the study, which were manufactured using basalt fiber roving of 4800tex and vinyl ester resin through pultrusion technology. The fiber volume fraction of each BFRP tendon was approximately 60%, and the total length of each specimen for the tension test was 1250 mm. The two ends were treated by sand blasting over a length of 300 mm and anchored with seamless steel tubes with an outer diameter of 20 mm and thickness of 2 mm. Epoxy resin was used to fill the gap between the steel tube and the BFRP tendon, and the specimen was allowed to cure for seven days to ensure that sufficient strength was achieved. Five specimens were tested with a loading rate of 500 MPa/min according to ACI 440.3R-04 [22]. All specimens failed in the middle portion of specimen without any failure in the anchorage. BFRP tendons with a diameter of 12 mm exhibit an average strength of 1208 MPa, which is relatively lower than the strength in thinner BFRP tendons, typically 1450 MPa for a diameter of 6 mm. However, the coefficient of variation (C.o.V) of the tensile strength is quite low (0.84%), which makes the utilization of tendons highly efficient. The mean value of elasticity modulus is 48.6 GPa, with the C.o.V equal to 0.53%. Based on the 95% strength guarantee, a characteristic value for the tensile strength of 1192 MPa is adopted for the following experiment. 3.2. Creep rupture stress limitation Creep rupture stress is a critical factor limiting the prestressing level of FRP tendons. It is characterized by a time-dependent increased strain up to rupture when an FRP tendon is subjected to a sustained load of a certain level. Thus, the determination of the tension stress of BFRP tendons should first take into consideration the creep rupture stress and ensure that the tendon can maintain loads without creep rupture. Based on the previous study results [14], a million-hour creep rupture stress of 6 mm BFRP tendons with a vinyl ester matrix is regressed to be 0.59fu, and the design recommendation of the creep rupture limitation is 0.52fu based on the reliability analysis with 95% assurance. Consequently, the tension stress of the BFRP tendons in the current study should be controlled below 620 MPa. Because BFRP is adopted for prestressing tendons for the first time, the final tension control stresses were adopted to be conservative values of 0.50fu and 0.38fu, respectively, as well as for convenience. 3.3. Bending angle for the BFRP tendon at the deviator The deviator plays a significant role in enhancing the structural behavior of externally prestressed RC beams by reducing second-order effects, which are defined as the gradual decrease of the effective prestressing force with respect to increasing deflection. However, the stress distribution of BFRP tendons near the deviator is inevitably complicated, which requires the necessity of cautious determination of the bending angle for the tendon at the deviator. Several types of stresses exist near the deviator, such as friction, axial tensile stress generated from tension along with
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bending, and transversal compression, which can result in a reduction of the ultimate strength of the FRP tendon. Thus, an appropriate bending angle should be studied to allow stress to transfer smoothly. Through the computational formula shown in Eq. (1), the strength reduction of a tendon at the bending area can be calculated based on the existing experimental results [23,24]. The bending angles ranging from 1° to 5° and the corresponding strength reduction percentages compared to the initial strength are shown in Table 1. 0
f fu ¼ f fu
2Ep Rp h pR
ð1Þ
where f0 fu is the actual strength; ffu is the initial ultimate strength without bending; and Ep = 48.2 GPa, Rp = 6 mm, h in rad and R = 72.5 mm are the elastic modulus of the tendon, radius of the tendon cross-section, bending angle and the radius of deviator, respectively. It can be found from Table 1 that the bending angle should be confined to less than 3° to avoid the strength reduction percentage exceeding 10%. Therefore, the bending angle for BFRP tendons in the current study was tentatively determined to be 2°. Because of the complexity of the stress state for BFRP tendons at the deviator, an FE analysis by ANSYS was also conducted to evaluate the stress distribution in the BFRP tendon at the bending area, comprehensively considering fiction and transverse compression between the deviator and the tendon. The element type of SOLID45 was adopted for the BFRP tendon and the deviator. The bending angle of the BFRP tendon was 2°. The geometric model used for the analysis is shown in Fig. 1(a). The analysis result shows that the axial stress of the tendon reaches a climax at the contact zone with the deviator, while the axial stress in the other area along the tendon is sufficiently uniform. When a maximum axial stress (fu = 1192 MPa) is reached, the stress value applied along the axial direction of tendon is equal to 1015 MPa, with relative error of 8% compared with the results from Eq. (1). The analysis shows that a bending angle of 2° is appropriate for the external BFRP prestressing tendon as the excessive stress concentration can be avoided. Above results can be observed from the Fig. 1(b) and (c), clearly illustrating the stress distribution at the bending area of the BFRP tendon. 3.4. Anchorage for BFRP prestressing tendons Several anchoring methods for BFRP tendons have been attempted to assure the performance of the tensile strength of BFRP tendons. The anchor methods included wrapping impregnated fiber roving at the anchorage zone (WR), utilizing bond anchorage with epoxy resin (SR), and utilizing friction anchorage with expansive cement filling a cylindrical steel sleeve (SC). The strength results from the above anchors are: 1064 MPa for WR, 1154 MPa for SC and 1208 MPa for SR. As a consequence, bond anchorage with epoxy resin was adopted as the anchoring method in the current study because there exists radial stress in the other two anchoring methods, leading to strength reduction at the anchorage zone of the tendon.
Fig. 1. Finite element analysis: (a) geometric model for FE analysis, (b) local stress nephogram for FRP tendon, (c) entire stress nephogram.
Table 1 Bending angles and corresponding strength reductions. Bending angle (°)
1
2
3
4
5
Strength at bending area (MPa) Strength reduction percentage (%)
1147.7 3.72%
1103.4 7.44%
1059.0 11.15%
1014.7 14.87%
970.4 18.59%
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X. Wang et al. / Engineering Structures 101 (2015) 34–44 Table 2 Details of specimens. Specimen number
BC
BD-0.38
BD-0.50
BS-0.50
Prestressing value (MPa) Prestressing level Diameter of BFRP prestressing tendon (mm) PPRa Tendon profile
– – –
447 0.38fu 12
596 0.5fu 12
596 0.5fu 12
0 –
0.57 Deviated
0.57 Deviated
0.57 Straight
4. Experiment on RC beams externally prestressed by BFRP tendons 4.1. Details of specimens
Fig. 2. Schematics for geometric dimensioning and reinforcements of specimens (dimensions in mm).
To validate the effectiveness of externally prestressing BFRP tendons for concrete beams, a proving test was conducted on four large-sized RC beams, among which BD-0.38, BD-0.50 and BS-0.50 were the beams externally prestressed by BFRP tendons and the BC was the control beam. The strength grade of the concrete for all of the specimens was C30. The main variables were the tension control stress and the tendon profile. Details such as material properties and the reinforcements for the specimens are given in Tables 2 and 3. All specimens had the same geometric dimensioning as shown in Fig. 2. The span of all specimens was determined to be 5700 mm, with a span-depth ratio of 11.4. The deviated tendons with horizontal bending angles of 2° or straight tendons (as shown in Fig. 3) were located symmetrically on both sides of the prestressed beams. The vertical distance from the anchoring zone to the bottom surface of the beam remained constant between the two types of tendon profiles to guarantee identical eccentricity. The configuration of the deviator is shown in Fig. 4. 4.2. Tension procedure of the BFRP prestressing tendon Tendons were fixed at the position of the anchor plates by nuts (Fig. 5(a)) and tensioned by the apparatus shown in Fig. 5(b). To minimize the loss of prestressing due to an asynchronous tension of the BFRP tendons, over-tensioning with stress values up to 1.1rcon and 1.05rcon (rcon = the tension control stress) was adopted to adjust the tension stress in both tendons to rcon. 4.3. Test setup, loading method and measurement As shown in Fig. 6, all the specimens were simply supported and tested under four-point loads. The load was applied on the specimens with a loading rate of 5 kN every two minutes. A hydraulic jack with a capacity of 500 kN was used. A load cell between the hydraulic jack and the distributive girder was installed to monitor the load values during the loading process. The strains of the steel reinforcements, BFRP prestressing tendons and the strains at different heights of the midspan cross-section were measured by strain gauges. Deflections at the
midspan and the supports were measured by dial indicators. All data were collected automatically by a TDS 530, produced by Tokyo Measuring Instrument Laboratory (TML), and transmitted synchronously to a computer once every two seconds. The distribution of cracks was recorded artificially by tracing the main cracks and recording the crack shapes on the surface of the specimens. 5. Results and discussion 5.1. Summary of experimental results The experimental results are given in Table 4, where Pcr is the cracking load; Py is the load at the yielding of the steel reinforcements (yielding load); Pmax is the ultimate load; Dy denotes the midspan deflections upon yielding of the steel reinforcements (yielding deflection); x donates the crack width at the stable stage of crack development of one main crack near the midspan; and Pl/400, Pl/300, and Pl/200 stand for the corresponding load values of the midspan deflections equal to l/400, l/300 and l/200, respectively, where l represents the center distance between the two supports, which is equal to 5700 mm. Photographs of the failure modes for the specimens are given in Fig. 7(a–d), which clearly show that the strengthened beam failed by concrete crushing, while the FRP tendons did not rupture, which is similar the concrete beams with unbonded FRP tendons [25]. The load–deflection curves of all of the tested beams are plotted in Fig. 8. It is observed that the overall flexural behavior of the beams strengthened by externally prestressed BFRP tendons has been significantly enhanced compared to that of the control beam (BC). All of the strengthened beams, including BD-0.38, BD-0.50 and BS-0.50, show 115.4%, 130.7%, and 115.4% higher cracking loads relative to the control specimen BC. For the yielding loads, corresponding increments of 36.2%, 51.1%, and 38.3% were observed, and for the ultimate load, 54.7%, 66.0%, and 43.4% were observed. Although the ductilities of the strengthened beams are generally lower than the control beam, they can still achieve 76.4%, 85.7% and 69.6% of the midspan deflection of the control
Table 3 Measured values for material properties of specimens. Material
Type or dimension
Elastic modulus (MPa)
Compressive strength (MPa)
Yield strength (MPa)
Ultimate tensile strength (MPa)
Ultimate strain (%)
Concrete Steel bar (stirrup) Steel bar (upper) Steel bar (lower) BFRP tendon
C30 A8
3.25 104 2.1 105
40.5 –
– 240
– 385
– 15
A10 B22 12 mm
2.1 105 2.0 105 4.82 104
– – –
275 340 –
375 450 1192
14.5 15 2.44
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Fig. 3. Lay-out drawing of specimens (dimensions in mm): (a) lay-out drawing for deviated tendons (1 through 5 stand for strain gauges), (b) lay-out drawing for straight tendons (1 through 3 stand for strain gauges).
