体外预应力纤维增强树脂基复合材料筋混凝土结构研究进展

史健喆

doi:10.13801/j.cnki.fhclxb.20210327.001

体外预应力纤维增强树脂基复合材料筋混凝土结构研究进展

doi: 10.13801/j.cnki.fhclxb.20210327.001

史健喆^,

河海大学　土木与交通学院，南京 210098

基金项目: 河海大学中央高校基本科研业务费项目(B200201074)

详细信息

通讯作者:
史健喆，博士，讲师，研究方向为纤维增强复合材料(FRP)及其加固/增强工程结构技术　E-mail：sjz@hhu.edu.cn

中图分类号: TU599
计量
- 文章访问数: 1225
- HTML全文浏览量: 292
- PDF下载量: 115
- 被引次数: 0
出版历程
- 收稿日期: 2021-02-08
- 录用日期: 2021-03-18
- 网络出版日期: 2021-03-29
- 刊出日期: 2021-07-15

A review of studies on concrete structures prestressed with external fiber reinforced polymer composites tendons

SHI Jianzhe^,

College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China

摘要

摘要: 本文从纤维增强树脂基复合材料(FRP)筋、关键技术和构件三个主要方面综述了体外预应力FRP筋混凝土结构的研究成果。首先，介绍了预应力FRP筋拉伸性能和长期性能，给出了面向设计的FRP筋蠕变断裂应力值、松弛率及疲劳最大应力和应力幅限值。阐述了预应力FRP筋三种主要锚固技术的优缺点和减小锚固端应力集中的方法，重点介绍了近年来新开发的复合材料夹片锚具，其锚固效率系数高于90%；同时，基于转向FRP筋力学性能试验结果，建议转向半径不宜小于FRP筋半径的200倍，转向角度不宜大于5°。梳理了体外预应力FRP筋混凝土构件的试验研究结果(单调加载、长期持荷和循环加载)，介绍了国内外规范中的设计方法，并基于既有文献中42根梁的试验结果评价了规范中计算方法的精度，验证了我国规范GB 50608—2020中体外预应力FRP筋混凝土结构设计计算方法的准确性。本综述将对体外预应力FRP筋混凝土结构的推广应用起积极推动作用。
- 体外预应力 /
- 混凝土结构 /
- 纤维增强树脂基复合材料(FRP)筋 /
- 长期性能 /
- 锚固 /
- 转向 /
- 试验研究 /
- 设计方法
Abstract: The studies on concrete structures prestressed with external fiber reinforced polymer (FRP) tendons are reviewed in the aspects of FRP tendon, key technology and structural component, in this review. The tensile properties and long-term behaviors of FRP tendon are firstly introduced. The design-oriented values of creep-rupture stress, relaxation rate and the limits of maximum fatigue stress and fatigue stress range are provided. The advantages and deficiencies of three main types of anchor for FRP tendon, and the methods of reducing the stress concentration on FRP tendon at anchor are elaborated. The newly-developed composite-wedge anchor is emphasized, which possesses an anchor efficiency coefficient exceeding 90%. Meanwhile, the curvature radius of deviator is recommended to be larger than 200 times of the radius the cross-section of FRP tendons, and the bending angle of FRP tendons should not exceed 5°, based on the experimental results on the mechanical properties of deviated FRP tendons. The experimental results of concrete beams prestressed with external FRP tendons are reviewed, including monotonic loading, sustained loading and cyclic loading. The design methodologies in the codes at home and overseas are introduced. The accuracies of the calculating methods in the codes are evaluated using the experimental data of forty-two beams, and the methods in the Chinese code GB 50608—2020 are validated to be accurate in the design calculation for concrete structures prestressed with external FRP tendons. This paper is expected to actively promote the popularization and application of concrete structures prestressed with external FRP tendons.
- external prestressing /
- concrete structure /
- fiber reinforced polymer composite (FRP) tendon /
- long-term behavior /
- anchor /
- deviation /
- experimental study /
- design methodology

