配置体外CFRP预应力筋混凝土梁的受力性能研究
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摘要
配置体外碳纤维(CFRP)预应力筋混凝土薄壁梁将成为新建桥梁结构修建和现有桥梁结构加固的一种较好的结构形式,而目前国内外尚缺乏有关该方面的设计规范,关于体外预应力筋应力增量的计算多用经验公式,或是借用体内无粘结预应力混凝梁预应力增量的计算公式,存在适用性差和准确性低的问题,关于配置体外CFRP预应力筋混凝土梁的受力性能和计算方法有待更全面和系统的研究。本文对体外CFRP预应力筋混凝土T梁和箱梁的弯曲受力性能进行了系统的试验研究和理论分析,以探求其受力性能和适用计算方法,完成了以下主要工作:
(1)通过配置体外CFRP预应力筋混凝土梁的抗弯性能的破坏试验研究,对其受力过程、承载力、延性性能和破坏模式等进行了描述。从试验结果得知:配置体外CFRP预应力筋可以大幅度提高混凝土梁的承载力;期望在受压区混凝土压碎之前体外CFRP预应力筋不被拉断;梁体内非预应力钢筋可以明显改善配置体外CFRP预应力筋混凝土梁的裂缝分布和延性,就本文试件而言,配置体外CFRP预应力筋部分预应力混凝土梁的延性指标可达2.5左右;张拉体外预应力筋时是否持荷以及持荷大小对梁的抗弯性能影响很小,可以忽略。
(2)编制了体外预应力混凝土梁的非线性分析程序。本程序可以对任意截面型式的预应力(体外预应力筋、体内无粘结预应力筋、体内有粘结预应力筋)混凝土梁和普通钢筋混凝土梁进行非线性全过程数值分析计算,程序可以就转向块的布置方式、体外预应力筋纵断面形状、体外筋有效预应力的大小及材性、张拉预应力筋时梁的持荷状态等因素对体外预应力混凝土梁在外荷载作用下的强度、变形特征、破坏模式等的影响进行分析研究。
(3)以体内非预应力钢筋配筋率、体外预应力筋配筋率、体外预应力筋布置形式、预应力度、跨高比、荷载形式等为参数,用非线性分析程序对体预应力筋混凝土梁进行了参数分析,依据分析结果提出了以综合配筋指标和预应力度为参数的等效变形区长度的计算公式,进而提出了基于等效变形区长度的极限挠度计算公式;体内非预应力钢筋屈服前的挠度计算采用常用的部分预应力混凝土梁挠度计算公式;依据试验和非线性数值计算结果,将不同转向块布置形式的体外预应力混凝土梁简化为跨中一个转向块的体外预应力混凝土梁,推导了基于跨中挠度的体外预应力筋应力增量的简化计算公式。
(4)通过配置体外CFRP预应力筋混凝土薄壁箱梁的短期均布荷载试验、长期持荷试验以及长期持荷后的破坏试验,研究了体外CFRP预应力筋的预应力损失、截面应力分布、变形性能及裂缝开展和分布,得到以下结论:混凝土开裂、长期持荷、体内非预应力受拉钢筋屈服等因素使翼缘有效宽度计算系数略有增加(小于8%);持续1001 d引起的CFRP筋预应力损失仅为1.47%,卸载后比卸载前仅减小1.27%;持荷1001d时L/2跨的长期挠曲变形实测值为初始变形的2.32~2.42倍,卸载20d后不可恢复变形为1001d变形的41%;持荷1001d受拉钢筋应变较初始值增加约65%,卸载后基本无残余应变;持荷1001d受压钢筋应变较初始值增加225%~268%,卸载并恢复20d后不可恢复应变为其1001d应变的53%;持续荷载作用顶板混凝土表面压应变前期发展较快,持荷2年左右基本上趋于稳定,持荷1001d压应变较初始值增加164%~224%;持续荷载作用下初始裂缝宽度随时间增加而增大,持荷2年左右裂缝宽度与长度基本上趋于稳定,持荷1001d实测裂缝宽度为初始值的1.59~2.69倍,卸载并恢复20d后变为不可见裂缝;箱梁底板横向裂缝一般自底板中部开展,并且在各试验阶段底板裂缝宽度沿横向分布均呈现中间宽两端窄;各试验阶段箱梁截面腹板处应变沿高度分布基本符合平截面假定。最后,针对配置体外CFRP预应力筋混凝土梁的受力特性,对各规范和规程中的裂缝计算公式进行了相应的修正,建立了适用于配置体外CFRP预应力筋混凝土箱梁和T梁短期和长期裂缝宽度的计算公式。
(5)以Mindlin-Reissener中厚板理论为基础,以U.L列式法建立平板型壳元的几何非线性有限元基本方程,并将龙驭球提出的厚薄板通用无剪切闭锁板单元和具有平面内旋转自由度的任意四边形膜单元组合成板壳单元,然后引入分层法建立了几何材料双重非线性板壳有限元模型,并建立了无粘结预应力筋和双弹簧单元的几何非线性有限元基本方程,用双弹簧单元模拟无粘结预应力筋和混凝土之间的相互作用。以此为理论基础,编制了大型非线性板壳有限元计算程序,程序可以对体内、体外无粘结预应力混凝土板壳结构和普通钢筋混凝土板壳结构进行线弹性及双重非线性计算,可以分级加载来模拟结构从张拉预应力筋到受力破坏的全过程受力反应。
(6)用有限元程序对配置体外CFRP预应力筋混凝土箱梁的抗弯性能进行参数分析,结果表明:梁的承载能力和刚度随混凝土强度的发展而提高;长期持荷会使已开裂梁的初始缺陷增大、承载能力和刚度降低;配置体外CFRP预应力筋的箱梁与配置体外预应力钢绞线的箱梁开裂荷载基本相等,箱梁开裂后配置体外CFRP预应力筋的箱梁刚度、屈服荷载和极限承载力略低。