Fig. 4. Deviator.
beam, which is much higher than the beams externally strengthened by prestressed high-strength steel or CFRP tendons [2,26]. The superior ductility is a result of the lower modulus and larger failure elongation of the BFRPs. It is also observed that the stiffness of the BFRP tendon prestressed RC beams is significantly improved after concrete cracking in comparison to that of the control beam. Thus, external prestressing of BFRP tendons is capable of effectively restraining cracks and deflections during service conditions and maintaining similar ductility to the control beam.
5.2. Flexural behavior discussion 5.2.1. Effect of tendon profile From the comparison of BD-0.50 and BS-0.50 in Fig. 8, it is observed that the tendon profile has a slight effect on the flexural behavior before concrete cracking because the deflections of the specimens are too small to generate an obvious second-order effect on the specimen. After concrete cracking, a slightly high stiffness and obvious high yielding load of the deviated specimen were observed in comparison to the straight line of BS-0.50 beam. As a result, a higher ultimate capacity and higher ductility were achieved by the deviated specimen of BD-0.50, which indicates that the second-order effect of the prestressing tendon profile affects the ultimate capacity as well as restrains deformations for concrete beams. Moreover, the BD-0.50 specimen better controls crack development compared to BS-0.50, but their maximum crack
widths are similar. The 16% enhanced ultimate loads of BD-0.50 in comparison to BS-0.50 indicates that the reduction magnitude of the second-order effect is significant for deviated external BFRP tendons, which benefits the simultaneous work of tendons and beam as a whole and the enhancement of the bearing capacity and stiffness of a structure. 5.2.2. Effect of tension control stress It can be concluded from the curves of BD-0.38 and BD-0.50 in Fig. 8 and Table 4 that as the tension control stress increases, the cracking, yielding and ultimate loads are improved accordingly. This is mainly because the failure of the external BFRP tendon strengthened beam is dominated by concrete crushing and because the potential strength of BFRP tendons with low tension stress cannot be utilized sufficiently. This phenomenon indicates that the higher initial stress in BFRP prestressing tendons benefits the whole structural strengthening effectiveness of externally prestressed beams. It should be noted that the upper limit of the initial stress should be lower than the creep rupture stress of BFRPs (52% of fu). 5.3. Crack patterns of specimens The crack propagation patterns of the four types of specimens are given in Fig. 9. Compared to the control beam BC, the specimens externally prestressed by BFRP tendons show relatively
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
fewer cracks with smaller crack widths, especially for BD-0.38 and BS-0.50. BD-0.50 shows more distributed cracking than BD-0.38 and BS-0.50 because of the integrated function of the high initial stress and the deviated tendon profile. In general, all beams exhibit similar crack patterns as a result of the restriction by internal steel reinforcements, without which abrupt failure may occur on externally prestressed beams as reported in the literature [19,27]. Thus, although the use of externally prestressed BFRP tendons can delay the occurrence of cracks, cracking distributions similar to normal RC beams remain. Furthermore, the distributions of RC beams prestressed by BFRP tendon perform more uniform than those prestressed by steel tendon [3]. This characteristic benefits BFRP-strengthened beams having similar ductility to RC beams. 5.4. Load–strain curves for specimens
Fig. 5. Tensioning apparatus of specimens: (a) Anchoring end. (b) Tensioning apparatus.
The relation between the loads and strains on the BFRP tendons and the steel reinforcements are shown in Fig. 10, in which the mean value of two strains at the midspan of the bottom steel reinforcements are included, and the mean values of the strains collected by the gauging points on a single BFRP tendon are used to represent the development tendency of the strain along the whole tendon. It is shown in Fig. 10 that the strains of the longitudinal steel reinforcements in the specimens with BFRP tendons are much less than those in the control beam, which is apparently a result of the prestressing provided by the external BFRP tendons. From the strain comparison of the steel reinforcements between the strengthened beams and the control beam, the enhanced cracking load and yielding load are easily observed. Three stages can be identified for each curve, with two inflection points representing the cracking of the concrete and the yielding of the steel reinforcements. By comparing the curves of the BFRP tendon and the steel reinforcement in the strengthened beams at different stages, it can be observed that they have approximately equal strain increments before the yielding of the steel reinforcements, after which their strain increments exhibit different trends depending on the different tendon profiles and prestressing levels. The strain increments in the BFRP tendon are 2.8 and 3.9 times that in the steel reinforcement for BD-0.38 and BD-0.50, respectively, from the yielding of the steel reinforcement to the failure of the specimen because external tendons are merely restrained at the anchorages and deviators. However, the steel reinforcements have effective bonds with the concrete. The corresponding increment of the BFRP tendon in BS-0.50 is 5% less than that in steel reinforcement because of significant second-order effects on BS-0.50. The results show that BFRP tendons on beams prestressed by a deviated profile can be more effectively used in comparison to that in straight-line strengthening. 5.5. Axial stress distribution along BFRP tendons The stress distribution of BFRP tendons along the length are shown in Fig. 11, which is converted from the measured strain multiplied by the elastic modulus, clearly demonstrating the strength utilization efficiency. In general, the figures show the different stress distributions with respect to the increasing load.
Fig. 6. Lay-out of loading device.
Table 4 Experimental results for specimens. Specimen number
Pcr (kN)
Py (kN)
Pmax (kN)
Pl/400 (kN)
Pl/300 (kN)
Pl/200 (kN)
Dy
BC BD-0.38 BD-0.50 BS-0.50
32.5 70.0 75.0 70.0
117.5 160.0 177.5 162.5
132.5 205.0 220.0 190.0
92.1 135.8 140.6 133.3
112.6 160.3 169.2 159.5
118.4 164.8 181.6 164.7
20.2 28.9 22.2 21.0
(mm)
x (mm)
Failure characteristics
0.14 0.10 0.08 0.14
Crush Crush Crush Crush
in in in in
concrete concrete, no failure in BFRP concrete, no failure in BFRP concrete, no failure in BFRP
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
Fig. 8. Load–deflection curves for specimens.