HTML全文

图 1 体外预应力纤维增强树脂基复合材料(FRP)筋混凝土结构示意图

Figure 1. Schematic diagram of concrete structure prestressed with external fiber-reinforced polymer composite (FRP) tendons

下载: 全尺寸图片幻灯片

图 2 FRP筋蠕变松弛性能提高机制示意图^[20]

Figure 2. Schematic diagram for improvement mechanism of creep and relaxation behaviors of FRP tendons^[20]

下载: 全尺寸图片幻灯片

图 3 FRP筋内部初始弯曲纤维和预张拉后的拉直纤维^[17]

Figure 3. Initially uneven fibers and straightened fibers after pretensioned in FRP tendon^[17]

下载: 全尺寸图片幻灯片

图 4 玄武岩纤维增强树脂基复合材料(BFRP)筋疲劳破坏机制^[22]

Figure 4. Mechanism of fatigue failure of basalt fiber reinforced polymer composite (BFRP) tendon^[22]

下载: 全尺寸图片幻灯片

图 5 FRP筋主要锚固形式

Figure 5. Main types of anchor of FRP tendons

下载: 全尺寸图片幻灯片

图 6 分段式复合材料夹片^[38]

Figure 6. Segmented composite wedge^[38]

下载: 全尺寸图片幻灯片

图 7 FRP筋转向区试验装置^[39]

Figure 7. Test setup for FRP tendons at a deviator^[39]

下载: 全尺寸图片幻灯片

图 8 转向半径和转向角度对弯折FRP筋承载力保留率的影响^[39]

Figure 8. Effects of curvature radius of deviator and bending angle on loading capacity retention of FRP tendon at deviator^[39]

下载: 全尺寸图片幻灯片

图 9 体外预应力混凝土梁长期变形和预应力损失^[6]

Figure 9. Long-term deformation and prestress loss of concrete beam prestressed with external tendon^[6]

下载: 全尺寸图片幻灯片

表 1 FRP筋、高强钢筋、钢绞线的拉伸性能^[8]

Table 1. Tensile properties of FRP tendons, high-strength steel bar and steel strand^[8]

Type of tendon	Density/ (g·cm⁻³)	Tensile strength/MPa	Elastic modulus/GPa	Elongation/ %	Longitudinal thermal expansivity/(10⁻⁶℃⁻¹)
CFRP tendon	1.50	1500–2500	120–160	0.5–1.7	−2–0
BFRP tendon	2.00	800–1800	50–60	1.6–3.0	6–8
AFRP tendon	1.40	1000–2 000	40–120	1.9–4.4	−6–−2
High-strength steel bar	7.85	490–700	200	>10	11.7
Steel strand	7.85	1400–1 860	180–200	>4	11.7
Notes: CFRP—Carbon fiber reinforced polymer composite; BFRP—Basalt fiber reinforced polymer composite; AFRP—Aramid fiber reinforced polymer composite.

下载: 导出CSV

表 2 FRP筋的蠕变断裂应力

Table 2. Values of creep rupture stress of FRP tendons

Reference	CFRP	AFRP	BFRP
Yamaguchi^[9]	0.93f_u	0.47f_u	—
Ando^[10]	0.79f_u	0.66f_u	—
Tokyo Rope^[11]	0.85f_u	—	—
Shi^[12]	—	—	0.54f_u
Banibayat^[13]	—	—	0.15f_u
ACI 440.1R-15^[14]	0.55f_u	0.30f_u	—
ACI 440.4R-04^[2]	0.70f_u	0.55f_u	—
Note: f_u—Tensile strength of FRP tendon.

