Volume 22 Issue 5
Oct.  2022
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Article Navigation >  Journal of Traffic and Transportation Engineering  > 2022  >  22(5): 217-230
ZHANG Guo-jing, LIU Yong-jian, LIU Jiang. Analytical solution and calculation method of reasonable arch axis of through arch bridge[J]. Journal of Traffic and Transportation Engineering, 2022, 22(5): 217-230. doi: 10.19818/j.cnki.1671-1637.2022.05.013
Citation: ZHANG Guo-jing, LIU Yong-jian, LIU Jiang. Analytical solution and calculation method of reasonable arch axis of through arch bridge[J]. Journal of Traffic and Transportation Engineering, 2022, 22(5): 217-230. doi: 10.19818/j.cnki.1671-1637.2022.05.013
shu

Analytical solution and calculation method of reasonable arch axis of through arch bridge

doi: 10.19818/j.cnki.1671-1637.2022.05.013
  • 1.

    School of Highway, Chang'an University, Xi'an 710064, Shaanxi, China

  • 2.

    Research Center of Highway Large Structure Engineering on Safety of Ministry of Education, Chang'an University, Xi'an 710064, Shaanxi, China

Funds:

National Key Research and Development Program of China 2016YFC0701202

National Natural Science Foundation of China 51178051

Fundamental Research Funds for the Central Universities 300102219310

More Information
    Abstract
  • To obtain the analytical solution and calculation method of the reasonable arch axis of through arch bridge, the dead load action mode and differential equation of the reasonable arch axis were established, and the analytical solution of the reasonable arch axis was determined. Based on the analytical solution, the dead load ratio of main arch was defined. Based on the rise-span ratio and dead load ratio of main arch, a quick calculation method of the reasonable arch axis was obtained. The reliability of the proposed method was confirmed by arch bridge design specifications, engineering cases, and related research achievements. Research results show that the dead load action mode of through arch bridge can be equivalent to the combination of continuous uniform dead load and arch dead load, the reasonable arch axis is catenary, and the corresponding arch axis coefficient is determined by the rise-span ratio and dead load ratio of main arch. The fitted functional relationships between the arch axis coefficients and dead load ratios of main arch under different rise-span ratios are a linear correlation, and the determination coefficients are greater than 0.99, indicating that the fitted equations are accurate. The rise-span ratio of through arch bridge is between 1/3 and 1/8 in engineerings, and the range of the corresponding arch axis coefficient is between 1.000 and 1.792. The common rise-span ratio ranges from 1/4 to 1/5, and the corresponding arch axis coefficient ranges from 1.000 to 1.465. The calculation results are in good agreement with the statistical results of arch axis coefficients of engineering cases, indicating that the calculation results are reliable. The common dead load ratio of main arch ranges from 0.1 to 0.5, and the corresponding arch axis coefficient ranges from 1.102 to 1.364. The calculation results are close to the value ranges in the arch bridge design specification, which proves the rationality of value range in the arch bridge design specification. When the dead load ratio of main arch is less than 0.5 and the rise-span ratio is less than 1/7, or the dead load ratio of main arch is less than 0.1, the arch axis coefficient is close to 1.000. As a result, the quadratic parabola can be used as reasonable arch axis. The reasonable arch axis equation can be obtained quickly by the look-up table method and simplified formula method. Compared with the mature research achievements, the deviations of bending moments, eccentricities and sums of squared eccentricities of main arch cross-section are within 5%, which proves the correctness of the solution method.