BD-0.38 at the midspan. In contrast, the stresses in BS-0.50 BFRP tendons maintain constant and uniform distribution up to failure. The different characteristics of the stress distributions of the three types of prestressed BFRP tendons are generated by the effects of the deviators and the tension stress. With higher initial tension stress, crack propagation and the deflection of the concrete beam can be restrained more effectively. Consequently, the ductility of BD-0.50 is also larger than that of BD-0.38 as shown in Fig. 8. Although the stress distribution of the BS-0.50 specimen exhibits a more uniform shape compared with BD-0.38 and BD-0.50, the ultimate capacity and ductility of BS-0.50 are lower than the other two deviated beams, which again proves that the secondary-order effect can greatly affect the structural strengthening behavior. 5.6. Stress increment-deflection curves
Fig. 7. Photographs of failure modes for specimens: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
Before the cracking load, the stress of all three types of BFRP tendons exhibits a similar uniform distribution regardless of the stress level and the effect of the deviators. The uniform distribution remains constant up to the yielding load (160–177 kN), at which a slight variation of the stress distribution can be observed for the two deviated BFRP tendons. Afterwards, the BFRP tendons with low tension stress exhibit significant differences between the stresses at midspan and the two ends. For the BFRP tendons with high tension stress, the stress at the midspan also increases faster than the stresses at the two ends, but the differences are much less than those of the BD-0.38 BFRP tendons. Low tension stress leads to earlier yielding of tensile steel reinforcements and consequently larger deflection, causing a sudden increase in the bending angle and more significant stress increments in the BFRP tendon on
The stress increments of prestressed BFRP tendons with respect to the deflection of the beam are given in Fig. 12. The mean values of the stress increment in the deviated BFRP tendons are analyzed due to the variation of stress along the tendons. As a type of linear elastic material, the stress increment of BFRP tendons exhibits an approximately linear relation with the midspan deflection. There is a slight fluctuation of each curve after yielding of the steel reinforcement due to a sharp increase of the deflection. As mentioned previously, the strain level of the BFRP tendon on BS-0.50 is relatively low at the failure of the specimen compared with BD-0.38 and BD-0.50, causing a small stress increment in its BFRP tendon. With the largest ultimate load, the ultimate deflection of BD-0.50 is also the largest among the three prestressed specimens. Furthermore, the stress increments in the BFRP tendons of BD-0.38 and BD-0.50 are more significant than those of BS-0.50 because of the existence of the deviator, which demonstrates once again the function of the deviator in allowing tendons to collaborate better with concrete beams. 5.7. Validation for plane cross-section assumption The mechanical analysis and the structure design for externally prestressed concrete beams are at the basis of the plane crosssection assumption, which was validated through the measurement of axial strains of concrete at different heights at the cross-section at the midspan. Five gauging points on the side surface of midspan were installed, and the distances from the bottom were 20, 140, 260, 380 and 450 mm. Values of the strain measured under 0.2Pmax, 0.4Pmax, 0.6Pmax and 0.8Pmax are chosen to represent the strain distribution during loading. The strains measured at each position of the midspan cross-section are shown in Fig. 13, in
X. Wang et al. / Engineering Structures 101 (2015) 34–44
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Fig. 9. Crack patterns of specimens: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
which it can be observed that the axial strains of the concrete at the midspan exhibit a linear distribution along the vertical axis of the cross-section with loads below 0.6Pmax, beyond which a non-linear stress distribution occurs as a result of crack development in the concrete. The distributions are consistent to the existing results [28]. 6. Evaluation of design methods 6.1. Calculation of ultimate capacity The design methods introduced here are all based on the analysis of unbonded prestressed structures. ACI 440.4R-04 is a recommendation provided by the American Concrete Institute (ACI) for
prestressed concrete structures with FRP tendons. BS 8110 is a code provided by the British Standards Institution (BSI) for practical design and construction, and JGJ 92-2004 is the technical specification provided by the China Academy of Building Research for unbonded prestressed concrete structures. The ultimate bearing capacity of concrete beams externally prestressed by BFRP tendons is calculated on the basis of the ultimate stress in the external tendon, which is recommended by the standards, as follows. For convenience, notations for the same parameter in different standards are modified to be identical. (1) ACI 440.4R-04 [29]
f ps ¼ f pe þ Ep Xu ecu ðdp =cu 1Þ
ð2Þ
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
Fig. 11. Axial stress distribution along the BFRP tendons: (a) BD-0.38, (b) BD-0.50, (c) BS-0.50.
(1) JGJ 92-2004 [31] Fig. 10. Load–strain relationship for specimen: (a) BD-0.38, (b) BD-0.50, (c) BS-0.50.
where fps is the stress in the prestressing tendon at failure; fpe is effective stress in the tendon, excluding prestress losses; Ep is the elastic modulus of the prestressing tendon; Xu is the strain reduction factor; ecu is the ultimate compressive strain of concrete; and dp and cu are the distance of the resultant point of the external prestressing tendon from the compressive edge of cross-section and the depth of the neutral axis at failure, respectively. (1) BS 8110 [30]
f ps ¼ f pe þ
1:7f pu Ap 7000 1 f cu bd p L=dp
ð3Þ
where fpu is the characteristic strength of the prestressing tendon (fps should not exceed 0.7fpu), Ap is the cross-sectional area of the prestressing tendon, fcu is the characteristic strength of the concrete and b and L are the width of the section and span of the beam, respectively.
f ps ¼ f pe þ ð240 335n0 Þð0:45 þ 5:5d=LÞ n0 ¼
f pe Ap þ f y As f c bdp
ð4Þ ð5Þ
where n0 is the integrated reinforcement index, which should not be larger than 0.4; d is the depth of the section; fc is the design value for the axial compressive strength of the concrete; and fy and As are the yielding strength and cross-sectional area of the steel reinforcements, respectively. Preliminary calculations show that the depth of the concrete compression zone is always less than the thickness of the flange, from which the ultimate bearing capacities of specimens can be calculated based on Eqs. (6) and (7):
f y As þ f ps Ap ¼ f c bf xc
ð6Þ
M ¼ f ps Ap ðdp xc =2Þ þ f y As ðh0 xc =2Þ
ð7Þ
43
X. Wang et al. / Engineering Structures 101 (2015) 34–44 Table 5 Ultimate bearing capacities obtained by several standards.
a
Specimen number
MExpa (kN m)
MACI (kN m)
MBS (kN m)
MJGJ (kN m)
MExp/ MACI
MExp/ MBS
MExp/ MJGJ
BD-0.38 BD-0.50 BS-0.50
205 220 190
234.02 234.02 213.81
212.48 226.61 200.51
182.98 197.13 183.25
0.88 0.94 0.89
0.96 0.97 0.95
1.12 1.12 1.04
MExp donates the experimental results.
Table 6 Experimental and theoretical values for cracking moment. Fig. 12. Stress increment–deflection curves.
where xc represents the equivalent compression height of the concrete, bf represents the width of the flange, and h0 is the distance from the resultant point of tensile steel reinforcements to the compressive edge of the cross-section. In terms of the above calculation formulae of the stress in the external tendon at failure, the ultimate bearing capacity of the external prestressed beam can be acquired, which is listed in Table 5. From Table 5, it can be determined that the theoretical results calculated by the formula provided by BS 8110 are closest to the experimental results, while ACI is the least conservative standard for the ultimate bearing capacity calculation.
6.2. Calculation for cracking moment, crack width and midspan deflection The calculation methods for the cracking moment of ACI [29,32] and JGJ [31] are fundamentally similar, with their differences lying
Specimen number
MExp (kN m)
MACI (kN m)
MJGJ (kN m)
MExp/ MACI
MExp/ MJGJ
BD-0.38 BD-0.50 BS-0.50
70.0 75.0 70.0
67.96 77.72 68.69
57.03 66.80 57.76
1.03 0.97 1.02
1.23 1.12 1.21
Table 7 Experimental and theoretical values for crack width. Specimen number
xExp
xACI
xBS
xJGJ
(mm)
(mm)
(mm)
(mm)
xExp/ xACI
xExp/ xBS
xExp/ xJGJ
BD-0.38 BD-0.50 BS-0.50
0.10 0.08 0.14
0.08 0.07 0.09
0.11 0.09 0.13
0.09 0.06 0.10
1.25 1.14 1.56
0.91 0.89 1.08
1.11 1.33 1.40
in the fact that the rupture strength of the concrete is adopted in ACI, while the tensile strength of the concrete is adopted in JGJ. From Table 6, it is obvious that ACI is more precise in the calculation of the cracking moment.
Fig. 13. Stress values at different heights on the midspan cross-section: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
44
X. Wang et al. / Engineering Structures 101 (2015) 34–44
(NSFC, No. 51378109) and the Transportation Science and Technology Project of Jiangsu Province (No. 2014Y01).