下载: 导出CSV

表 3 FRP筋蠕变断裂应力建议值

Table 3. Recommended values of creep rupture stress of FRP tendons

Type of tendon	CFRP	AFRP	BFRP
Creep rupture stress	0.70f_u	0.55f_u	0.54f_u

下载: 导出CSV

表 4 0.5f_u初始应力下FRP筋百万小时松弛率预测值

Table 4. Predictive values of one-million-hour relaxation rates of FRP tendons at 0.5f_u initial level

Type of tendon	CFRP	AFRP	BFRP
Relaxation rate/%	3.0	10–13	6.7

下载: 导出CSV

表 5 FRP筋疲劳强度(括号中为对应的应力幅)

Table 5. Values of fatigue strength of FRP tendons (with corresponding stress range in brackets)

References	CFRP	AFRP	BFRP
Saadatmanesh^[23-24]	0.9f_u (0.05f_u)	0.5f_u (0.025f_u)	—
Adimi^[27]	0.35f_u (0.21f_u)	—	—
El Refai^{[25, 28]}	0.5f_u (0.1f_u)	—	0.39f_u (0.04f_u)
Song^[29]	0.64f_u (0.09f_u)	—	—
	0.53f_u (0.19f_u)
	0.37f_u (0.28f_u)
Xie^[30]	0.5f_u (0.09f_u)	—	—
Zhuge^[31]	0.42f_u (0.04f_u)	—	—
Zhang^[32]	0.5f_u (0.25f_u)	—	—
Odagiri^[33]	—	0.54f_u (0.05 f_u)	—
Wang^[22]	—	—	0.6f_u (0.05f_u)
Atutis^[34]	—	—	0.65f_u (0.07f_u)

下载: 导出CSV

表 6 FRP筋主要锚具形式的优缺点

Table 6. Advantages and deficiencies of main types of anchor for FRP tendons

Type of anchor	Advantages	Deficiencies
Bond type	No radial stress, hence inducing no decrease in strength of tendon	Inconvenient grouting, prestress loss due to long-term creep deformation of bonding material in anchor
Friction type	Radial stress is beneficial for the long-term behavior of anchor	Inconvenient grouting
Wedge type	Convenient assembly	Notch effect on FRP tendon

下载: 导出CSV

表 7 FRP筋张拉控制应力σ_con

Table 7. Tension control stress σ_con of FRP tendons

Type of FRP	CFRP	AFRP	BFRP
Upper limit	0.65f_u	0.55f_u	0.50f_u
Lower limit	0.50f_u	0.35f_u	0.35f_u

下载: 导出CSV

表 8 不同R/r下的弯折FRP筋强度折减系数

Table 8. Strength reduction coefficients of deviated FRP tendon at different values of R/r

R/r	CFRP tendon	AFRP tendon	BFRP tendon
200	0.61	0.75	0.79
300	0.74	0.83	0.86
400	0.81	0.88	0.89
Notes: r—Radius of prestressed FRP bars; R—Curvature radius of deviator.

下载: 导出CSV

表 9 体外预应力FRP筋混凝土梁抗弯性能研究数据库

Table 9. Database of studies on flexural behaviors of concrete beams prestressed with external FRP tendons

Reference	Number of specimen	Type of tendon
Shi^[6]	3	BFRP
Ghallab^[43]	12	AFRP
Wang^[7]	3	BFRP
Du^[60]	4	CFRP
El-Refai^[61]	3	CFRP
Bennitz^[62]	6	CFRP
Jung^[63]	2	CFRP
Au^[64]	3	AFRP
Tan^[65]	2	CFRP

下载: 导出CSV

表 10 体外预应力FRP筋混凝土梁长期性能研究数据库

Table 10. Database of studies on long-term behaviors of concrete beams prestressed with external FRP tendons

Reference	Number of specimen	Type of tendon
Shi^[6]	3	BFRP
Cao^[45]	1	CFRP

下载: 导出CSV

表 11 体外预应力FRP筋极限状态应力增量Δσ_pu的试验值与理论值之比

Table 11. Ratios of experimental value to theoretical value of stress increment Δσ_pu of external prestressing FRP tendons at ultimate state