     

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    • References(26)
  • [1]
    BLOCK P, DEJONG M, OCHSENDORF J. As hangs the flexible line: equilibrium of masonry arches[J]. Nexus Network Journal, 2006, 8(2): 13-24. doi: 10.1007/s00004-006-0015-9
    [2]
    LEWIS W J, RUSSELL J M, LI T Q. Moment-less arches for reduced stress state. Comparisons with conventional arch forms[J]. Computers and Structures, 2021, 251: 106524. doi: 10.1016/j.compstruc.2021.106524
    [3]
    NIKOLI AC'G D. Catenary arch of finite thickness as the optimal arch shape[J]. Structural and Multidisciplinary Optimization, 2019, 60(5): 1957-1966. doi: 10.1007/s00158-019-02304-9
    [4]
    陈宝春, 刘君平. 世界拱桥建设与技术发展综述[J]. 交通运输工程学报, 2020, 20(1): 27-41. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202001005.htm

    CHEN Bao-chun, LIU Jun-ping. Review of construction and technology development of arch bridges in the world[J]. Journal of Traffic and Transportation Engineering, 2020, 20(1): 27-41. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202001005.htm
    [5]
    ZHANG Guo-jing, LIU Yong-jian, ZHAO Wei, et al. Optimal arch shape of long-span open-spandrel arch bridges under vertical permanent loads[J]. Structures, 2022, 45: 1012-1030. doi: 10.1016/j.istruc.2022.09.086
    [6]
    侯春辉, 宋顺心. 基于APDL语言的拱轴线优化及立柱布置研究[J]. 铁道工程学报, 2017, 34(10): 55-59. https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201710011.htm

    HOU Chun-hui, SONG Shun-xin. Research on the optimization of arch-axis and column layout based on APDL language[J]. Journal of Railway Engineering Society, 2017, 34(10): 55-59. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDGC201710011.htm
    [7]
    宰国军, 周志祥. 钢箱砼组合拱桥的拱轴线优化算法研究[J]. 土木建筑与环境工程, 2014, 36(S1): 20-23. https://www.cnki.com.cn/Article/CJFDTOTAL-JIAN2014S1006.htm

    ZAI Guo-jun, ZHOU Zhi-xiang. Optimization algorithm research on the arch axis of steel box-concrete composite arch bridge[J]. Journal of Civil, Architectural and Environmental Engineering, 2014, 36(S1): 20-23. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JIAN2014S1006.htm
    [8]
    蒋启平. 三次样条插值确定拱桥合理拱轴线的方法探讨[J]. 武汉理工大学学报(交通科学与工程版), 2001, 25(1): 101-104. https://www.cnki.com.cn/Article/CJFDTOTAL-JTKJ200101027.htm

    JIANG Qi-ping. A study of method of determining rational arch axis using three ordersplin interpolation[J]. Journal of Wuhan University of Technology (Transportation Science and Engineering), 2001, 25(1): 101-104. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JTKJ200101027.htm
    [9]
    罗辉. 一种新型的拱轴线及拱圈优化设计[J]. 桥梁建设, 1997, 27(2): 14-17. https://www.cnki.com.cn/Article/CJFDTOTAL-QLJS702.002.htm

    LUO Hui. Anew type of arch axis curve and optimization design of arch ring[J]. Bridge Construction, 1997, 27(2): 14-17. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-QLJS702.002.htm
    [10]
    ZHANG Xue-song, LIANG Ning-yi, LU Xiao-hong, et al. Optimization method for solving the reasonable arch axis of long-span CFST arch bridges[J]. Advances in Civil Engineering, 2019, 2019: 7235656.
    [11]
    刘毓湘, 高敬红. 基于4次样条函数拱轴线优化设计的T-V求解法[J]. 公路交通科技, 2007, 24(6): 80-85. https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK200706018.htm

    LIU Yu-xiang, GAO Jing-hong. Topkis-Veinott feasible direction method for optimum axis of arch bridge based on quartic spline function[J]. Journal of Highway and Transportation Research and Development, 2007, 24(6): 80-85. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GLJK200706018.htm
    [12]
    范重, 胡纯炀, 刘先明, 等. 鄂尔多斯东胜体育场巨型拱索结构设计优化[J]. 建筑结构学报, 2016, 37(6): 9-18. https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB201606002.htm