Table 8 Experimental and theoretical values for midspan deflection. Specimen number
fExp (mm)
fACI (mm)
fBS (mm)
fJGJ (mm)
fExp/ fACI
fExp/ fBS
fExp/ fJGJ
BD-0.38 BD-0.50 BS-0.50
8.60 7.51 8.56
8.43 6.72 9.35
11.80 8.08 11.63
7.94 7.14 7.21
1.02 1.12 0.92
0.73 0.93 0.74
1.08 1.05 1.19
Calculations for the crack width and the midspan deflection refer to ACI [29,32], BS 8110 [30,33] and JGJ [31], with the bending moment equal to 100 kN, and the results are listed in Tables 7 and 8. For the crack width, BS 8110 is the most accurate standard, while the theoretical results of ACI and JGJ tend to be lower than the experimental results because they both fail to consider second-order effects well. However, for the deflection calculation, the accuracy of BS 8110 is not satisfactory, while deviations of the theoretical results of ACI and JGJ from the experimental results are less than 20%. One other point to note is that the values of the deflections from BS 8110 are conservative, but the other two standards do not tend to be very safe. 7. Conclusion To validate the effectiveness of BFRP tendons as an external prestressing material, several key factors affecting the strengthening effect and a series of RC beams strengthened by external prestressed BFRP tendons were studied. The effects of tension stress and the tendon profile of the prestressing tendons on the flexural behavior of strengthened RC beams, including cracking load, yielding load, ultimate load, stiffness and ductility, were addressed. The major conclusions are as follows: (1) By integral consideration of the creep rupture stress, the deviator angle and anchor methods, the prestressing BFRP tendons with a tension stress upper limit of 50%fu, a deviator angle of 2° and bonding anchors are determined for externally strengthening RC beams, satisfying requirements for long-term safety and high efficiency. (2) Using BFRP tendons as externally prestressed materials, an apparent enhancement of the cracking, yielding and ultimate load is achieved, regardless of the tension stress and the tendon profile. Moreover, ductile failure of all of the strengthened beams is realized. (3) Deviated BFRP tendons can benefit more from the increase in the cracking, yielding, and ultimate loads as well as the ductility of the strengthened beams, whereas the strengthening effectiveness of the straight tendon profile of the BFRP tendons is lowered due to obvious secondary-order effects after steel yielding. (4) A higher tension stress of the BFRP tendons can result in higher structural performance and sufficient material utilization of BFRP, whereas a lower tensile stress can induce a non-uniform stress distribution along the BFRP tendons and has a risk of structural failure by early fracture of FRP. (5) BS 8110 is accurate for the ultimate bearing and the crack width, while ACI is appropriate for the cracking moment and has almost the same accuracy in the deflection calculation compared to JGJ, with deviations below 20%.
Acknowledgements The authors gratefully acknowledge the financial supports from the National Program on Key Basic Research Project (973 Program, No. 2012CB026200), the National Science Foundation of China
References [1] Aravinthan T, Witchukreangkrai E, Mutsuyoshi H. Flexural behavior of twospan continuous prestressed concrete girders with highly eccentric external tendons. ACI Struct J 2005;102(3):402–11. [2] Aparicio AC, Ramos G, Casas JR. Testing of externally prestressed concrete beams. Eng Struct 2002;24:73–84. [3] Tan KH, Ng CK. Effects of deviators and tendon configuration on behavior of externally prestressed beams. ACI Struct J 1997;94(1). [4] Harajli MH. Strengthening of concrete beams by external prestressing. J Precast/Prestress Concr Inst 1993;38(6). [5] Pisani MA. A numerical survey on the behaviour of beams pre-stressed with FRP cables. Constr Build Mater 1998;12:221–32. [6] Elrefai A, West J, Soudki K. Fatigue of reinforced concrete beams strengthened with externally post-tensioned CFRP tendons. Constr Build Mater 2002;29:246–56. [7] Bakis CE, Bank LC, Brown VL, Cosenza E, Davalos JF, Lesko JJ, et al. Fiberreinforce polymer composites for construction—state-of-the-art review. J Compos Constr 2002;6:73–87. [8] Dai J, Ueda T, Sato Y, et al. Flexural strengthening of RC beams using externally bonded FRP sheets through flexible adhesive bonding. In: International symposium on bond behavior of FRP in structures (BBFS 2005), Hong Kong; 2005. p. 7–9. [9] Wang W, Dai J, Harries KA, et al. Prestress losses and flexural behavior of reinforced concrete beams strengthened with posttensioned CFRP sheets. J Compos Constr 2011;16(2):207–16. [10] Garden HN, Hollaway LC. An experimental study of the failure modes of reinforced concrete beams strengthened with prestressed carbon composite plates. Compos B Eng 1998;29(4):411–24. [11] Ghallab A. Calculating ultimate tendon stress in externally prestressed continuous concrete beams using simplified formulas. Eng Struct 2013;46:417–30. [12] Wu Z, Wang X, Zhao X, Noori M. State-of-the-art review of FRP composites for major construction with high performance and longevity. Int J Sustain Mater Struct Syst 2014;1(3):201–31. [13] Sim J, Park C, Moon DY. Characteristics of basalt fiber as a strengthening material for concrete structures. Compos B Eng 2005;36(6–7):504–12. [14] Wang X, Shi J, Liu J, Yang L, Wu Z. Creep behavior of basalt fiber reinforced polymer tendons for prestressing application. J Mater Des 2014;59:558–64. [15] Wang X, Xu P, Wu Z, Shi J. A novel anchor method for multitendon FRP cable: manufacturing and experimental study. J Compos Constr 2015 [10.1061/ (ASCE)CC.1943-5614.0000563, 04015010]. [16] Wang X, Xu P, Wu Z, Shi J. A novel anchor method for multi-tendon FRP cable: concept and FE study. Compos Struct 2015;120:552–64. [17] Wang X, Wu Z. Evaluation of FRP and hybrid FRP cables for super long-span cable-stayed bridges. Compos Struct 2010;92(10):2582–90. [18] Wang X, Wu G, Wu Z, Dong Z, Xie Q. Evaluation of prestressed basalt fiber reinforced polymer and hybrid FRP tendons under marine environment. J Mater Des 2014;64:721–8. [19] Lou T, Lopes SMR, Lopes AV. Numerical analysis of behaviour of concrete beams with external FRP tendons. Constr Build Mater 2012;35:970–8. [20] Ghallab A, Beeby AW. Factors affecting the external prestressing stress in externally strengthened prestressed concrete beams. Cement Concr Compos 2005;27:945–57. [21] Saadatmanesh H, Tannous FE. Long-term behavior of aramid fiber reinforced plastic (AFRP) tendon. ACI Mater J 1999;96(3):297–305. [22] ACI 440.3R-04. Guide test methods for fiber-reinforced polymers (FRPs) for reinforcing or strengthening concrete structures. American Concrete Institute; 2004. [23] Wang P. Study on the application of CFRP tendons in external prestressed bridges. Nanjing: Southeast University; 2008. [24] Santoh N. CFCC: carbon fiber composite cable. fiber-reinforced-plastic (FRP) reinforcement for concrete structures: properties and applications, vol. 42; 1993. p. 223–48. [25] Au FTK, Du JS. Deformability of concrete beams with unbonded FRP tendons. Eng Struct 2008;30:3764–70. [26] Tan KW, Tjandra RA. Strengthening of RC continuous beams by external prestressing. J Struct Eng 2007;133:195–204. [27] Lou T, Xiang Y. Finite element modeling of concrete beams prestressed with external tendons. Eng Struct 2006;28:1919–26. [28] Wang X. Experimental and theoretical studies on concrete beams with FRP tendons. Shanghai: Tongji University; 2005. [29] ACI 440.4R-04. Prestressing concrete structures with FRP tendons. American Concrete Institute; 2004. [30] BS 8110. Structural use of concrete, Part 1: Code of practice for design and construction. British Standards Institution; 1997. [31] JGJ 92-2004. Technical specification for unbonded prestressed concrete structures. China Academy of Building Research; 2004. [32] ACI 318-11. Building code requirement for structural concrete. American Concrete Institute; 2011. [33] BS 8110. Structural use of concrete, Part 2: Code of practice for special circumstances. British Standards Institution; 1985.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique Xin Wang a,b, Jianzhe Shi b, Gang Wu a,b, Long Yang b, Zhishen Wu a,b,⇑ a b
Key Laboratory of C & PC Structures Ministry of Education, Southeast University, Nanjing 210096, China International Institute for Urban Systems Engineering, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 10 June 2014 Revised 26 June 2015 Accepted 29 June 2015
Keywords: BFRP tendon External prestressing Flexural performance Tension control stress Bending angle
