变高度悬臂箱梁剪力滞效应的半解析解

潘旦光; 付相球; 韦杉杉; 陈钒; 杨少平

doi:10.6052/j.issn.1000-4750.2017.08.0643

变高度悬臂箱梁剪力滞效应的半解析解

doi: 10.6052/j.issn.1000-4750.2017.08.0643

1.
北京科技大学土木工程系, 北京 100083;
2.
中电建路桥集团有限公司, 北京 100048;
3.
中国水电建设集团十五工程局有限公司, 西安 710068

基金项目: 北京市自然科学基金项目（8143037）；北京科技大学教改项目（JG2013M11）.

详细信息

作者简介:
付相球(1994-),男,江西人,硕士生,主要从事防灾减灾及防护工程研究(E-mail:1376369310@qq.com);韦杉杉(1993-),女,河北人,硕士生,主要从事工程结构与工程系统抗震方向的研究(E-mail:814440337@qq.com);陈钒(1972-),男,江西人,教授级高工,硕士,主要从事道路桥梁设计、施工研究(E-mail:cfsc_1037@163.com);杨少平(1990-),男,陕西人,助工,学士,主要从事道路桥梁施工研究(E-mail:505703213@qq.com).

通讯作者:
潘旦光(1974-),男,浙江人,研究员,博士,博导,主要从事防灾减灾及防护工程研究(E-mail:pdg@ustb.edu.cn).

中图分类号: U441+5
计量
- 文章访问数: 349
- HTML全文浏览量: 23
- PDF下载量: 54
- 被引次数: 0
出版历程
- 收稿日期: 2017-08-23
- 修回日期: 2018-01-16
- 刊出日期: 2018-09-29

SEMI-ANALYTIC SOLUTION FOR SHEAR LAG EFFECT OF CANTILEVER BOX GIRDERS WITH VARYING DEPTH

1.
Department of Civil Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2.
Power China Road Bridge Group Co., Beijing 100048, China;
3.
Sinohydro Engineering Bureau 15 Co., Ltd, Xi'an 710068, China

摘要

摘要: 以等截面Euler梁的自由振动模态为Ritz基函数，提出了一种求解变高度箱梁剪力滞微分方程组的Ritz法。该方法首先进行与箱梁相同跨度相同边界条件等截面欧拉梁模态分析，然后将箱梁的竖向挠度和剪切转角用模态及其导数的线性组合来表达，从而将变分法所得箱梁剪力滞微分方程组转化为线性代数方程组进行求解。在此基础上，研究了参与计算模态阶数和截面高度变化率对计算误差的影响，算例分析结果表明：箱梁高度变化越大，Ritz法的收敛速度越慢；但随着参与计算模态阶数的增加，Ritz法将收敛到解析解。采用12阶以上模态进行计算，所得的剪力滞系数误差小于5%。
- 箱梁 /
- 变高度 /
- 剪力滞 /
- Euler梁 /
- 模态
Abstract: By using the free vibration mode of an Euler beam as Ritz base function, a new Ritz method is proposed to solve the set of shear lag differential equations of a varying depth box girder. Firstly, the modal analysis of a uniform cross-sectional Euler beam which is the same length and boundary condition with the box girder is carried out. The vertical deflection and the shear rotation of the box girder are expressed by the linear combination of the model and its derivative. And then the set of shear-lag differential equations of the box girder obtained by the calculus of variations are transformed into a set of linear algebraic equations. Then, the influences of the number of modes and variation ratio of section height on the errors are investigated. The numerical examples show that:the more significant the height of the box girder varies, the slower the Ritz method converges; but the results by Ritz method would converge to the analytic solution with the increasing of the number of modes. The errors of shear lag coefficients are less than 5%, when more than 12 of modes are included.
- box girder /
- varying depth /
- shear lag /
- Euler beam /
- modes of shape

HTML全文

参考文献(16)