    FAN Zhong, HU Chun-yang, LIU Xian-ming, et al. Optimized design of giant arch-cable structure of the Ordos Dongsheng Stadium[J]. Journal of Building Structures, 2016, 37(6): 9-18. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JZJB201606002.htm
    [13]
    SHI Zhou, HU Hao, LI Jia-qi. Axis optimization of arch-shaped pylons for high-speed railway cable-stayed bridges[J]. Engineering Structures, 2021, 227: 111424.
    [14]
    NODARGI N A, BISEGNA P. Thrust line analysis revisited and applied to optimization of masonry arches[J]. International Journal of Mechanical Sciences, 2020, 179: 105690.
    [15]
    MICHIELS T, NAPOLITANO R, ADRIAENSSENS S, et al. Comparison of thrust line analysis, limit state analysis and distinct element modeling to predict the collapse load and collapse mechanism of a rammed earth arch[J]. Engineering Structures, 2017, 148: 145-156.
    [16]
    NIKOLICH D. Thrust line analysis of triangular arches[J]. Archive of Applied Mechanics, 2020, 90(9): 1861-1874.
    [17]
    任伟新, 胡常福, 上官兴, 等. 空腹式拱桥新型拱轴线研究[J]. 交通科学与工程, 2010, 26(2): 26-30, 47. https://www.cnki.com.cn/Article/CJFDTOTAL-CSJX201002006.htm

    REN Wei-xin, HU Chang-fu, SHANGGUAN Xing, et al. Research on new arch axis of open-spandrel arch bridge[J]. Journal of Transport Science and Engineering, 2010, 26(2): 26-30, 47. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CSJX201002006.htm
    [18]
    胡常福, 廖妙星. 多源荷载作用下合理拱轴的近似解析[J]. 华东交通大学学报, 2018, 35(2): 46-55. https://www.cnki.com.cn/Article/CJFDTOTAL-HDJT201802007.htm

    HU Chang-fu, LIAO Miao-xing. Approximate analytical solution for rational arch axis under multi-type loads[J]. Journal of East China Jiaotong University, 2018, 35(2): 46-55. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HDJT201802007.htm
    [19]
    唐春艳. T构-系杆拱组合体系桥静力及动力性能研究[D]. 大连: 大连理工大学, 2018.

    TANG Chun-yan. Research on the static and dynamic characteristics of T-frame and tied arch composite bridge[D]. Dalian: Dalian University of Technology, 2018. (in Chinese)
    [20]
    LEWIS W J. Mathematical model of a moment-less arch[J]. Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, 2016, 472: 20160019.
    [21]
    GIL-MARTÍN L M, HERNÁNDEZ-MONTES E, PALOMARES A, et al. The optimum shape of an arch under non-symmetric loading conditions[J]. Archive of Applied Mechanics, 2016, 86(8): 1509-1520.
    [22]
    MARANO G C, TRENTADUE F, PETRONE F. Optimal arch shape solution under static vertical loads[J]. Acta Mechanica, 2014, 225(3): 679-686.
    [23]
    LEWIS W J. Constant stress arches and their design space[J]. Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, 2022, 478: 20210428.
    [24]
    陈宝春, 韦建刚, 周俊, 等. 我国钢管混凝土拱桥应用现状与展望[J]. 土木工程学报, 2017, 50(6): 50-61. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201706006.htm

    CHEN Bao-chun, WEI Jian-gang, ZHOU Jun, et al. Application of concrete-filled steel tube arch bridges in China: current status and prospects[J]. China Civil Engineering Journal, 2017, 50(6): 50-61. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC201706006.htm
    [25]
    易云焜. 梁拱组合体系设计理论关键问题研究[D]. 上海: 同济大学, 2007.

    YI Yun-kun. Key problem study for design theory of beam-arch association bridges[D]. Shanghai: Tongji University, 2007. (in Chinese)
    [26]
    SALONGA J, GAUVREAU P. Comparative study of the proportions, form, and efficiency of concrete arch bridges[J]. Journal of Bridge Engineering, 2014, 19(3): 04013010.
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