考虑滑移的体外预应力筋的分析理论
|
摘要
体外预应力筋在结构加固以及钢混组合结构中应用广泛,但是针对该类结构受力特性的分析方法并不完善,主要原因是在外荷载作用下,预应力筋与结构会产生相对滑移,传统分析方法中截面上应变协调的假设无法继续采用。体外预应力筋由于结构变形导致的应力增量是体外预应力筋分析理论中的一项重要内容,目前已有的应力增量计算方法,大多只适用于特定结构形式,或者没有考虑预应力筋在转向块处的滑移,局限性大。该文充分考虑体外预应力筋在转向块处的滑移,通过分析预应力筋的变形与结构整体变形的几何关系并进行线性化,导出了通用的体外预应力筋应力增量的计算公式,得到了其刚度矩阵的显式表达式,并构造了适用于考虑滑移的体外预应力筋的有限单元,在此基础上还提出了体外预应力筋应力增量的简化计算方法。最后通过数值算例验证了该文方法,结果表明该方法使用简便,精确度高。
Externally prestressed tendons have been used widely in repairing or retrofitting aged structures and new steel-concrete composite structures. Analytical methods for such structures, however, were not yet developed deeply enough because of the relative slip between the tendons and the deviators. In particular, the strain compatibility condition of tendons and the host structure, which is the fundamental hypothesis in conventional analysis methods, was no more available. The incremental stress induced by the deformation of the structure is of great importance in the analysis of such structures. Most existing methods in the literature are limited and only suitable for some certain types of structures or without considering the relative slip between tendons with deviators. This work investigated the kinematic relationship between the elongation of external tendons and the deformation of the host structures with the slip between the tendons and the deviators considered. A manipulation of linearizing this kinematic relationship yielded a general formula for the incremental stress of externally prestressed tendons caused by the deformation of the host structures. The stiffness matrix was also obtained explicitly. A new element was then developed for externally prestressed tendons considering the influence of the relative slip. Meanwhile, a simplified method for the evaluation of the incremental stress of externally prestressed tendons was proposed. Finally, some numerical examples demonstrated the convenience and accuracy of the proposed new element and simplified method.
Externally prestressed tendons have been used widely in repairing or retrofitting aged structures and new steel-concrete composite structures. Analytical methods for such structures, however, were not yet developed deeply enough because of the relative slip between the tendons and the deviators. In particular, the strain compatibility condition of tendons and the host structure, which is the fundamental hypothesis in conventional analysis methods, was no more available. The incremental stress induced by the deformation of the structure is of great importance in the analysis of such structures. Most existing methods in the literature are limited and only suitable for some certain types of structures or without considering the relative slip between tendons with deviators. This work investigated the kinematic relationship between the elongation of external tendons and the deformation of the host structures with the slip between the tendons and the deviators considered. A manipulation of linearizing this kinematic relationship yielded a general formula for the incremental stress of externally prestressed tendons caused by the deformation of the host structures. The stiffness matrix was also obtained explicitly. A new element was then developed for externally prestressed tendons considering the influence of the relative slip. Meanwhile, a simplified method for the evaluation of the incremental stress of externally prestressed tendons was proposed. Finally, some numerical examples demonstrated the convenience and accuracy of the proposed new element and simplified method.
引文
[1]熊学玉.体外预应力结构设计[M].北京:中国建筑工业出版社,2005:42―43.Xiong Xueyu.External-prestressed structure design[M].Beijing:China Architecture Industry Press,2005:42―43.(in Chinese)
[2]Harajli M H,Kanjli M Y.Ultimate flexural strength of concrete members prestressed with unbounded tendons[J].ACI Structural Journal,1991,88(6):13―22.
[3]Tong Y,Zhu J.Experimental study on reinforced concrete beams strengthened by externally prestressed vertical tensioning method[J].Industrial Construction,2012,42(6):83―87.
[4]Guiglia M,Taliano M,Debernardi P G.Calculation of the ultimate stress of unbonded tendons in prestressed concrete members considering the rotation capacity[J].Magazine of Concrete Research,2013,65(1):14―26.
[5]Zeng J,Su X.Variation of secondary moment and moment redistribution in prestressed continuous beams with unbounded tendons[J].Journal of Tongji University(Natural Science),2014,42(12):1797―1804.
[6]Baker A L L.Plastic theory of design for ordinary reinforced and prestressed concrete including moment redistribution in continuous members[J].Magazine of Concrete Research,1949,1(2):57―66.
[7]Naaman A E,Alkhairi F M.Stress at ultimate in unbonded post-tensioning tendons:part2-Proposed methodology[J].ACI Structural Journal,1991,88(6):683―692.
[8]Harajli M,Khairallah N,Nassif H.External prestressed members:evaluation of second-order effects[J].Journal of Structural Engineering,1999,125(10):1151―1161.