(7)用有限元程序对配置体外CFRP预应力筋混凝土箱梁的剪力滞效应进行分析,结果表明:体外预应力混凝土箱梁在线弹性阶段的受力适用叠加原理;体外预应力混凝土箱梁在外荷载作用下的翼缘有效宽度计算系数ρf与普通钢筋混凝土箱梁基本相同;箱梁在体外预应力筋作用下的ρf与箱梁体在体外预应力筋等效荷载作用下的ρf基本相同;不设转向块直线布置的体外预应力筋张拉力作用下,跨中附近梁段基本不存在剪力现象。
(8)依据试验和分析结果,对配置体外CFRP预应力筋混凝土箱梁的有效宽度计算系数适当简化,并对配置体外CFRP预应力筋混凝土梁的张拉控制应力、体内非预应力受拉钢筋配筋率、相对受压区高度、极限承载能力计算、正常使用阶段验算等内容进行了系统建议和总结。
The thin-walled concrete beams prestressed with external CFRP tendons would become more popular both in new construction and in strengthening of existing structures. But there is no the design code for it so far at home and abroad. The prestress increment in external prestressed tendons is always analyzed with emprical formulas or analytical model for the analysis of the unbonded prestressed tendons, which is not inapplicable or inaccuracy sometimes. So the fomula for the external prestresse increment and the behaviors of concrete beam prestressed with external CFRP tendons need to be studied better. The flexural behaviors of the concrete T/box beam prestressed with external tendons were studied experimentally and theoretically, and the following works have been done:
(1) Tests were carried out on 5 beams under four-point load, of which four beams were reinforced with hybrid both external CFRP tendons and internal reinforcement and another one only reinforced with internal ordinary steel bar. The beams’bearing capacity, deformation, ductility index, cracking pattern and failure mode were studied. It was showed that the the bearing capacity of the concrete beam can ben improved effectively by external prestressed tendons. The expected failure mode is the concrete crushing rather than the externally prestressed CFRP tendons rupturing. Non-prestressing internal reinforcement can improve the flexural behaviors of beams prestressed with external CFRP tendons effectively since it can lead to a more rational crack distribution and better ductility, and the ductility index of beams prestressed with external CFRP tendons in this paper can reach about 2.5. The initial loading state on the beam before tendon jacking has no significant influence on the ultimate capacity and deflection.