Code	ACI 440.4R- 04^[2]	BS 8110^[56]	fib^[55]	GB 50608— 2020^[53]
Average value	1.39	2.14	1.58	1.01
Variance	0.58	0.89	0.45	0.20

下载: 导出CSV

表 12 体外预应力FRP筋混凝土梁抗弯承载力的试验值与理论值之比

Table 12. Ratios of experimental value to theoretical value of flexural capacity of concrete beams prestressed with external FRP tendons

Code	ACI 440.4R- 04^[2]	BS 8110^[56]	fib^[55]	GB 50608— 2020^[53]
Average value	1.09	1.47	1.10	1.05
Variance	0.15	0.22	0.13	0.07

下载: 导出CSV

表 13 预应力FRP筋混凝土梁裂缝宽度的试验值与理论值之比

Table 13. Ratios of experimental value to theoretical value of crack width of concrete beams prestressed with external FRP tendons

Code	ACI 440.4R-04^[2]	fib^[55]	GB 50608—2020^[53]
Average value	0.94	1.03	0.92
Variance	0.53	0.59	0.65

下载: 导出CSV

表 14 预应力FRP筋混凝土梁挠度的试验值与理论值之比

Table 14. Ratios of experimental value to theoretical value of deflection of concrete beams prestressed with external FRP tendons

Code	ACI 440.4R-04^[2]	fib^[55]	GB 50608—2020^[53]
Average value	0.94	0.95	0.92
Variance	0.34	0.38	0.25

下载: 导出CSV

表 15 预应力FRP筋混凝土梁长期挠度(反拱)试验结果与龄期调整有效模量法(AEMM)计算的理论值之比

Table 15. Ratios of experimental value to theoretical value calculated using age-adjusted effective modulus method (AEMM) of long-term deflection (camber) of concrete beams prestressed with external FRP tendons

Duration of loading/d	50	100	150	300	500	1000
Average value of Shi^[6]	0.92	1.04	1.12	—	—	—
Variance of Shi^[6]	0.33	0.24	0.46	—	—	—
Cao^[45]	1.08	1.12	0.95	0.94	1.15	1.13

下载: 导出CSV

表 16 预应力FRP筋混凝土梁长期预应力损失试验结果与AEMM计算的理论值之比

Table 16. Ratios of experimental value to theoretical value calculated using AEMM of prestress loss of concrete beams prestressed with external FRP tendons

Duration of loading/d	50	100	150
Average value of Shi^[6]	1.05	0.94	1.08
Variance of Shi^[6]	0.23	0.41	0.33

下载: 导出CSV

参考文献(65)