[9]Kim K S,Lee D H.Nonlinear analysis method for continuous post-tensioned concrete members with unbonded tendons[J].Engineering Structures,2012,40(7):487―500.
[10]杜进生,刘西拉.基于结构变形的无粘结预应力筋应力变化研究[J].土木工程学报,2003,36(8):12―19.Du Jinsheng,Liu Xila.Research on the variations of unbounded prestressed tendon stresses based upon the structure deformation[J].China Civil Engineering Journal,2003,36(8):12―19.(in Chinese)
[11]Ghallab A.Calculating ultimate tendon stress in externally prestressed continuous concrete beams using simplified formulas[J].Engineering Structures,2013,46(1):417―430.
[12]Yuan A,Dai H,Sun D,Cai J.Behaviors of segmental concrete box beams with internal tendons and external tendons under bending[J].Engineering Structures,2013,48(5):623―634.
[13]Bilal El-Ariss.Stiffness of reinforced concrete beams with external tendons[J].Engineering Structures,2004,26(14):2047―2051.
[14]Zona A,Ragni L,Dall A A.Finite element formulation for geometric and material nonlinear analysis of beams prestressed with external slipping tendons[J].Finite Elements in Analysis and Design,2008,44(15):910―919.
[15]Lou T,Lopes S M R,Lopes A V.Flexural response of continuous concrete beams prestressed with external tendons[J].Journal of Bridge Engineering,2013,18(6):525―537.
[16]朱正伟.基于能量法的体外预应力筋应力增量计算方法研究[D].重庆:重庆大学,2005.Zhu Zhengwei.Study on stress increments calculating technique of external tendons based on energy method[D].Chongqing:Chongqing University,2005.(in Chinese)
[2]Harajli M H,Kanjli M Y.Ultimate flexural strength of concrete members prestressed with unbounded tendons[J].ACI Structural Journal,1991,88(6):13―22.
[3]Tong Y,Zhu J.Experimental study on reinforced concrete beams strengthened by externally prestressed vertical tensioning method[J].Industrial Construction,2012,42(6):83―87.
[4]Guiglia M,Taliano M,Debernardi P G.Calculation of the ultimate stress of unbonded tendons in prestressed concrete members considering the rotation capacity[J].Magazine of Concrete Research,2013,65(1):14―26.
[5]Zeng J,Su X.Variation of secondary moment and moment redistribution in prestressed continuous beams with unbounded tendons[J].Journal of Tongji University(Natural Science),2014,42(12):1797―1804.
[6]Baker A L L.Plastic theory of design for ordinary reinforced and prestressed concrete including moment redistribution in continuous members[J].Magazine of Concrete Research,1949,1(2):57―66.
[7]Naaman A E,Alkhairi F M.Stress at ultimate in unbonded post-tensioning tendons:part2-Proposed methodology[J].ACI Structural Journal,1991,88(6):683―692.
[8]Harajli M,Khairallah N,Nassif H.External prestressed members:evaluation of second-order effects[J].Journal of Structural Engineering,1999,125(10):1151―1161.
[9]Kim K S,Lee D H.Nonlinear analysis method for continuous post-tensioned concrete members with unbonded tendons[J].Engineering Structures,2012,40(7):487―500.
[10]杜进生,刘西拉.基于结构变形的无粘结预应力筋应力变化研究[J].土木工程学报,2003,36(8):12―19.Du Jinsheng,Liu Xila.Research on the variations of unbounded prestressed tendon stresses based upon the structure deformation[J].China Civil Engineering Journal,2003,36(8):12―19.(in Chinese)
[11]Ghallab A.Calculating ultimate tendon stress in externally prestressed continuous concrete beams using simplified formulas[J].Engineering Structures,2013,46(1):417―430.
[12]Yuan A,Dai H,Sun D,Cai J.Behaviors of segmental concrete box beams with internal tendons and external tendons under bending[J].Engineering Structures,2013,48(5):623―634.
[13]Bilal El-Ariss.Stiffness of reinforced concrete beams with external tendons[J].Engineering Structures,2004,26(14):2047―2051.
[14]Zona A,Ragni L,Dall A A.Finite element formulation for geometric and material nonlinear analysis of beams prestressed with external slipping tendons[J].Finite Elements in Analysis and Design,2008,44(15):910―919.
[15]Lou T,Lopes S M R,Lopes A V.Flexural response of continuous concrete beams prestressed with external tendons[J].Journal of Bridge Engineering,2013,18(6):525―537.
[16]朱正伟.基于能量法的体外预应力筋应力增量计算方法研究[D].重庆:重庆大学,2005.Zhu Zhengwei.Study on stress increments calculating technique of external tendons based on energy method[D].Chongqing:Chongqing University,2005.(in Chinese)