(2) A program was developed to predict the behaviors of those beams prestressed with externally prestressed tendons. The flexural capacity, deformation and failure modes of beams with different parameters can be analyzed using the program, such as types of plan and prestressed tendons(extrenal prestessed tendons, internal unbonded prestressed tendons, internal bonded prestressed tendons), jacking and effective stress in external prestressed tendons, configuration of the deviators, properties of tendon, ratio of span to effective depth of the beam and load pattern, initial loading state at tendon jacking, etc.
(3) Nonlinear behaviors of the concrete beam prestressed with external or internal unbonded tendons were studied by the program developed. Such parameters as the percentage of ordinary reinforcment, amounts and configuration of unbonded prestressed tendons, the ratio of span to depth and the loading patterns were considered. Based on the results, the fomula for the eqivalent length of deformation zone on the beams at ultimate were developed. A simple formula was developed for the ultimate mid-span deflection of concrete beams with concept of equivalent length of deformation zone, and the deformation of beam before internal reinforcement yielding was predicted by the traditional formula for the deformation of partically prestressed concrete beam. Then an analytical model was deduced for analyzing the ultimate stress increment in those concrete beams prestressed with external or internal unbonded tendons based on the mid-span deflection.
(4) Testes were carried out on a thin-walled concrete box beam presressed with external CFRP tendons to study its short-term performances under uniform load, long-term behaviors under uniform load, and full-time performance under four-point load in turn. Prestressing loss of CFRP, stress/strain distribution in flange, deformation and crack distribution were studied. The results indicated that: effective width coefficient of compression top flange increased by less than 8% due to concrete cracking, long-term loading, and ordinary tension reinforcement yielding; the test value of deflection at mid-span at 1001 day was 2.32~2.42 times of the initial deflection, plastic deformation at 20 days after unloading was 41% of 1001 day’s; the strain of tensile reinforcement had a 65% increase than that of its initial value, and residual strain after unloading was about zero; the strain of compressed reinforcing steel bar had a 225%~268% increase than that of its initial value, and residual strain at 20 days after unloading was 53% of 1001 day’s; compression strain on top plate of the box girder under long-term load increased quickly in the early stage and became stable after 2 years, and it had a 164%~224% increase than that of its initial value at 1001 day; the crack width increased as time increased under long-term load, then it became stable after more or less 2 years, and it was 1.59~2.69 times than that of its initial value at 1001 day; most of the cracks in the bottom plate of box girder developed from middle of bottom plate, and they were wider in the middle of the bottom plate than at the bottom ends of the webs; the strain distributed over the section depth of web agreed well with plane assumption. Based on the behaviors of concrete beams prestressed with external CFRP tendons, the comformable formulars for predicting crack width of concrete box/T girder prestressed with external CFRP tendons were proposed by modifying traditional formulas in design codes for predicting the crack with of ordinary prestressed concrete beams.
