考虑复合边界条件的中、下承式拱桥吊杆张力计算公式
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摘要
基于Euler-Bernoulli梁理论,建立考虑吊杆两端拱肋、系杆梁弹性支承和减振垫影响的吊杆张力计算模型,推导中、下承式拱桥吊杆张力计算公式。对于吊杆两端铰支情况,导出以横向振动频率表达的吊杆张力解析式;对于吊杆两端固支情况,运用Newton-Raphson法迭代求解,采用统一函数形式分段拟合得出分别以吊杆前4阶横向振动频率显式表达的吊杆张力计算公式。依据京港澳高速公路郑州黄河二桥现场施工数据对给出的吊杆张力计算公式进行验证。结果表明,运用给出的吊杆张力公式计算得到的结果与实测值相近,误差在4%以内。说明给出计算公式适用于中、下承式拱桥的吊杆张力计算。
Based on Euler-Bernoulli beam theory,a computational model for suspender tension was established,considering the influences of the arch ribs at both ends of suspender,the elastic supports of tie beams and the damping effect of shock pads.The computational formulas for the suspender tension of half-through and through arch bridge were deduced.For hinged suspender,an analytic expression of suspender tension expressed by transverse vibration frequency was established.For clamped support suspender,by means of Newton-Raphson iterative solution and using a uniform function for piecewise fitting,the computational formula for suspender tension was obtained,which was explicitly expressed by the first 4-step transverse vibration frequency of suspender respectively.The proposed formula was validated by the field construction data of the Second Yellow River Bridge in Zhengzhou on Beijing-Hongkong-Macao expressway.The results show that the computed values of the tension obtained by the proposed formula are similar to measured values,and the errors are less than 4%,which shows that the proposed computational formulas are applicable to the suspender tensions of half-through and through arch bridge.
Based on Euler-Bernoulli beam theory,a computational model for suspender tension was established,considering the influences of the arch ribs at both ends of suspender,the elastic supports of tie beams and the damping effect of shock pads.The computational formulas for the suspender tension of half-through and through arch bridge were deduced.For hinged suspender,an analytic expression of suspender tension expressed by transverse vibration frequency was established.For clamped support suspender,by means of Newton-Raphson iterative solution and using a uniform function for piecewise fitting,the computational formula for suspender tension was obtained,which was explicitly expressed by the first 4-step transverse vibration frequency of suspender respectively.The proposed formula was validated by the field construction data of the Second Yellow River Bridge in Zhengzhou on Beijing-Hongkong-Macao expressway.The results show that the computed values of the tension obtained by the proposed formula are similar to measured values,and the errors are less than 4%,which shows that the proposed computational formulas are applicable to the suspender tensions of half-through and through arch bridge.
引文
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[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 of Suspender Tension Measurement Based on Frequency Methodwith Complex Boundary Conditions[J].China Civil Engineering Journal,2012,45(3):93-98.in Chinese)
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[6]许俊.斜拉索索力简化计算中的精度分析[J].同济大学学报:自然科学版,2001,29(5):611-615.(XU Jun.Precision Analysis of Calculating Tension Force of Cable[J].Journal of Tongji University:Natural Sci-ence,2001,29(5):611-615.in Chinese)
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[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 of Vibration Method for Suspender Tension Measure on Half-Through and Through Arch Bridge[J].China Journal of Highway and Transport,2007,20(3):66-70.in Chi-nese)
[9]CLOUGH R W,PENZIEN J.Dynamics of Structure[M].2nd ed.California:Computers and Structures,Inc.,1995.
[10]李冬生.拱桥吊杆损伤监测与健康诊断[D].哈尔滨:哈尔滨工业大学,2007.LI Dongsheng.Damage Monitoring and Health Diagnosis for Arch Bridge Suspender[D].Harbin:Harbin Instituteof Technology,2007.in Chinese)
[11]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.(HE Wei.Research on the Key Problem of Damage Identification Method for Half Through or Through ConcreteFilled Steel Tubular Arch Bridge[D].Zhengzhou:Zhengzhou University,2010.in Chinese)
[2]谢旭,孙良凤,王渊,等.基于神经网络算法和附加质量法的短吊杆张力识别[J].中国铁道科学,2010,31(4):33-38.(XIE Xu,SUN Liangfeng,WANG Yuan,et al.The Tension Identification of Short Hangers Based on Neural Net-work Algorithm and Additional Mass Method[J].China Railway Science,2010,31(4):33-38.in Chinese)
[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 of Suspender Tension Measurement Based on Frequency Methodwith Complex Boundary Conditions[J].China Civil Engineering Journal,2012,45(3):93-98.in Chinese)
[4]ZUI H,SHINKE T,NAMITA Y H.Practical Formulas for Estimation of Cable Tension by Vibration Method[J].Journal of Structure Engineering,1996,122(6):651-656.
[5]张志国,靳明君,邹振祝.自重荷载作用下悬索静力解析解[J].中国铁道科学,2004,25(3):67-70.(ZHANG Zhiguo,JIN Mingjun,ZOU Zhenzhu.Static Solution of Suspension Cables under Tare Load[J].ChinaRailway Science,2004,25(3):67-70.in Chinese)
[6]许俊.斜拉索索力简化计算中的精度分析[J].同济大学学报:自然科学版,2001,29(5):611-615.(XU Jun.Precision Analysis of Calculating Tension Force of Cable[J].Journal of Tongji University:Natural Sci-ence,2001,29(5):611-615.in Chinese)
[7]张宏跃,田石柱.提高斜拉索索力估算精度的方法[J].地震工程与工程震动,2004,24(4):1-4.(ZHANG Hongyue,TIAN Shizhu.Improved Method to Enhance the Estimation Accuracy of Stay Cable Tension[J].Earthquake Engineering and Engineering Vibration,2004,24(4):1-4.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 of Vibration Method for Suspender Tension Measure on Half-Through and Through Arch Bridge[J].China Journal of Highway and Transport,2007,20(3):66-70.in Chi-nese)
[9]CLOUGH R W,PENZIEN J.Dynamics of Structure[M].2nd ed.California:Computers and Structures,Inc.,1995.
[10]李冬生.拱桥吊杆损伤监测与健康诊断[D].哈尔滨:哈尔滨工业大学,2007.LI Dongsheng.Damage Monitoring and Health Diagnosis for Arch Bridge Suspender[D].Harbin:Harbin Instituteof Technology,2007.in Chinese)
[11]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.(HE Wei.Research on the Key Problem of Damage Identification Method for Half Through or Through ConcreteFilled Steel Tubular Arch Bridge[D].Zhengzhou:Zhengzhou University,2010.in Chinese)
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