a b s t r a c t This paper investigates the feasibility of newly developed basalt fiber reinforced polymer (BFRP) as prestressing material and the structural behavior of reinforced concrete (RC) beams strengthened with externally prestressing BFRP tendons. Three main factors potential controlling structural strengthening effects, including tension stresses, bending angles and anchorages of the tendons, were first discussed based on literature review and finite element (FE) simulation. In the structural experiment, the effects of tension stresses and the tendon profiles on the flexural behavior of RC beams were discussed and the evaluation on the ultimate bearing capacity, cracking moment, crack width and deflection of strengthened beams was conducted by theoretical calculation and experimental results. The results show that the prestressing level of BFRP tendon can be determined to be 0.50fu and 0.38fu (fu is the tensile strength) according to creep rupture limit. The bending angle at the deviator is optimized to be 2° and the bond anchorage with resin epoxy was adopted to maximize strength utilization. For strengthening behavior, the second-order effect of the externally prestressed beam can be effectively relieved by using proper deviators, which is demonstrated by enhanced ultimate capacity. All of the strengthened RC beams are failed by concrete crushing, with satisfactory crack patterns and superior ductility compared to the control beam, which demonstrates the simultaneous working of internal steel reinforcements and external prestressing BFRP tendons during loading. The evaluation on mechanical behavior of strengthened RC beams indicates theoretical calculation according to several existing standards can well predict strengthening effect. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Strengthening of reinforced concrete (RC) beam by external prestressing technology with steel tendons has been developed for strengthening bridge and building structures as well as for use in new construction in recent decades [1,2]. The technology is characterized by several advantages, including the possibility of replacing tendons, reducing web thickness by eliminating internal tendons and the capability of applying precast segmental construction methods. Numerous researches have demonstrated that the behavior of service and ultimate states under static load can be effectively enhanced and the deflection induced by fatigue can be significantly decreased by external prestressing tendons [2–4]. However, the issues of steel corrosion and related fatigue degradation, which can greatly affect the structural durability and result in ⇑ Corresponding author at: International Institute for Urban Systems Engineering, Southeast University, Nanjing 210096, China. Tel.: +86 2583793232. E-mail address: [email protected] (Z. Wu). http://dx.doi.org/10.1016/j.engstruct.2015.06.052 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
catastrophic failure, still restrict their wider applications [5,6]. To overcome the above shortcomings, fiber-reinforced polymer (FRP) composites have been developed in the application of the structural strengthening owing to their high strength, light weight, and corrosion and fatigue resistance [7]. Because of the anisotropic property of unidirectional FRP members, the most efficient application of FRP is considered to be a tension-only element with prestressing technology in the forms of sheets, plates and tendons. For instance, the external-bonded prestressing CFRP sheets, plates and external unbounded prestressing FRP tendons have demonstrated their effectiveness in enhancing service and ultimate behavior of the RC beams [8] and the prestress losses due to FRP material are limited [9–11]. For prestressing materials, conventional carbon FRP (CFRP) and aramid FRP (AFRP) tendons are adopted because of their high creep rupture stress in comparison to glass FRP (GFRP), which is not allowable for prestressing because its creep rupture stress is less than 30% of the tensile strength (fu). However, the constant high cost and brittle behavior of CFRPs and large relaxation and cost issue for AFRPs continue to limit their
X. Wang et al. / Engineering Structures 101 (2015) 34–44
acceptance for replacing steel tendons in external prestressing applications. Basalt FRP (BFRP) is a newly developed composite material that has receiving significant attention in strengthening constructions. Basalt fibers are environmentally friendly inorganic materials produced from volcanic rock by using single-component raw materials and drawing fibers from the molten rock at a temperature of 1400–1500 °C. The greatest attraction of BFRPs lies in their superior integrated properties compared with conventional FRP composites, such as their greater than 25% higher strength and modulus, similar cost, and increased chemical stability compared to GFRPs as well as a wider range of working temperatures and much lower cost compared with CFRPs [12,13]. Recent studies reveal that BFRPs can be tensioned up to approximately 52%fu without creep rupture [14] and perform efficiently as cables for long-span bridges [15–17]. Moreover, BFRPs and their hybrid tendons also show superior performance under marine environment [18]. These advantages allow their potential application as prestressing tendons. Therefore, the combination of external prestressing technology and BFRP tendons should be a promising way to realize a new prestressing method.
2. Review of previous work In previous studies, the CFRPs, AFRPs and GFRPs were all investigated as the external prestressing tendons in RC beams strengthening. Lou et al. [19] focused on the static behavior of RC beams strengthened with CFRP and GFRP tendons and concluded that the structural performance of beams externally prestressed by CFRP tendons was similar to those prestressed by steel tendons, and the ductility of beams externally prestressed by GFRP tendons was even better, although their ultimate strength was lower than external steel tendon-strengthened beams. Similar studies by Pisani [5] also concluded that GFRP cables were reliable when applied to external prestressing and AFRP cables were suitable for bonded prestressing. Although GFRP achieved superior structural behavior by external prestressing strengthening, the low creep rupture limitation of GFRP tendon, usually less than 30%fu, greatly restricts its high efficiency in prestressing application. While, no recommendation on CFRP tendon was proposed because of their high cost and low ductility. Because of the importance of deviators in external prestressing applications, Ghallab et al. [11,20] conducted a comprehensive study on RC beams prestressed by deviated Parafil ropes (AFRP) to explore several factors affecting external prestressing stresses. They concluded that the number of deviators, the effective prestressing stress of tendon and the horizontal distance between deviators had significant effects on the stress distribution in external tendons. Regarding the long-term performance, Saadatmanesh et al. [21] reported that although the fatigue and creep performance of AFRP tendons were good, its relaxation losses were excessively high, especially in alkaline or acidic solutions. Investigations of RC beams strengthened with externally prestressed BFRP tendons have not been found in the existing literature. Based on the above review, it can be concluded that the application of BFRP tendons as external prestressing materials not only provides advantages in the ductility of strengthened structures but also avoids limitations of low creep rupture stress such as that with GFRPs. Thus, a comprehensive study of the mechanical properties of BFRP tendons as prestressing components, the relevant key factors controlling strengthening effects and the strengthening performance of structures should be conducted. In this study, an experiment was conducted on a series of large-sized concrete beams with T-shaped sections prestressed by external BFRP tendons. The tension control stress and bending angle for the BFRP tendons were determined based on the creep
35
rupture behavior and on existing study together with a finite element (FE) analysis, respectively. The effects of the tension control stress and the tendon profile on the flexural performance of the strengthened RC beam were discussed. Finally, the evaluation of design methods for BFRP externally prestressed concrete beams was conducted based on the existing specifications. 3. Key factor determination for BFRP prestressing tendons 3.1. Tensile strength of BFRP tendons BFRP tendons with a diameter of 12 mm were adopted in the study, which were manufactured using basalt fiber roving of 4800tex and vinyl ester resin through pultrusion technology. The fiber volume fraction of each BFRP tendon was approximately 60%, and the total length of each specimen for the tension test was 1250 mm. The two ends were treated by sand blasting over a length of 300 mm and anchored with seamless steel tubes with an outer diameter of 20 mm and thickness of 2 mm. Epoxy resin was used to fill the gap between the steel tube and the BFRP tendon, and the specimen was allowed to cure for seven days to ensure that sufficient strength was achieved. Five specimens were tested with a loading rate of 500 MPa/min according to ACI 440.3R-04 [22]. All specimens failed in the middle portion of specimen without any failure in the anchorage. BFRP tendons with a diameter of 12 mm exhibit an average strength of 1208 MPa, which is relatively lower than the strength in thinner BFRP tendons, typically 1450 MPa for a diameter of 6 mm. However, the coefficient of variation (C.o.V) of the tensile strength is quite low (0.84%), which makes the utilization of tendons highly efficient. The mean value of elasticity modulus is 48.6 GPa, with the C.o.V equal to 0.53%. Based on the 95% strength guarantee, a characteristic value for the tensile strength of 1192 MPa is adopted for the following experiment. 3.2. Creep rupture stress limitation Creep rupture stress is a critical factor limiting the prestressing level of FRP tendons. It is characterized by a time-dependent increased strain up to rupture when an FRP tendon is subjected to a sustained load of a certain level. Thus, the determination of the tension stress of BFRP tendons should first take into consideration the creep rupture stress and ensure that the tendon can maintain loads without creep rupture. Based on the previous study results [14], a million-hour creep rupture stress of 6 mm BFRP tendons with a vinyl ester matrix is regressed to be 0.59fu, and the design recommendation of the creep rupture limitation is 0.52fu based on the reliability analysis with 95% assurance. Consequently, the tension stress of the BFRP tendons in the current study should be controlled below 620 MPa. Because BFRP is adopted for prestressing tendons for the first time, the final tension control stresses were adopted to be conservative values of 0.50fu and 0.38fu, respectively, as well as for convenience. 3.3. Bending angle for the BFRP tendon at the deviator The deviator plays a significant role in enhancing the structural behavior of externally prestressed RC beams by reducing second-order effects, which are defined as the gradual decrease of the effective prestressing force with respect to increasing deflection. However, the stress distribution of BFRP tendons near the deviator is inevitably complicated, which requires the necessity of cautious determination of the bending angle for the tendon at the deviator. Several types of stresses exist near the deviator, such as friction, axial tensile stress generated from tension along with