[1]	孙宝俊, 周国华. 体外预应力结构技术及应用综述[J]. 东南大学学报(自然科学版), 2001, 31(1):109-113. SUN B J, ZHOU G H. A survey on structural techniques and applications of external prestressing[J]. Journal of Southeast University (Natural Science Edition),2001,31(1):109-113(in Chinese).
[2]	American Concrete Institute. Prestressing concrete structure with FRP tendons: ACI 440.4 R-04[S]. USA: American Concrete Institute, 2004.
[3]	GRACE N F, NAVARRE F C, NACEY R B, et al. Design-construction of bridge street bridge-first CFRP bridge in the United States[J]. PCI Journal,2002,47(5):20-35. doi: 10.15554/pcij.09012002.20.35
[4]	KARBHARI V M. Use of composite materials in civil infrastructure in Japan: PB98-158215[R]. California: University of California, 1998.
[5]	鲁平印, 汪晶, 向星赟. 荷兰Dintelhaven桥的设计建造特色[J]. 中外公路, 2008(9):245-248. LU P Y, WANG J, XIANG X Y. Design and construction features of Dintelhaven Bridge in Netherland[J]. Journal of China & Foreign Highway,2008(9):245-248(in Chinese).
[6]	史健喆. 海洋环境下BFRP筋体外预应力加固钢筋混凝土梁长期性能研究[D]. 南京: 东南大学, 2019. SHI J Z. Long-term behaviors of RC beam prestressed with external BFRP tendons in marine environment[D]. Nanjing: Southeast University, 2019(in Chinese).
[7]	WANG X, SHI J, WU G, et al. Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique[J]. Engineering Structures,2015,101:34-44. doi: 10.1016/j.engstruct.2015.06.052
[8]	吴智深, 汪昕, 吴刚. FRP增强工程结构体系[M]. 北京: 科学出版社, 2016. WU Z S, WANG X, WU G. FRP Reinforced engineering structural systems[M]. Beijing: Science Press, 2016(in Chinese).
[9]	YAMAGUCHI T, NISHIMURA T, UOMOTO T. Creep rupture of FRP rods made of aramid, carbon and glass fibers[J]. Structural Engineering & Construction: Tradition, Present and Future,1998,2:1331-1336.
[10]	ANDO N, MATSUKAWA H, KAWAMURA M, et al. Experimental studies on the long-term tensile properties of FRP tendons[C]//Proceedings of the Third International Symposium on Non-metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3). Sapporo: Japan Concrete Institute, 1997, 2: 203-210.
[11]	Tokyo Rope. CFCC, carbon fiber composite cable[EB/OL] Tokyo: Tokyo Rope Manufacturing Co. Ltd, 2000 [2021-03-15]. http://www.tokyorope.co.jp/
[12]	SHI J, WANG X, WU Z, et al. Creep behavior enhancement of a basalt fiber-reinforced polymer tendon[J]. Construction and Building Materials,2015,94:750-757. doi: 10.1016/j.conbuildmat.2015.07.118
[13]	BANIBAYAT P, PATNAIK A. Creep rupture performance of basalt fiber-reinforced polymer bars[J]. Journal of Aerospace Engineering,2013,28(3):04014074.
[14]	American Concrete Institute. Guide for the design and construction of concrete reinforced with FRP bars: ACI 440.1R-15[S]. USA: American Concrete Institute, 2015.
[15]	GUNNARSSON A. Bearing capacity, relaxation and finite element simulation for prestressed concrete beams reinforced with BFRP tendons[D]. Iceland: Reykjavik University, 2013.
[16]	THORHALLSSON E, JONSSON B S. Test of prestressed concrete beams with BFRP tendons[C]//Workshop Structural Engineering and Composites Laboratory. Reykjavik: Reykjavik University, 2012.
[17]	SHI J, WANG X, HUANG H, et al. Relaxation behavior of prestressing basalt fiber-reinforced polymer tendons considering anchorage slippage[J]. Journal of Composite Materials,2016,51(9):1275-1284.
[18]	ZOU P X W. Long-term properties and transfer length of fiber-reinforced polymers[J]. Journal of Composites for Construction,2003,7(1):10-19. doi: 10.1061/(ASCE)1090-0268(2003)7:1(10)
