复合边界条件下基于能量法吊索张力实用公式
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摘要
为提高工程中吊杆张力计算精度,考虑了中、下承式拱桥吊索两端拱肋和系杆梁附加质量、减振垫减振作用及弹性支承等复合边界条件,基于Rayleigh能量法建立了吊索横向振动频率和吊索张力的显式关系式。采用京港澳高速公路郑州黄河二桥主桥施工现场测试数据,对所推导的计算公式进行了验证。结果表明,该计算公式比较全面地考虑了吊索两端实际复合边界条件,与传统计算公式相比,其计算结果精度更高,且为显式表达式,更适用于中、下承式拱桥吊索的张力计算及工程现场测试使用。对于郑州黄河二桥主桥等采用刚性系杆梁的中、下承式拱桥,吊索两端约束条件更接近于固接。
To improve the calculation precision of hanger tension in engineering, the complex boundary conditions such as addition masses of tied beams and ribs at both ends of hanger,damping effect of shock pads and elastic supports are considered,some explicit relational expressions between hanger tension and the transverse vibration frequency are established based on Rayleigh theory.The expressions are verified by the measured construction data of the Second Yellow River Bridge in Zhengzhou on Beijing-Hong Kong-Macao expressway.The results show that the expressions considered the combined boundary conditions are suited to calculate tensions of long or short hangers with high precision.And the expressions are strongly practical for their explicit forms.For the Second Yellow River Bridge in Zhengzhou,the restraint at the ends of hanger is mostly close to fixed.
To improve the calculation precision of hanger tension in engineering, the complex boundary conditions such as addition masses of tied beams and ribs at both ends of hanger,damping effect of shock pads and elastic supports are considered,some explicit relational expressions between hanger tension and the transverse vibration frequency are established based on Rayleigh theory.The expressions are verified by the measured construction data of the Second Yellow River Bridge in Zhengzhou on Beijing-Hong Kong-Macao expressway.The results show that the expressions considered the combined boundary conditions are suited to calculate tensions of long or short hangers with high precision.And the expressions are strongly practical for their explicit forms.For the Second Yellow River Bridge in Zhengzhou,the restraint at the ends of hanger is mostly close to fixed.
引文
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[13]郭向荣,陈淮.弹性支承对斜拉桥拉索自振特性的影响[J].郑州工业大学学报,2000,21(1):34-36.Guo Xiangrong,Chen Huai.The effect of elasticsupport on the natural frequency of flexible cable ofcable stayed bridge[J].Journal of ZhengzhouUniversity of Technology,2000,21(1):34-36.(inChinese)
[2]任伟新,胡卫华,刘浩亮.索的动刚度与模态参数识别[J].工程力学,2008,25(4):93-98.Ren Weixin,Hu Weihua,Liu Haoliang.Identificationfor dynamic stiffness and modal parameter of cables[J].Engineering Mechanics,2008,25(4):93-98.(inChinese)
[3]何伟,陈淮,王博,等.复杂边界条件下基于频率法的吊杆张力测定研究[J].土木工程学报,2012,45(3):93-98.He Wei,Chen Huai,Wang Bo,et al.Study ofsuspender tension measurement based on frequencymethod with complex boundary conditions[J].ChinaCivil Engineering Journal,2012,45(3):93-98.(inChinese)
[4]魏金波,李国强,段欣,等.弹性支承索参数识别方法[J].振动、测试与诊断,2012,32(2):312-316.Wei Jinbo,Li Guoqiang,Duan Xin,et al.Parameteridentification for flexibility support cable[J].Journalof Vibration,Measurement&Diagnosis,2012,32(2):312-316.(in Chinese)
[5]董建华.中、下承式拱桥吊索的模态分析与张力测定[D].郑州:郑州大学,2004.
[6]陈刚.振动法测索力与实用公式[D].福州:福州大学,2004.
[7]任伟新,陈刚.由基频计算拉索拉力的实用公式[J].土木工程学报,2005,38(11):26-31.Ren Weixin,Chen Gang.Practical formulas todetermine cable tension by using cable fundamentalfrequency[J].China Civil Engineering Journal,2005,38(11):26-31.(in Chinese)
[8]陈淮,董建华.中、下承式拱桥吊索张力测定的振动法实用公式[J].中国公路学报,2007,20(3):66-70.Chen Huai,Dong Jianhua.Practical formulae ofvibration method for suspender tension measure onhalf-through and through arch bridge[J].ChinaJournal of Highway and Transport,2007,20(3):66-70.(in Chinese)
[9]方志,张智勇.斜拉桥的索力测试[J].中国公路学报,1997,10(1):51-58.Fang Zhi,Zhang Zhiyong.Test of cable tension incable-stayed bridges[J].China Journal of Highwayand Transport,1997,10(1):51-58.(in Chinese)
[10]王朝华,李国蔚,何祖发,等.斜拉桥索力测量的影响因素分析[J].世界桥梁,2004,3:64-67.Wang Chaohua,Li Guowei,He Zufa,et al.Analysisof influential factors in cable force measurement ofcable-stayed bridges[J].World Bridges,2004,3:64-67.(in Chinese)
[11]Clough R W,Penzien J.Dynamics of structure[M].2nd ed.California:Computers and Structures Inc.,1995:120-129.
[12]何伟.中、下承式钢管混凝土拱桥损伤识别关键问题研究[D].郑州:郑州大学,2010.
[13]郭向荣,陈淮.弹性支承对斜拉桥拉索自振特性的影响[J].郑州工业大学学报,2000,21(1):34-36.Guo Xiangrong,Chen Huai.The effect of elasticsupport on the natural frequency of flexible cable ofcable stayed bridge[J].Journal of ZhengzhouUniversity of Technology,2000,21(1):34-36.(inChinese)
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