36
X. Wang et al. / Engineering Structures 101 (2015) 34–44
bending, and transversal compression, which can result in a reduction of the ultimate strength of the FRP tendon. Thus, an appropriate bending angle should be studied to allow stress to transfer smoothly. Through the computational formula shown in Eq. (1), the strength reduction of a tendon at the bending area can be calculated based on the existing experimental results [23,24]. The bending angles ranging from 1° to 5° and the corresponding strength reduction percentages compared to the initial strength are shown in Table 1. 0
f fu ¼ f fu
2Ep Rp h pR
ð1Þ
where f0 fu is the actual strength; ffu is the initial ultimate strength without bending; and Ep = 48.2 GPa, Rp = 6 mm, h in rad and R = 72.5 mm are the elastic modulus of the tendon, radius of the tendon cross-section, bending angle and the radius of deviator, respectively. It can be found from Table 1 that the bending angle should be confined to less than 3° to avoid the strength reduction percentage exceeding 10%. Therefore, the bending angle for BFRP tendons in the current study was tentatively determined to be 2°. Because of the complexity of the stress state for BFRP tendons at the deviator, an FE analysis by ANSYS was also conducted to evaluate the stress distribution in the BFRP tendon at the bending area, comprehensively considering fiction and transverse compression between the deviator and the tendon. The element type of SOLID45 was adopted for the BFRP tendon and the deviator. The bending angle of the BFRP tendon was 2°. The geometric model used for the analysis is shown in Fig. 1(a). The analysis result shows that the axial stress of the tendon reaches a climax at the contact zone with the deviator, while the axial stress in the other area along the tendon is sufficiently uniform. When a maximum axial stress (fu = 1192 MPa) is reached, the stress value applied along the axial direction of tendon is equal to 1015 MPa, with relative error of 8% compared with the results from Eq. (1). The analysis shows that a bending angle of 2° is appropriate for the external BFRP prestressing tendon as the excessive stress concentration can be avoided. Above results can be observed from the Fig. 1(b) and (c), clearly illustrating the stress distribution at the bending area of the BFRP tendon. 3.4. Anchorage for BFRP prestressing tendons Several anchoring methods for BFRP tendons have been attempted to assure the performance of the tensile strength of BFRP tendons. The anchor methods included wrapping impregnated fiber roving at the anchorage zone (WR), utilizing bond anchorage with epoxy resin (SR), and utilizing friction anchorage with expansive cement filling a cylindrical steel sleeve (SC). The strength results from the above anchors are: 1064 MPa for WR, 1154 MPa for SC and 1208 MPa for SR. As a consequence, bond anchorage with epoxy resin was adopted as the anchoring method in the current study because there exists radial stress in the other two anchoring methods, leading to strength reduction at the anchorage zone of the tendon.
Fig. 1. Finite element analysis: (a) geometric model for FE analysis, (b) local stress nephogram for FRP tendon, (c) entire stress nephogram.
Table 1 Bending angles and corresponding strength reductions. Bending angle (°)
1
2
3
4
5
Strength at bending area (MPa) Strength reduction percentage (%)
1147.7 3.72%
1103.4 7.44%
1059.0 11.15%
1014.7 14.87%
970.4 18.59%
37
X. Wang et al. / Engineering Structures 101 (2015) 34–44 Table 2 Details of specimens. Specimen number
BC
BD-0.38
BD-0.50
BS-0.50
Prestressing value (MPa) Prestressing level Diameter of BFRP prestressing tendon (mm) PPRa Tendon profile
– – –
447 0.38fu 12
596 0.5fu 12
596 0.5fu 12
0 –
0.57 Deviated
0.57 Deviated
0.57 Straight
4. Experiment on RC beams externally prestressed by BFRP tendons 4.1. Details of specimens
Fig. 2. Schematics for geometric dimensioning and reinforcements of specimens (dimensions in mm).
To validate the effectiveness of externally prestressing BFRP tendons for concrete beams, a proving test was conducted on four large-sized RC beams, among which BD-0.38, BD-0.50 and BS-0.50 were the beams externally prestressed by BFRP tendons and the BC was the control beam. The strength grade of the concrete for all of the specimens was C30. The main variables were the tension control stress and the tendon profile. Details such as material properties and the reinforcements for the specimens are given in Tables 2 and 3. All specimens had the same geometric dimensioning as shown in Fig. 2. The span of all specimens was determined to be 5700 mm, with a span-depth ratio of 11.4. The deviated tendons with horizontal bending angles of 2° or straight tendons (as shown in Fig. 3) were located symmetrically on both sides of the prestressed beams. The vertical distance from the anchoring zone to the bottom surface of the beam remained constant between the two types of tendon profiles to guarantee identical eccentricity. The configuration of the deviator is shown in Fig. 4. 4.2. Tension procedure of the BFRP prestressing tendon Tendons were fixed at the position of the anchor plates by nuts (Fig. 5(a)) and tensioned by the apparatus shown in Fig. 5(b). To minimize the loss of prestressing due to an asynchronous tension of the BFRP tendons, over-tensioning with stress values up to 1.1rcon and 1.05rcon (rcon = the tension control stress) was adopted to adjust the tension stress in both tendons to rcon. 4.3. Test setup, loading method and measurement As shown in Fig. 6, all the specimens were simply supported and tested under four-point loads. The load was applied on the specimens with a loading rate of 5 kN every two minutes. A hydraulic jack with a capacity of 500 kN was used. A load cell between the hydraulic jack and the distributive girder was installed to monitor the load values during the loading process. The strains of the steel reinforcements, BFRP prestressing tendons and the strains at different heights of the midspan cross-section were measured by strain gauges. Deflections at the
midspan and the supports were measured by dial indicators. All data were collected automatically by a TDS 530, produced by Tokyo Measuring Instrument Laboratory (TML), and transmitted synchronously to a computer once every two seconds. The distribution of cracks was recorded artificially by tracing the main cracks and recording the crack shapes on the surface of the specimens. 5. Results and discussion 5.1. Summary of experimental results The experimental results are given in Table 4, where Pcr is the cracking load; Py is the load at the yielding of the steel reinforcements (yielding load); Pmax is the ultimate load; Dy denotes the midspan deflections upon yielding of the steel reinforcements (yielding deflection); x donates the crack width at the stable stage of crack development of one main crack near the midspan; and Pl/400, Pl/300, and Pl/200 stand for the corresponding load values of the midspan deflections equal to l/400, l/300 and l/200, respectively, where l represents the center distance between the two supports, which is equal to 5700 mm. Photographs of the failure modes for the specimens are given in Fig. 7(a–d), which clearly show that the strengthened beam failed by concrete crushing, while the FRP tendons did not rupture, which is similar the concrete beams with unbonded FRP tendons [25]. The load–deflection curves of all of the tested beams are plotted in Fig. 8. It is observed that the overall flexural behavior of the beams strengthened by externally prestressed BFRP tendons has been significantly enhanced compared to that of the control beam (BC). All of the strengthened beams, including BD-0.38, BD-0.50 and BS-0.50, show 115.4%, 130.7%, and 115.4% higher cracking loads relative to the control specimen BC. For the yielding loads, corresponding increments of 36.2%, 51.1%, and 38.3% were observed, and for the ultimate load, 54.7%, 66.0%, and 43.4% were observed. Although the ductilities of the strengthened beams are generally lower than the control beam, they can still achieve 76.4%, 85.7% and 69.6% of the midspan deflection of the control
Table 3 Measured values for material properties of specimens. Material
Type or dimension
Elastic modulus (MPa)
Compressive strength (MPa)
Yield strength (MPa)
Ultimate tensile strength (MPa)
Ultimate strain (%)
Concrete Steel bar (stirrup) Steel bar (upper) Steel bar (lower) BFRP tendon
C30 A8
3.25 104 2.1 105
40.5 –
– 240
– 385
– 15
A10 B22 12 mm
2.1 105 2.0 105 4.82 104
– – –
275 340 –
375 450 1192
14.5 15 2.44
38
X. Wang et al. / Engineering Structures 101 (2015) 34–44
Fig. 3. Lay-out drawing of specimens (dimensions in mm): (a) lay-out drawing for deviated tendons (1 through 5 stand for strain gauges), (b) lay-out drawing for straight tendons (1 through 3 stand for strain gauges).
Fig. 4. Deviator.
beam, which is much higher than the beams externally strengthened by prestressed high-strength steel or CFRP tendons [2,26]. The superior ductility is a result of the lower modulus and larger failure elongation of the BFRPs. It is also observed that the stiffness of the BFRP tendon prestressed RC beams is significantly improved after concrete cracking in comparison to that of the control beam. Thus, external prestressing of BFRP tendons is capable of effectively restraining cracks and deflections during service conditions and maintaining similar ductility to the control beam.