[19]	周祝林, 杨云娣. 纤维增强塑料蠕变机理的初步探讨[J]. 玻璃钢/复合材料, 1985(4):31-35. ZHOU Z L, YANG Y D. A preliminary discussion on creep mechanism of fiber-reinforced plastic (FRP)[J]. Fiber Reinforced Plastics/Composites,1985(4):31-35(in Chinese).
[20]	WANG X, SHI J, WU Z, et al. Creep strain control by pretension for basalt fiber-reinforced polymer tendon in civil applications[J]. Materials & Design,2016,89:1270-1277.
[21]	WU Z, WANG X, IWASHITA K, et al. Tensile fatigue behaviour of FRP and hybrid FRP sheets[J]. Composites Part B: Engineering,2010,41(5):396-402. doi: 10.1016/j.compositesb.2010.02.001
[22]	WANG X, SHI J, WU Z, et al. Fatigue behavior of basalt fiber-reinforced polymer tendons for prestressing applications[J]. Journal of Composites for Construction,2015,20(3):04015079.
[23]	SAADATMANESH H, TANNOUS F E. Relaxation, creep, and fatigue behavior of carbon fiber reinforced plastic tendons[J]. ACI Materials Journal,1999,96(2):143-153.
[24]	SAADATMANESH H, TANNOUS F E. Long-term behavior of aramid fiber reinforced plastic (AFRP) tendons[J]. ACI Materials Journal,1999,96(3):297-305.
[25]	EL REFAI A. Durability and fatigue of basalt fiber-reinforced polymer bars gripped with steel wedge anchors[J]. Journal of Composites for Construction,2013,17(6):04013006. doi: 10.1061/(ASCE)CC.1943-5614.0000417
[26]	曾凡星. FRP拉索疲劳特性及其长寿命RC斜拉桥研究[D]. 南京: 东南大学, 2012. ZENG F X. Study on fatigue properties of FRP cables and longevity of RC cable-stayed bridge[D]. Nanjing: Southeast University, 2012(in Chinese).
[27]	ADIMI M R, RAHMAN A H, BENMOKRANE B. New method for testing fiber-reinforced polymer rods under fatigue[J]. Journal of Composites for Construction,2000,4(4):206-213. doi: 10.1061/(ASCE)1090-0268(2000)4:4(206)
[28]	ELREFAI A, WEST JS, SOUDKI K. Performance of CFRP tendon-anchor assembly under fatigue loading[J]. Composite Structures,2007,80(3):352-360.
[29]	SONG S T, ZANG H, DUAN, N, et al. Experimental research and analysis on fatigue life of carbon fiber reinforced polymer (CFRP) tendons[J]. Materials,2019,12(20):786-795.
[30]	XIE G H, TANG Y S, WANG C M, et al. Experimental study on fatigue performance of adhesively bonded anchorage system for CFRP tendons[J]. Composites: Part B,2018,150:47-59. doi: 10.1016/j.compositesb.2018.05.047
[31]	诸葛萍, 丁勇, 侯苏伟, 等. 新型CFRP筋锚具优化设计及疲劳性能试验[J]. 浙江大学学报(工学版), 2014, 48(10):1822-1827, 1842. ZHUGE P, DING Y, HOU S W, et al. Optimization design and fatigue test of new CFRP tendon anchor assembly[J]. Journal of Zhejiang University (Engineering Science),2014,48(10):1822-1827, 1842(in Chinese).
[32]	张新越, 欧进萍. CFRP筋的疲劳性能[J]. 材料研究学报, 2006, 20(6):565-570. doi: 10.3321/j.issn:1005-3093.2006.06.002 ZHANG X Y, OU J P. Experimental study on fatigue behavior of CFRP bars[J]. Chinese Journal of Materials Research,2006,20(6):565-570(in Chinese). doi: 10.3321/j.issn:1005-3093.2006.06.002
[33]	ODAGIRI T, MATSUMOTO K, NAKAI H. Fatigue and relaxation characteristics of continuous aramid fiber reinforced plastic rods[C]//Proceedings of the Third International Symposium on Non-metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3). Sapporo: Japan Concrete Institute, 1997, 2: 14-16.
[34]	ATUTIS E, VALIVONIS J, ATUTIS M. Experimental study of concrete beams prestressed with basalt fiber reinforced polymers under cyclic load[J]. Composite Structures,2018,183:389-396.