(5) Based on Mindlin-Reissener theories of thick plate, the fundamental geometric nonlinearity equations for flat-shell element were set up with U.L formulas. A flat-shell element was composed with the lock-free element for thick/thin plates(Yuqiu Long) and the four-nodded arbitrary quadrilateral finite element with in-plane rotational degree of freedom. Then the fundamental equations for plate/shell bi-nonlinear finite element model were set up with layered finite method. the fundamental geometric nonlinearity equations for the unbonded prestressed tendon and double spring element were proposed, and the double spring element was used to simulate the interaction of unbonded prestressed tendon and deviator. Based on these theories mentioned above, a finite element program for bi-nonlinear analysis of plate/shell concrete structure prestressed with external tendons was developed. Using this program, either linear elastic or bi-nonlinear anslysis can be conducted for both plate/shell concrete structures prestressed with external or internal unbonded tendons or ordinary reinforced concrete plate/shell structures. Further more, analysis for prestressed structure, where from the beginning of stretching prestressed tendons to failure at last, can be simulated with the method of incremental step loading.
(6) Parametric studies on the flexural behaviors of the concrete box beam prestressed with external CFRP tendons were conducted using the finite element program. It’s concluded that the bearing capacity and the stiffness of the beam enhanced with the development of the concrete strength, the initial defect of the beam with crack increased and the bearing capacity and the stiffness reduced as time increased under the long-term load. The cracking load of the beam prestressed with external CFRP tendons was about same as that of beam prestressed with external stranded steel wire. The stiffness of the beam after the concrete cracking, yielding load and the ultimate bearing capacity of beam prestressed with external CFRP tendons were smaller than that prestressed with external stranded steel wire.
(7) Shear-lag effect in flange of concrete box beam prestressed with external CFRP tendons was analyzed using the finite element program. The results indicated that the superposition principle can be used in the concrete box beam prestressed with external tendons in the linear elastic stage. Effective width coefficient of the flangeρf of box beam under the action of external prestressed force is the same as theρf of normal reinforced concrete box beam under the equivalent loads of external prestressed tendons. Theρf of the box girder under the action of the external prestressed tendon is basically the same as that of the reinforced concrete box girder under the action of the equivalent load of the external prestressed tendons. Basically there were no shear-lag effect existed in the elements beside the mid-span of the beam under the action of external prestressed tendons which lay out straightly with no deviator.