5.2. Flexural behavior discussion 5.2.1. Effect of tendon profile From the comparison of BD-0.50 and BS-0.50 in Fig. 8, it is observed that the tendon profile has a slight effect on the flexural behavior before concrete cracking because the deflections of the specimens are too small to generate an obvious second-order effect on the specimen. After concrete cracking, a slightly high stiffness and obvious high yielding load of the deviated specimen were observed in comparison to the straight line of BS-0.50 beam. As a result, a higher ultimate capacity and higher ductility were achieved by the deviated specimen of BD-0.50, which indicates that the second-order effect of the prestressing tendon profile affects the ultimate capacity as well as restrains deformations for concrete beams. Moreover, the BD-0.50 specimen better controls crack development compared to BS-0.50, but their maximum crack
widths are similar. The 16% enhanced ultimate loads of BD-0.50 in comparison to BS-0.50 indicates that the reduction magnitude of the second-order effect is significant for deviated external BFRP tendons, which benefits the simultaneous work of tendons and beam as a whole and the enhancement of the bearing capacity and stiffness of a structure. 5.2.2. Effect of tension control stress It can be concluded from the curves of BD-0.38 and BD-0.50 in Fig. 8 and Table 4 that as the tension control stress increases, the cracking, yielding and ultimate loads are improved accordingly. This is mainly because the failure of the external BFRP tendon strengthened beam is dominated by concrete crushing and because the potential strength of BFRP tendons with low tension stress cannot be utilized sufficiently. This phenomenon indicates that the higher initial stress in BFRP prestressing tendons benefits the whole structural strengthening effectiveness of externally prestressed beams. It should be noted that the upper limit of the initial stress should be lower than the creep rupture stress of BFRPs (52% of fu). 5.3. Crack patterns of specimens The crack propagation patterns of the four types of specimens are given in Fig. 9. Compared to the control beam BC, the specimens externally prestressed by BFRP tendons show relatively
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
fewer cracks with smaller crack widths, especially for BD-0.38 and BS-0.50. BD-0.50 shows more distributed cracking than BD-0.38 and BS-0.50 because of the integrated function of the high initial stress and the deviated tendon profile. In general, all beams exhibit similar crack patterns as a result of the restriction by internal steel reinforcements, without which abrupt failure may occur on externally prestressed beams as reported in the literature [19,27]. Thus, although the use of externally prestressed BFRP tendons can delay the occurrence of cracks, cracking distributions similar to normal RC beams remain. Furthermore, the distributions of RC beams prestressed by BFRP tendon perform more uniform than those prestressed by steel tendon [3]. This characteristic benefits BFRP-strengthened beams having similar ductility to RC beams. 5.4. Load–strain curves for specimens
Fig. 5. Tensioning apparatus of specimens: (a) Anchoring end. (b) Tensioning apparatus.
The relation between the loads and strains on the BFRP tendons and the steel reinforcements are shown in Fig. 10, in which the mean value of two strains at the midspan of the bottom steel reinforcements are included, and the mean values of the strains collected by the gauging points on a single BFRP tendon are used to represent the development tendency of the strain along the whole tendon. It is shown in Fig. 10 that the strains of the longitudinal steel reinforcements in the specimens with BFRP tendons are much less than those in the control beam, which is apparently a result of the prestressing provided by the external BFRP tendons. From the strain comparison of the steel reinforcements between the strengthened beams and the control beam, the enhanced cracking load and yielding load are easily observed. Three stages can be identified for each curve, with two inflection points representing the cracking of the concrete and the yielding of the steel reinforcements. By comparing the curves of the BFRP tendon and the steel reinforcement in the strengthened beams at different stages, it can be observed that they have approximately equal strain increments before the yielding of the steel reinforcements, after which their strain increments exhibit different trends depending on the different tendon profiles and prestressing levels. The strain increments in the BFRP tendon are 2.8 and 3.9 times that in the steel reinforcement for BD-0.38 and BD-0.50, respectively, from the yielding of the steel reinforcement to the failure of the specimen because external tendons are merely restrained at the anchorages and deviators. However, the steel reinforcements have effective bonds with the concrete. The corresponding increment of the BFRP tendon in BS-0.50 is 5% less than that in steel reinforcement because of significant second-order effects on BS-0.50. The results show that BFRP tendons on beams prestressed by a deviated profile can be more effectively used in comparison to that in straight-line strengthening. 5.5. Axial stress distribution along BFRP tendons The stress distribution of BFRP tendons along the length are shown in Fig. 11, which is converted from the measured strain multiplied by the elastic modulus, clearly demonstrating the strength utilization efficiency. In general, the figures show the different stress distributions with respect to the increasing load.
Fig. 6. Lay-out of loading device.
Table 4 Experimental results for specimens. Specimen number
Pcr (kN)
Py (kN)
Pmax (kN)
Pl/400 (kN)
Pl/300 (kN)
Pl/200 (kN)
Dy
BC BD-0.38 BD-0.50 BS-0.50
32.5 70.0 75.0 70.0
117.5 160.0 177.5 162.5
132.5 205.0 220.0 190.0
92.1 135.8 140.6 133.3
112.6 160.3 169.2 159.5
118.4 164.8 181.6 164.7
20.2 28.9 22.2 21.0
(mm)
x (mm)
Failure characteristics
0.14 0.10 0.08 0.14
Crush Crush Crush Crush
in in in in
concrete concrete, no failure in BFRP concrete, no failure in BFRP concrete, no failure in BFRP
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
Fig. 8. Load–deflection curves for specimens.
BD-0.38 at the midspan. In contrast, the stresses in BS-0.50 BFRP tendons maintain constant and uniform distribution up to failure. The different characteristics of the stress distributions of the three types of prestressed BFRP tendons are generated by the effects of the deviators and the tension stress. With higher initial tension stress, crack propagation and the deflection of the concrete beam can be restrained more effectively. Consequently, the ductility of BD-0.50 is also larger than that of BD-0.38 as shown in Fig. 8. Although the stress distribution of the BS-0.50 specimen exhibits a more uniform shape compared with BD-0.38 and BD-0.50, the ultimate capacity and ductility of BS-0.50 are lower than the other two deviated beams, which again proves that the secondary-order effect can greatly affect the structural strengthening behavior. 5.6. Stress increment-deflection curves
Fig. 7. Photographs of failure modes for specimens: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
Before the cracking load, the stress of all three types of BFRP tendons exhibits a similar uniform distribution regardless of the stress level and the effect of the deviators. The uniform distribution remains constant up to the yielding load (160–177 kN), at which a slight variation of the stress distribution can be observed for the two deviated BFRP tendons. Afterwards, the BFRP tendons with low tension stress exhibit significant differences between the stresses at midspan and the two ends. For the BFRP tendons with high tension stress, the stress at the midspan also increases faster than the stresses at the two ends, but the differences are much less than those of the BD-0.38 BFRP tendons. Low tension stress leads to earlier yielding of tensile steel reinforcements and consequently larger deflection, causing a sudden increase in the bending angle and more significant stress increments in the BFRP tendon on
The stress increments of prestressed BFRP tendons with respect to the deflection of the beam are given in Fig. 12. The mean values of the stress increment in the deviated BFRP tendons are analyzed due to the variation of stress along the tendons. As a type of linear elastic material, the stress increment of BFRP tendons exhibits an approximately linear relation with the midspan deflection. There is a slight fluctuation of each curve after yielding of the steel reinforcement due to a sharp increase of the deflection. As mentioned previously, the strain level of the BFRP tendon on BS-0.50 is relatively low at the failure of the specimen compared with BD-0.38 and BD-0.50, causing a small stress increment in its BFRP tendon. With the largest ultimate load, the ultimate deflection of BD-0.50 is also the largest among the three prestressed specimens. Furthermore, the stress increments in the BFRP tendons of BD-0.38 and BD-0.50 are more significant than those of BS-0.50 because of the existence of the deviator, which demonstrates once again the function of the deviator in allowing tendons to collaborate better with concrete beams. 5.7. Validation for plane cross-section assumption The mechanical analysis and the structure design for externally prestressed concrete beams are at the basis of the plane crosssection assumption, which was validated through the measurement of axial strains of concrete at different heights at the cross-section at the midspan. Five gauging points on the side surface of midspan were installed, and the distances from the bottom were 20, 140, 260, 380 and 450 mm. Values of the strain measured under 0.2Pmax, 0.4Pmax, 0.6Pmax and 0.8Pmax are chosen to represent the strain distribution during loading. The strains measured at each position of the midspan cross-section are shown in Fig. 13, in
X. Wang et al. / Engineering Structures 101 (2015) 34–44
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Fig. 9. Crack patterns of specimens: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
which it can be observed that the axial strains of the concrete at the midspan exhibit a linear distribution along the vertical axis of the cross-section with loads below 0.6Pmax, beyond which a non-linear stress distribution occurs as a result of crack development in the concrete. The distributions are consistent to the existing results [28]. 6. Evaluation of design methods 6.1. Calculation of ultimate capacity The design methods introduced here are all based on the analysis of unbonded prestressed structures. ACI 440.4R-04 is a recommendation provided by the American Concrete Institute (ACI) for
prestressed concrete structures with FRP tendons. BS 8110 is a code provided by the British Standards Institution (BSI) for practical design and construction, and JGJ 92-2004 is the technical specification provided by the China Academy of Building Research for unbonded prestressed concrete structures. The ultimate bearing capacity of concrete beams externally prestressed by BFRP tendons is calculated on the basis of the ultimate stress in the external tendon, which is recommended by the standards, as follows. For convenience, notations for the same parameter in different standards are modified to be identical. (1) ACI 440.4R-04 [29]
f ps ¼ f pe þ Ep Xu ecu ðdp =cu 1Þ
ð2Þ
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
Fig. 11. Axial stress distribution along the BFRP tendons: (a) BD-0.38, (b) BD-0.50, (c) BS-0.50.