[35]	SCHMIDT J W, BENNITZ A, TÄLJSTEN B, et al. Mechanical anchorage of FRP tendons: A literature review[J]. Construction & Building Materials,2012,32:110-121.
[36]	SCHMIDT J W, BENNITZ A, TÄLJSTEN B, et al. Development of mechanical anchor for CFRP tendons using integrated sleeve[J]. Journal of Composites for Construction,2010,14(4):397-405. doi: 10.1061/(ASCE)CC.1943-5614.0000096
[37]	TERRASI G P, AFFOLTER C, BARBEZAT M. Numerical optimization of a compact and reusable pretensioning anchorage system for CFRP tendons[J]. Journal of Composites for Construction,2011,15(2):126-135. doi: 10.1061/(ASCE)CC.1943-5614.0000080
[38]	张磊. 基于同源材料的FRP筋夹片式锚具优化设计及性能研究[D]. 南京: 东南大学, 2019. ZHANG L. Study on optimization design for a wedge anchor of FRP tendon based on homologous materials and its performance[D]. Nanjing: Southeast University, 2019(in Chinese).
[39]	ZHU H, DONG Z Q, WU G, et al. Experimental evaluation of bent FRP tendons for strengthening by external prestressing[J]. Journal of Composites for Construction,2017,21(5):04017032. doi: 10.1061/(ASCE)CC.1943-5614.0000811
[40]	SANTOH N. CFCC (Carbon fiber composite cable)[M]//NANNI A. Fiber-Reinforced-Plastic (FRP) Reinforcement for Concrete Structures. Amsterdam: Elsevier Science Publishers, 1993: 223-248.
[41]	LOU T, LOPES S M R, LOPES A V. Numerical analysis of behaviour of concrete beams with external FRP tendons[J]. Construction and Building Materials,2012,35:970-978. doi: 10.1016/j.conbuildmat.2012.04.055
[42]	GHALLAB A. Calculating ultimate tendon stress in externally prestressed continuous concrete beams using simplified formulas[J]. Engineering Structures,2013,46:417-430. doi: 10.1016/j.engstruct.2012.07.018
[43]	GHALLAB A, BEEBY A W. Factors affecting the external prestressing stress in externally strengthened prestressed concrete beams[J]. Cement & Concrete Composites,2005,27(9):945-957.
[44]	史健喆, 汪昕, 吴智深. 采用同源材料夹片锚具的玄武岩纤维复材筋体外预应力加固混凝土梁受弯性能研究[J]. 工业建筑, 2019, 49(9):156-160. SHI J Z, WANG X, WU Z S. Flexural behavior of RC beams prestressed with external BFRP tendons using a composite-wedge anchorage[J]. Industrial Construction,2019,49(9):156-160(in Chinese).
[45]	曹国辉, 方志. 体外CFRP筋预应力混凝土箱梁长期受力性能试验研究[J]. 土木工程学报, 2007, 40(2):18-24. doi: 10.3321/j.issn:1000-131X.2007.02.004 CAO G H, FANG Z. Experimental study on the long-term behavior of concrete box girders prestressed with external CFRP tendons[J]. China Civil Engineering Journal,2007,40(2):18-24(in Chinese). doi: 10.3321/j.issn:1000-131X.2007.02.004
[46]	高宏. 体外预应力FRP筋加固混凝土梁的疲劳性能研究[D]. 南京: 东南大学, 2006. GAO H. Research of the fatigue performance of RC beams externally prestressed with FRP tendons[D]. Nanjing: Southeast University, 2006(in Chinese).
[47]	BRAIMAH A, GREEN M F, CAMPBELL T I. Fatigue behaviour of concrete beams post-tensioned with unbonded carbon fibre reinforced polymer tendons[J]. Canadian Journal of Civil Engineering,2006,33(9):1140-1155. doi: 10.1139/l06-063
[48]	GRACE N F. Response of continuous CFRP prestressed concrete bridges under static and repeated loadings[J]. PCI Journal,2000,45(6):84-102. doi: 10.15554/pcij.11012000.84.102
[49]	ELREFAI A, WEST J, SOUDKI K. Fatigue of reinforced concrete beams strengthened with externally post-tensioned CFRP tendons[J]. Construction and Building Materials,2012,29:246-256. doi: 10.1016/j.conbuildmat.2011.10.014