(8) Based on the results of experimental and theoretical studies, the effective width coefficient of flange of box beam prestressed with external CFRP tendons was simplified appropriately, and design proposals of concrete beams prestressed with external CFRP tendons were put forward systematized, such as the stretching control stress of CFRP tendons, amount of the normal reinforcement, relative height of equivalent compression zone,method for ultimate bearing capacity and checking computations of the normal serviceability stage and so on.
(1)通过配置体外CFRP预应力筋混凝土梁的抗弯性能的破坏试验研究,对其受力过程、承载力、延性性能和破坏模式等进行了描述。从试验结果得知:配置体外CFRP预应力筋可以大幅度提高混凝土梁的承载力;期望在受压区混凝土压碎之前体外CFRP预应力筋不被拉断;梁体内非预应力钢筋可以明显改善配置体外CFRP预应力筋混凝土梁的裂缝分布和延性,就本文试件而言,配置体外CFRP预应力筋部分预应力混凝土梁的延性指标可达2.5左右;张拉体外预应力筋时是否持荷以及持荷大小对梁的抗弯性能影响很小,可以忽略。
(2)编制了体外预应力混凝土梁的非线性分析程序。本程序可以对任意截面型式的预应力(体外预应力筋、体内无粘结预应力筋、体内有粘结预应力筋)混凝土梁和普通钢筋混凝土梁进行非线性全过程数值分析计算,程序可以就转向块的布置方式、体外预应力筋纵断面形状、体外筋有效预应力的大小及材性、张拉预应力筋时梁的持荷状态等因素对体外预应力混凝土梁在外荷载作用下的强度、变形特征、破坏模式等的影响进行分析研究。
(3)以体内非预应力钢筋配筋率、体外预应力筋配筋率、体外预应力筋布置形式、预应力度、跨高比、荷载形式等为参数,用非线性分析程序对体预应力筋混凝土梁进行了参数分析,依据分析结果提出了以综合配筋指标和预应力度为参数的等效变形区长度的计算公式,进而提出了基于等效变形区长度的极限挠度计算公式;体内非预应力钢筋屈服前的挠度计算采用常用的部分预应力混凝土梁挠度计算公式;依据试验和非线性数值计算结果,将不同转向块布置形式的体外预应力混凝土梁简化为跨中一个转向块的体外预应力混凝土梁,推导了基于跨中挠度的体外预应力筋应力增量的简化计算公式。
(4)通过配置体外CFRP预应力筋混凝土薄壁箱梁的短期均布荷载试验、长期持荷试验以及长期持荷后的破坏试验,研究了体外CFRP预应力筋的预应力损失、截面应力分布、变形性能及裂缝开展和分布,得到以下结论:混凝土开裂、长期持荷、体内非预应力受拉钢筋屈服等因素使翼缘有效宽度计算系数略有增加(小于8%);持续1001 d引起的CFRP筋预应力损失仅为1.47%,卸载后比卸载前仅减小1.27%;持荷1001d时L/2跨的长期挠曲变形实测值为初始变形的2.32~2.42倍,卸载20d后不可恢复变形为1001d变形的41%;持荷1001d受拉钢筋应变较初始值增加约65%,卸载后基本无残余应变;持荷1001d受压钢筋应变较初始值增加225%~268%,卸载并恢复20d后不可恢复应变为其1001d应变的53%;持续荷载作用顶板混凝土表面压应变前期发展较快,持荷2年左右基本上趋于稳定,持荷1001d压应变较初始值增加164%~224%;持续荷载作用下初始裂缝宽度随时间增加而增大,持荷2年左右裂缝宽度与长度基本上趋于稳定,持荷1001d实测裂缝宽度为初始值的1.59~2.69倍,卸载并恢复20d后变为不可见裂缝;箱梁底板横向裂缝一般自底板中部开展,并且在各试验阶段底板裂缝宽度沿横向分布均呈现中间宽两端窄;各试验阶段箱梁截面腹板处应变沿高度分布基本符合平截面假定。最后,针对配置体外CFRP预应力筋混凝土梁的受力特性,对各规范和规程中的裂缝计算公式进行了相应的修正,建立了适用于配置体外CFRP预应力筋混凝土箱梁和T梁短期和长期裂缝宽度的计算公式。
(5)以Mindlin-Reissener中厚板理论为基础,以U.L列式法建立平板型壳元的几何非线性有限元基本方程,并将龙驭球提出的厚薄板通用无剪切闭锁板单元和具有平面内旋转自由度的任意四边形膜单元组合成板壳单元,然后引入分层法建立了几何材料双重非线性板壳有限元模型,并建立了无粘结预应力筋和双弹簧单元的几何非线性有限元基本方程,用双弹簧单元模拟无粘结预应力筋和混凝土之间的相互作用。以此为理论基础,编制了大型非线性板壳有限元计算程序,程序可以对体内、体外无粘结预应力混凝土板壳结构和普通钢筋混凝土板壳结构进行线弹性及双重非线性计算,可以分级加载来模拟结构从张拉预应力筋到受力破坏的全过程受力反应。
(6)用有限元程序对配置体外CFRP预应力筋混凝土箱梁的抗弯性能进行参数分析,结果表明:梁的承载能力和刚度随混凝土强度的发展而提高;长期持荷会使已开裂梁的初始缺陷增大、承载能力和刚度降低;配置体外CFRP预应力筋的箱梁与配置体外预应力钢绞线的箱梁开裂荷载基本相等,箱梁开裂后配置体外CFRP预应力筋的箱梁刚度、屈服荷载和极限承载力略低。
(7)用有限元程序对配置体外CFRP预应力筋混凝土箱梁的剪力滞效应进行分析,结果表明:体外预应力混凝土箱梁在线弹性阶段的受力适用叠加原理;体外预应力混凝土箱梁在外荷载作用下的翼缘有效宽度计算系数ρf与普通钢筋混凝土箱梁基本相同;箱梁在体外预应力筋作用下的ρf与箱梁体在体外预应力筋等效荷载作用下的ρf基本相同;不设转向块直线布置的体外预应力筋张拉力作用下,跨中附近梁段基本不存在剪力现象。
(8)依据试验和分析结果,对配置体外CFRP预应力筋混凝土箱梁的有效宽度计算系数适当简化,并对配置体外CFRP预应力筋混凝土梁的张拉控制应力、体内非预应力受拉钢筋配筋率、相对受压区高度、极限承载能力计算、正常使用阶段验算等内容进行了系统建议和总结。