(1) JGJ 92-2004 [31] Fig. 10. Load–strain relationship for specimen: (a) BD-0.38, (b) BD-0.50, (c) BS-0.50.
where fps is the stress in the prestressing tendon at failure; fpe is effective stress in the tendon, excluding prestress losses; Ep is the elastic modulus of the prestressing tendon; Xu is the strain reduction factor; ecu is the ultimate compressive strain of concrete; and dp and cu are the distance of the resultant point of the external prestressing tendon from the compressive edge of cross-section and the depth of the neutral axis at failure, respectively. (1) BS 8110 [30]
f ps ¼ f pe þ
1:7f pu Ap 7000 1 f cu bd p L=dp
ð3Þ
where fpu is the characteristic strength of the prestressing tendon (fps should not exceed 0.7fpu), Ap is the cross-sectional area of the prestressing tendon, fcu is the characteristic strength of the concrete and b and L are the width of the section and span of the beam, respectively.
f ps ¼ f pe þ ð240 335n0 Þð0:45 þ 5:5d=LÞ n0 ¼
f pe Ap þ f y As f c bdp
ð4Þ ð5Þ
where n0 is the integrated reinforcement index, which should not be larger than 0.4; d is the depth of the section; fc is the design value for the axial compressive strength of the concrete; and fy and As are the yielding strength and cross-sectional area of the steel reinforcements, respectively. Preliminary calculations show that the depth of the concrete compression zone is always less than the thickness of the flange, from which the ultimate bearing capacities of specimens can be calculated based on Eqs. (6) and (7):
f y As þ f ps Ap ¼ f c bf xc
ð6Þ
M ¼ f ps Ap ðdp xc =2Þ þ f y As ðh0 xc =2Þ
ð7Þ
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X. Wang et al. / Engineering Structures 101 (2015) 34–44 Table 5 Ultimate bearing capacities obtained by several standards.
a
Specimen number
MExpa (kN m)
MACI (kN m)
MBS (kN m)
MJGJ (kN m)
MExp/ MACI
MExp/ MBS
MExp/ MJGJ
BD-0.38 BD-0.50 BS-0.50
205 220 190
234.02 234.02 213.81
212.48 226.61 200.51
182.98 197.13 183.25
0.88 0.94 0.89
0.96 0.97 0.95
1.12 1.12 1.04
MExp donates the experimental results.
Table 6 Experimental and theoretical values for cracking moment. Fig. 12. Stress increment–deflection curves.
where xc represents the equivalent compression height of the concrete, bf represents the width of the flange, and h0 is the distance from the resultant point of tensile steel reinforcements to the compressive edge of the cross-section. In terms of the above calculation formulae of the stress in the external tendon at failure, the ultimate bearing capacity of the external prestressed beam can be acquired, which is listed in Table 5. From Table 5, it can be determined that the theoretical results calculated by the formula provided by BS 8110 are closest to the experimental results, while ACI is the least conservative standard for the ultimate bearing capacity calculation.
6.2. Calculation for cracking moment, crack width and midspan deflection The calculation methods for the cracking moment of ACI [29,32] and JGJ [31] are fundamentally similar, with their differences lying
Specimen number
MExp (kN m)
MACI (kN m)
MJGJ (kN m)
MExp/ MACI
MExp/ MJGJ
BD-0.38 BD-0.50 BS-0.50
70.0 75.0 70.0
67.96 77.72 68.69
57.03 66.80 57.76
1.03 0.97 1.02
1.23 1.12 1.21
Table 7 Experimental and theoretical values for crack width. Specimen number
xExp
xACI
xBS
xJGJ
(mm)
(mm)
(mm)
(mm)
xExp/ xACI
xExp/ xBS
xExp/ xJGJ
BD-0.38 BD-0.50 BS-0.50
0.10 0.08 0.14
0.08 0.07 0.09
0.11 0.09 0.13
0.09 0.06 0.10
1.25 1.14 1.56
0.91 0.89 1.08
1.11 1.33 1.40
in the fact that the rupture strength of the concrete is adopted in ACI, while the tensile strength of the concrete is adopted in JGJ. From Table 6, it is obvious that ACI is more precise in the calculation of the cracking moment.
Fig. 13. Stress values at different heights on the midspan cross-section: (a) BC, (b) BD-0.38, (c) BD-0.50, (d) BS-0.50.
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X. Wang et al. / Engineering Structures 101 (2015) 34–44
(NSFC, No. 51378109) and the Transportation Science and Technology Project of Jiangsu Province (No. 2014Y01).
Table 8 Experimental and theoretical values for midspan deflection. Specimen number
fExp (mm)
fACI (mm)
fBS (mm)
fJGJ (mm)
fExp/ fACI
fExp/ fBS
fExp/ fJGJ
BD-0.38 BD-0.50 BS-0.50
8.60 7.51 8.56
8.43 6.72 9.35
11.80 8.08 11.63
7.94 7.14 7.21
1.02 1.12 0.92
0.73 0.93 0.74
1.08 1.05 1.19
Calculations for the crack width and the midspan deflection refer to ACI [29,32], BS 8110 [30,33] and JGJ [31], with the bending moment equal to 100 kN, and the results are listed in Tables 7 and 8. For the crack width, BS 8110 is the most accurate standard, while the theoretical results of ACI and JGJ tend to be lower than the experimental results because they both fail to consider second-order effects well. However, for the deflection calculation, the accuracy of BS 8110 is not satisfactory, while deviations of the theoretical results of ACI and JGJ from the experimental results are less than 20%. One other point to note is that the values of the deflections from BS 8110 are conservative, but the other two standards do not tend to be very safe. 7. Conclusion To validate the effectiveness of BFRP tendons as an external prestressing material, several key factors affecting the strengthening effect and a series of RC beams strengthened by external prestressed BFRP tendons were studied. The effects of tension stress and the tendon profile of the prestressing tendons on the flexural behavior of strengthened RC beams, including cracking load, yielding load, ultimate load, stiffness and ductility, were addressed. The major conclusions are as follows: (1) By integral consideration of the creep rupture stress, the deviator angle and anchor methods, the prestressing BFRP tendons with a tension stress upper limit of 50%fu, a deviator angle of 2° and bonding anchors are determined for externally strengthening RC beams, satisfying requirements for long-term safety and high efficiency. (2) Using BFRP tendons as externally prestressed materials, an apparent enhancement of the cracking, yielding and ultimate load is achieved, regardless of the tension stress and the tendon profile. Moreover, ductile failure of all of the strengthened beams is realized. (3) Deviated BFRP tendons can benefit more from the increase in the cracking, yielding, and ultimate loads as well as the ductility of the strengthened beams, whereas the strengthening effectiveness of the straight tendon profile of the BFRP tendons is lowered due to obvious secondary-order effects after steel yielding. (4) A higher tension stress of the BFRP tendons can result in higher structural performance and sufficient material utilization of BFRP, whereas a lower tensile stress can induce a non-uniform stress distribution along the BFRP tendons and has a risk of structural failure by early fracture of FRP. (5) BS 8110 is accurate for the ultimate bearing and the crack width, while ACI is appropriate for the cracking moment and has almost the same accuracy in the deflection calculation compared to JGJ, with deviations below 20%.
Acknowledgements The authors gratefully acknowledge the financial supports from the National Program on Key Basic Research Project (973 Program, No. 2012CB026200), the National Science Foundation of China
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