移动车载作用下桥梁弯曲变形的时变特性研究
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摘要
以相向运动双车载作用下的三跨桥梁为例,引用奇异函数列出整桥的弯矩方程,通过奇异函数积分法则及力、位移边界条件,推导出桥梁在相应车载作用下的挠度方程。利用Mathcad求解进一步得到了单车载、双车载、多车载作用下桥梁的挠曲线,比较了不同车载速度及不同移动方向对桥梁各截面弯矩及挠度时变规律的影响,研究了在车载移动过程中各截面挠度达到最大时,截面与多个车载的相对位置关系。研究表明:随车载速度增加,截面挠度最大值先增后减;车载相向运动时,各截面在挠度达到最大时,截面与车载间距随车载移动呈先减后增的趋势;车载同向运动时,车载即将驶近或越过截面时,该截面挠度达到最大,截面与车载的距离很小,到桥梁中间截面时,这个距离迅速增大,随后截面与车载的距离呈线性减小趋势。
This paper takes the three-span bridge under the two vehicles moving along opposite directions as an example. By using the Singular Function to list the moment equation of the whole bridge, the integral rule of Singular Function and the force, and displacement boundary conditions, the deflection equation of bridge under corresponding vehicles is deduced. Furthermore, the deflection curve of the bridge at each time under the action of one vehicle, dual-vehicles and multi-vehicles moving along the forward direction and reverse motion is obtained by using Mathcad software. Comparing the influence of different vehicle speeds and shifting direction on the bending moment and deflection regularity of bridge's each section, the relative position relationship between the cross section and the vehicle is studied when the deflection of each section is maximized during the vehicle movement. With the increase of vehicle speed, the maximum value of section deflection increases first and then decreases. When the vehicle is moving along opposite direction, the distance between the section and the vehicle decreases first and then increases with the movement of the vehicle when the deflection of each section reaches the maximum. When the vehicle is moving in the same direction, no matter the vehicle is approaching or crossing the cross section, the deflection of the section reaches the maximum, and the distance between the section and the vehicle is very small. To the middle section of the bridge, the distance increases rapidly, and then the distance between the cross-section and the vehicle linearly reduced trend.
This paper takes the three-span bridge under the two vehicles moving along opposite directions as an example. By using the Singular Function to list the moment equation of the whole bridge, the integral rule of Singular Function and the force, and displacement boundary conditions, the deflection equation of bridge under corresponding vehicles is deduced. Furthermore, the deflection curve of the bridge at each time under the action of one vehicle, dual-vehicles and multi-vehicles moving along the forward direction and reverse motion is obtained by using Mathcad software. Comparing the influence of different vehicle speeds and shifting direction on the bending moment and deflection regularity of bridge's each section, the relative position relationship between the cross section and the vehicle is studied when the deflection of each section is maximized during the vehicle movement. With the increase of vehicle speed, the maximum value of section deflection increases first and then decreases. When the vehicle is moving along opposite direction, the distance between the section and the vehicle decreases first and then increases with the movement of the vehicle when the deflection of each section reaches the maximum. When the vehicle is moving in the same direction, no matter the vehicle is approaching or crossing the cross section, the deflection of the section reaches the maximum, and the distance between the section and the vehicle is very small. To the middle section of the bridge, the distance increases rapidly, and then the distance between the cross-section and the vehicle linearly reduced trend.
引文
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[2]Deng L,Wang W,Cai C S.Effect of pavement maintenance cycle on the fatigue reliability of simply-supported steel I-girder bridges under dynamic vehicle loading[J].Engineering Structures,2017,133:124-132.
[3]Mohammed A M,Almansour H H,Martín-Pérez B.Evaluation of dynamic deformations of slab-on-girder bridge under moving trucks with corrosion-damaged columns[J].Engineering Structures,2014,66(66):159-172.
[4]Yi T H,Li H N,Gu M.Experimental assessment of high-rate GPS receivers for deformation monitoring of bridge[J].Measurement,2013,46(1):420-432.
[5]Handayani H H,Yuwono,Taufik M.Preliminary Study of Bridge Deformation Monitoring Using GPS and CRP(Case Study:Suramadu Bridge)[J].Procedia Environmental Sciences,2015,24:266-276.
[6]Hidehiko Sekiya,Osamu Maruyama,Chitoshi Miki.Visualization system for bridge deformations under live load based on multipoint simultaneous measurements of displacement and rotational response using MEMS sensors[J].Engineering Structures,2017,146:43-53.
[7]Khuyen H T,Iwasaki E.An approximate method of dynamic amplification factor for alternate load path in redundancy and progressive collapse linear static analysis for steel truss bridges[J].Case Studies in Structural Engineering,2016,6:53-62.
[8]卓士创,蔡瑜玮,李顺才.移动载荷作用下多跨超静定梁内力及变形计算的奇异函数法[J].徐州师范大学学报,2010,28(3):55-59.
[9]王燮山.用奇异函数法求解某些变截面梁的变形[J].力学与实践,1984,4:55-57.
[10]徐光铭,王磊,张婷.利用MATHCAD计算公路桥梁荷载的横向分布系数[J].中国水运,2013,13(12):302-303.
[11]李立,李森.在桥梁设计中应用MATHCAD[J].华东公路,2001,1:45-46.
[12]袁宏智,马建敏.移动载荷作用下斜拉桥结构的动态响应计算分析[J].噪声与振动控制,2014,34(3):148-154.
[13]柳红霞.共轭梁法在梁变形计算中的运用[J].长沙大学学报,2002,16(2):63-66.
[14]张立彬,周京京,刘磊,等.多跨梁弯矩图与剪力图模拟显示软件的设计[J].河北大学学报自然科学版,2003,23(3):312-316.
[15]王连广,哈娜,于建军.基于能量法的U型钢与混凝土组合梁变形计算分析[J].东北大学学报(自然科学版),2009,30(3):438-440.
[16]王燮山.奇异函数及其在力学中的应用[M].北京:科学出版社,1993.