The thin-walled concrete beams prestressed with external CFRP tendons would become more popular both in new construction and in strengthening of existing structures. But there is no the design code for it so far at home and abroad. The prestress increment in external prestressed tendons is always analyzed with emprical formulas or analytical model for the analysis of the unbonded prestressed tendons, which is not inapplicable or inaccuracy sometimes. So the fomula for the external prestresse increment and the behaviors of concrete beam prestressed with external CFRP tendons need to be studied better. The flexural behaviors of the concrete T/box beam prestressed with external tendons were studied experimentally and theoretically, and the following works have been done:
(1) Tests were carried out on 5 beams under four-point load, of which four beams were reinforced with hybrid both external CFRP tendons and internal reinforcement and another one only reinforced with internal ordinary steel bar. The beams’bearing capacity, deformation, ductility index, cracking pattern and failure mode were studied. It was showed that the the bearing capacity of the concrete beam can ben improved effectively by external prestressed tendons. The expected failure mode is the concrete crushing rather than the externally prestressed CFRP tendons rupturing. Non-prestressing internal reinforcement can improve the flexural behaviors of beams prestressed with external CFRP tendons effectively since it can lead to a more rational crack distribution and better ductility, and the ductility index of beams prestressed with external CFRP tendons in this paper can reach about 2.5. The initial loading state on the beam before tendon jacking has no significant influence on the ultimate capacity and deflection.
(2) A program was developed to predict the behaviors of those beams prestressed with externally prestressed tendons. The flexural capacity, deformation and failure modes of beams with different parameters can be analyzed using the program, such as types of plan and prestressed tendons(extrenal prestessed tendons, internal unbonded prestressed tendons, internal bonded prestressed tendons), jacking and effective stress in external prestressed tendons, configuration of the deviators, properties of tendon, ratio of span to effective depth of the beam and load pattern, initial loading state at tendon jacking, etc.
(3) Nonlinear behaviors of the concrete beam prestressed with external or internal unbonded tendons were studied by the program developed. Such parameters as the percentage of ordinary reinforcment, amounts and configuration of unbonded prestressed tendons, the ratio of span to depth and the loading patterns were considered. Based on the results, the fomula for the eqivalent length of deformation zone on the beams at ultimate were developed. A simple formula was developed for the ultimate mid-span deflection of concrete beams with concept of equivalent length of deformation zone, and the deformation of beam before internal reinforcement yielding was predicted by the traditional formula for the deformation of partically prestressed concrete beam. Then an analytical model was deduced for analyzing the ultimate stress increment in those concrete beams prestressed with external or internal unbonded tendons based on the mid-span deflection.
