体外预应力连续梁动力特性的等效刚度分析法
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摘要
在已有的体外预应力连续梁动力特性分析中,采用了正比假设和面积等效假设。本文指出了这两个假设存在的问题,放弃了这两个假设,提出了等效刚度法,同时引入两个新的假设:计算第1对称振型自振频率时,体外筋拉力增量产生的综合弯矩图等效为该振型的2阶导数的比例图,将体外预应力梁转化为具有等效刚度的受压梁,体外筋的效应体现为梁刚度的增加;忽略了体外筋对其他自振频率的效应。与已有算法相比,由于假设更为合理,梁的自振频率的计算结果更为准确,与数值解吻合良好。计算表明:已有算法低估了体外筋对第1对称振型自振频率的效应;随着体外筋面积和偏心距的增加,梁的第1对称振型自振频率也随之增加,其他频率的变化很小;体外筋线形的线性变换不影响梁的自振频率。
In the existent analysis of dynamic behavior of externally prestressed continuous beam,the proportional assumption and the equivalent area assumption were adopted. The problems of these two assumptions were pointed out. The equivalent stiffness method was put forward,which gave up two old assumptions and introduced two new assumptions. In calculation of 1stnatural frequency of symmetric vibration mode. The resultant bending moment diagram caused by the tension increment of external tendon was equivalent to the diagram proportional to the 2ndorder derivative of this mode. The externally prestressed beam was transformed into the compressive beam with equivalent stiffness. The effect of external tendon was regarded as the increment of beam stiffness and the effect of external tendon on the other natural frequencies was neglected. Compared with the existent method,due to more rational assumptions,the calculation results of natural frequencies were more accurate,and conformed well to the numerical results. The calculation results show: the effect of external tendon on 1stnatural frequency of symmetric vibration mode is underestimated by the existent method. With increasing the area and the eccentricity of external tendon,the 1stnatural frequency of symmetric vibration mode increases,and other frequencies change slightly. The linear transformation of external tendon configuration doesn't influence the natural frequency.
In the existent analysis of dynamic behavior of externally prestressed continuous beam,the proportional assumption and the equivalent area assumption were adopted. The problems of these two assumptions were pointed out. The equivalent stiffness method was put forward,which gave up two old assumptions and introduced two new assumptions. In calculation of 1stnatural frequency of symmetric vibration mode. The resultant bending moment diagram caused by the tension increment of external tendon was equivalent to the diagram proportional to the 2ndorder derivative of this mode. The externally prestressed beam was transformed into the compressive beam with equivalent stiffness. The effect of external tendon was regarded as the increment of beam stiffness and the effect of external tendon on the other natural frequencies was neglected. Compared with the existent method,due to more rational assumptions,the calculation results of natural frequencies were more accurate,and conformed well to the numerical results. The calculation results show: the effect of external tendon on 1stnatural frequency of symmetric vibration mode is underestimated by the existent method. With increasing the area and the eccentricity of external tendon,the 1stnatural frequency of symmetric vibration mode increases,and other frequencies change slightly. The linear transformation of external tendon configuration doesn't influence the natural frequency.
引文
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[3]Ayaho Miyagawa,Katsuji Tei,Hideaki Nakamura,et al.Behavior of prestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE.2000,126(9):1033-1044.
[4]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55-61XIONG Xueyu,WANG Shousheng.Analysis and research of externally prestressed beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55-61.(in Chinese)
[5]熊辉霞,张耀庭.体外预应力混凝土梁自振频率分析[J].工程力学,2008,25(SupplementⅡ):173-176XIONG Huixia,ZHANG Yaoting.Analysis of natural frequency of externally prestressed concrete beam[J].Engineering Mechanics,2008,25(SupplementⅡ):173-176.(in Chinese)
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[7]焦春节,丁洁民.体外预应力钢—混凝土组合连续梁自振频率分析[J].工程力学,2011,28(2):193-197.JIAO Chunjie,DING Jiemin.Analysis of natural frequency of prestressed composite beam with external tendons[J].Engineering Mechanics.2011,28(2):193-197.(in Chinese)
[8]熊学玉,高峰,李阳.体外预应力连续梁振动特性的分析与研究[J].振动与冲击,2011,30(6):104-108.XIONG Xueyu,GAO Feng,LI Yang.Analysis on vibration behavior of externally prestressed concrete continous beam[J].Journal of Vibration and Shock,2011,30(6):104-108.(in Chinese)
[9]方德平,王全凤.体外预应力梁动力特性分析的一种新方法[J].地震工程与工程振动,2010,30(4):66-71.FANG Deping,WANG Quanfeng.A new method for analyzing dynamic behavior of externally prestressed beam[J].Journal of Earthquake Engineering and Engineering Vibration,2010,30(4):66-71.(in Chinese)
[10]方德平.大偏心体外预应力梁的弯矩-曲率分析法[J].建筑结构,2002,32(6):19-22.FANG Deping.Analysis method of moment-curvature for externally prestressed beams with large eccentricity[J].Building Structure,2002,32(6):19-22.(in Chinese)
[2]杜进生,区达光.体外预应力筋的极限应力:既有典型计算方法评述[J].工程力学,2010,27(9):63-68.DU Jinsheng,Francis Tk Au.Ultimate stress in external tendons:comments on the existing typical methods[J].Engineering Mechanics.2010,27(9):63-68.(in Chinese)
[3]Ayaho Miyagawa,Katsuji Tei,Hideaki Nakamura,et al.Behavior of prestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE.2000,126(9):1033-1044.
[4]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55-61XIONG Xueyu,WANG Shousheng.Analysis and research of externally prestressed beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55-61.(in Chinese)
[5]熊辉霞,张耀庭.体外预应力混凝土梁自振频率分析[J].工程力学,2008,25(SupplementⅡ):173-176XIONG Huixia,ZHANG Yaoting.Analysis of natural frequency of externally prestressed concrete beam[J].Engineering Mechanics,2008,25(SupplementⅡ):173-176.(in Chinese)
[6]李军强,方同.轴向力作用下连续梁固有振动分析[J].机械科学与技术,1998,17(4):541-547.LI Junqiang,FANG Tong.Analysis of natural transverse vibration of continuous beam subjected to axial force[J].Mechanical Science and Technology.1998,17(4):541-547.(in Chinese)
[7]焦春节,丁洁民.体外预应力钢—混凝土组合连续梁自振频率分析[J].工程力学,2011,28(2):193-197.JIAO Chunjie,DING Jiemin.Analysis of natural frequency of prestressed composite beam with external tendons[J].Engineering Mechanics.2011,28(2):193-197.(in Chinese)
[8]熊学玉,高峰,李阳.体外预应力连续梁振动特性的分析与研究[J].振动与冲击,2011,30(6):104-108.XIONG Xueyu,GAO Feng,LI Yang.Analysis on vibration behavior of externally prestressed concrete continous beam[J].Journal of Vibration and Shock,2011,30(6):104-108.(in Chinese)
[9]方德平,王全凤.体外预应力梁动力特性分析的一种新方法[J].地震工程与工程振动,2010,30(4):66-71.FANG Deping,WANG Quanfeng.A new method for analyzing dynamic behavior of externally prestressed beam[J].Journal of Earthquake Engineering and Engineering Vibration,2010,30(4):66-71.(in Chinese)
[10]方德平.大偏心体外预应力梁的弯矩-曲率分析法[J].建筑结构,2002,32(6):19-22.FANG Deping.Analysis method of moment-curvature for externally prestressed beams with large eccentricity[J].Building Structure,2002,32(6):19-22.(in Chinese)
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