[50]	朱虹. 新型预应力FRP筋预应力混凝土结构的研究[D]. 南京: 东南大学, 2004. ZHU H. Study on concrete structure prestressed with FRP tendons[D]. Nanjing: Southeast University, 2004(in Chinese).
[51]	GRACE N F, ENOMOTO T, YAGI K. Behavior of CFCC and CFRP leadline prestressing systems in bridge construction[J]. PCI Journal,2002,47(3):90-103. doi: 10.15554/pcij.05012002.90.103
[52]	程君. 体外预应力CFRP筋混凝土连续梁疲劳性能研究[D]. 南京: 东南大学, 2017. CHENG J. Study on the fatigue behavior of reinforced concrete continuous beams prestressed with external CFRP tendons[D]. Nanjing: Southeast University, 2017(in Chinese).
[53]	中华人民共和国住房和城乡建设部. 纤维增强复合材料工程应用技术标准: GB 50608—2020[S]. 北京: 中国计划出版社, 2020. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Technical standard for fiber reinforced polymer (FRP) in construction: GB 50608—2020[S]. Beijing: China Planning Press, 2020(in Chinese).
[54]	YOUAKIM S A, KARBHARI V M. An approach to determine long-term behavior of concrete members prestressed with FRP tendons[J]. Construction and Building Materials,2007,21(5):1052-1060. doi: 10.1016/j.conbuildmat.2006.02.006
[55]	International Federation for Structural Concrete (FIB). fib Model code for concrete structures 2010[S]. Hoboken: Ernst & Sohn, 2010.
[56]	BSI Technical Committee. Structural use of concrete Part 1: Code of practice for design and construction: BS 8110-1-1997[S]. Britain: British Standard Institute, 1997.
[57]	PENG F, XUE W, TAN Y. Design approach for flexural capacity of prestressed concrete beams with external tendons[J]. Journal of Structural Engineering,2018,144(12):04018215. doi: 10.1061/(ASCE)ST.1943-541X.0002208
[58]	DOLAN C W. Design recommendations for concrete structures prestressed with FRP tendons: FHWA contract, final report[R]. USA: Federal Highway Administration, 2001.
[59]	中华人民共和国住房和城乡建设部. 混凝土结构设计规范: GB 50010—2010[S]. 北京: 中国建筑工业出版社, 2016. Ministry of Housing and Urban-Rural Development of the People’s Republic of China. Code for design of concrete structures: GB 50010—2010[S]. Beijing: China Architecture & Building Press, 2016(in Chinese).
[60]	DU J S, YANG D, NG P L, et al. Response of concrete beams partially prestressed with external unbonded carbon fiber-reinforced polymer tendons[J]. Advanced Materials Research,2010,150-151:344-349. doi: 10.4028/www.scientific.net/AMR.150-151.344
[61]	EL-REFAI A, WEST J, SOUDKI K. Strengthening of RC beams with external post-tensioned CFRP tendons: Case histories and use of FRP for prestressing applications[J]. ACI Special Publication,2007,245:123-142.
[62]	BENNITZ A, SCHMIDT J W, NILIMAA J, et al. Reinforced concrete T-beams externally prestressed with unbonded carbon fiber-reinforced polymer tendons[J]. ACI Structural Journal,2012,109(4):521-530.
[63]	JUNG W T, PARK J S, PARK Y H, et al. An experimental study on the flexural behavior of post-tensioned concrete beams with CFRP tendons[J]. Applied Mechanics and Materials,2013,351-352:717-721. doi: 10.4028/www.scientific.net/AMM.351-352.717
[64]	AU F T, SU R K, TSO K, et al. Behaviour of partially prestressed beams with external tendons[J]. Magazine of Concrete Research,2008,60(6):455-467. doi: 10.1680/macr.2008.60.6.455
[65]	TAN K, FAROOQ M, NG C, et al. Behavior of simple-span reinforced concrete beams locally strengthened with external tendons[J]. ACI Structural Journal,2001,98(2):174-183.