(4) Testes were carried out on a thin-walled concrete box beam presressed with external CFRP tendons to study its short-term performances under uniform load, long-term behaviors under uniform load, and full-time performance under four-point load in turn. Prestressing loss of CFRP, stress/strain distribution in flange, deformation and crack distribution were studied. The results indicated that: effective width coefficient of compression top flange increased by less than 8% due to concrete cracking, long-term loading, and ordinary tension reinforcement yielding; the test value of deflection at mid-span at 1001 day was 2.32~2.42 times of the initial deflection, plastic deformation at 20 days after unloading was 41% of 1001 day’s; the strain of tensile reinforcement had a 65% increase than that of its initial value, and residual strain after unloading was about zero; the strain of compressed reinforcing steel bar had a 225%~268% increase than that of its initial value, and residual strain at 20 days after unloading was 53% of 1001 day’s; compression strain on top plate of the box girder under long-term load increased quickly in the early stage and became stable after 2 years, and it had a 164%~224% increase than that of its initial value at 1001 day; the crack width increased as time increased under long-term load, then it became stable after more or less 2 years, and it was 1.59~2.69 times than that of its initial value at 1001 day; most of the cracks in the bottom plate of box girder developed from middle of bottom plate, and they were wider in the middle of the bottom plate than at the bottom ends of the webs; the strain distributed over the section depth of web agreed well with plane assumption. Based on the behaviors of concrete beams prestressed with external CFRP tendons, the comformable formulars for predicting crack width of concrete box/T girder prestressed with external CFRP tendons were proposed by modifying traditional formulas in design codes for predicting the crack with of ordinary prestressed concrete beams.
(5) Based on Mindlin-Reissener theories of thick plate, the fundamental geometric nonlinearity equations for flat-shell element were set up with U.L formulas. A flat-shell element was composed with the lock-free element for thick/thin plates(Yuqiu Long) and the four-nodded arbitrary quadrilateral finite element with in-plane rotational degree of freedom. Then the fundamental equations for plate/shell bi-nonlinear finite element model were set up with layered finite method. the fundamental geometric nonlinearity equations for the unbonded prestressed tendon and double spring element were proposed, and the double spring element was used to simulate the interaction of unbonded prestressed tendon and deviator. Based on these theories mentioned above, a finite element program for bi-nonlinear analysis of plate/shell concrete structure prestressed with external tendons was developed. Using this program, either linear elastic or bi-nonlinear anslysis can be conducted for both plate/shell concrete structures prestressed with external or internal unbonded tendons or ordinary reinforced concrete plate/shell structures. Further more, analysis for prestressed structure, where from the beginning of stretching prestressed tendons to failure at last, can be simulated with the method of incremental step loading.
(6) Parametric studies on the flexural behaviors of the concrete box beam prestressed with external CFRP tendons were conducted using the finite element program. It’s concluded that the bearing capacity and the stiffness of the beam enhanced with the development of the concrete strength, the initial defect of the beam with crack increased and the bearing capacity and the stiffness reduced as time increased under the long-term load. The cracking load of the beam prestressed with external CFRP tendons was about same as that of beam prestressed with external stranded steel wire. The stiffness of the beam after the concrete cracking, yielding load and the ultimate bearing capacity of beam prestressed with external CFRP tendons were smaller than that prestressed with external stranded steel wire.
(7) Shear-lag effect in flange of concrete box beam prestressed with external CFRP tendons was analyzed using the finite element program. The results indicated that the superposition principle can be used in the concrete box beam prestressed with external tendons in the linear elastic stage. Effective width coefficient of the flangeρf of box beam under the action of external prestressed force is the same as theρf of normal reinforced concrete box beam under the equivalent loads of external prestressed tendons. Theρf of the box girder under the action of the external prestressed tendon is basically the same as that of the reinforced concrete box girder under the action of the equivalent load of the external prestressed tendons. Basically there were no shear-lag effect existed in the elements beside the mid-span of the beam under the action of external prestressed tendons which lay out straightly with no deviator.
(8) Based on the results of experimental and theoretical studies, the effective width coefficient of flange of box beam prestressed with external CFRP tendons was simplified appropriately, and design proposals of concrete beams prestressed with external CFRP tendons were put forward systematized, such as the stretching control stress of CFRP tendons, amount of the normal reinforcement, relative height of equivalent compression zone,method for ultimate bearing capacity and checking computations of the normal serviceability stage and so on.
引文
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