[1]	Cambronero-Barrientos F, Diaz-Del-Valle J, MartinezMartinez J A. Beam element for thin-walled beams with torsion, distortion and shear lag[J]. Engineering Structures, 2017, 143(15):571-588.
[2]	Zhu L, Nie J G, Li F X, et al. Simplified analysis method accounting for shear-lag effect of steel-concrete composite decks[J]. Journal of Constructional Steel Research, 2015, 115(7):62-80.
[3]	姚浩, 程进. 基于变分原理的波形钢腹板箱梁挠度计算解析法[J]. 工程力学, 2016, 33(8):177-184. Yao Hao, Cheng Jin. Analytical method for calculating defection of corrugated box girders based on variational principle[J]. Engineering Mechanics, 2016, 33(8):177-184. (in Chinese)
[4]	吴文清, 万水, 叶见曙, 等. 波纹钢腹板组合箱梁剪力滞效应的空间有限元分析[J]. 土木工程学报, 2004, 37(9):31-36. Wu Wenqing, Wan Shui, Ye Jianshu, et al. 3-D finite element analysis on shear lag effect in composite box girder with corrugated steel web[J]. China Civil Engineering Journal, 2004, 37(9):31-36. (in Chinese)
[5]	张元海, 林丽霞. 薄壁箱梁剪力滞效应分析的初参数法[J]. 工程力学, 2013, 30(8):205-211. Zhang Yuanhai, Lin Lixia. Initial parameter method for analysis shear lag effect of thin-walled box girders[J]. Engineering Mechanics, 2013, 30(8):205-211. (in Chinese)
[6]	甘亚南, 石飞停. 梯形箱梁剪力滞后效应的精细化分析[J]. 计算力学学报, 2014, 31(3):351-356. Gan Yanan, Shi Feiting. The delicate analysis of shear lag effect on trapezoidal box girders[J]. Chinese Journal of Computational Mechanics, 2014, 31(3):351-356. (in Chinese)
[7]	张士铎, 丁芸. 变截面悬臂箱梁负剪力滞差分解[J]. 重庆交通学院学报, 1984(4):34-47. Zhang Shiduo, Ding Yun. Finite difference solution in shear lag effect on cantilever box gerder with linear varying depths[J]. Journal of Chongqing Jiaotong University, 1984(4):34-47. (in Chinese)
[8]	罗旗帜. 变截面多跨箱梁桥剪滞效应分析[J]. 中国公路学报, 1998, 11(1):63-70. Luo Qizhi. Analysis of the shear lag effect on continuous box girder bridges with variable depth[J]. China Journal of Highway and Transport, 1998, 11(1):63-70. (in Chinese)
[9]	Zhang Y H, Lin L X. Shear lag analysis of thin-walled box girders based on a new generalized displacement[J]. Engineering Structures, 2014, 61(1):73-83.
[10]	周世军. 箱梁的剪力滞效应分析[J]. 工程力学, 2008, 25(2):204-208. Zhou Shijun. Shear lag analysis of box girders[J]. Engineering Mechanics, 2008, 25(2):204-208. (in Chinese)
[11]	刘世忠, 欧阳永金, 吴亚平, 等. 变截面薄壁箱梁剪力滞剪切变形效应分析[J]. 中国公路学报, 2002, 15(3):61-63, 67. Liu Shizhong, Ouyang Yongjin, Wu Yaping, et al. Non-uniform thin wall box analysis of considering both shear lag and shear deformation[J]. China Journal of Highway and Transport, 2002, 15(3):61-63, 67. (in Chinese)
[12]	吴幼明, 罗旗帜, 岳珠峰. 变高度连续箱梁剪力滞效应试验研究[J]. 实验力学, 2004, 19(1):85-90. Wu Youming, Luo Qizhi, Yue Zhufeng. An experimental study on the shear lag effect of continuous box girder with varying depth[J]. Journal of Experimental Mechanics, 2004, 19(1):85-90. (in Chinese)
[13]	刘杰, 成圣翱. 变截面矩形箱梁剪力滞效应的样条配点法[J]. 中南公路工程, 1995(1):35-38. Liu Jie, Cheng Shengao. Spline collocation method for the shear lag effect of non-uniform rectangle box girder[J]. Central South Highway Engineering, 1995(1):35-38. (in Chinese)
[14]	丁南宏, 林丽霞, 钱永久. 变截面箱梁剪力滞及剪切变形效应近似计算方法[J]. 铁道科学与工程学报, 2011, 8(1):14-18. Ding Nanhong, Lin Lixia, Qian Yongjiu. An approximate method to analyze the effect of shear lag and shear deformation of box beam with varying depth[J]. Journal of Railway Science and Engineering, 2011, 8(1):14-18. (in Chinese)
[15]	项海帆. 高等桥梁结构理论[M]. 北京:人民交通出版社, 2001:71-72. Xiang Haifan. Advanced theory of bridge structures[M]. Beijing:China Communications Press, 2001:71-72. (in Chinese)
[16]	楼梦麟, 吴京宁. 复杂梁动力问题的近似分析方法[J]. 上海力学, 1997, 18(3):234-240. Lou Menglin, Wu Jingning. An approach to solve dynamic problems of complicated beams[J]. Shanghai Journal of Mechanics, 1997, 18(3):234-240. (in Chinese)