According to the structural characteristics of the cable-stayed bridge with hybrid girder, an active set method is proposed to determine the reasonable completion state for the cable-stayed bridge with hybrid girder. A quadratic programming model is built, with the total bending and axial energy of the girder and the pylon as the objective function, and the vertical displacement of the steel box girder, the horizontal displacement of the pylon, the normal stress in the concrete girder and pylon, the cable force and their distributional uniformity as the constraint conditions. The active set method is employed to optimize the completion state of the cablestayed bridge with hybrid girder. The optimization and comparison results show that under the condition of the completion state obtained through the method proposed in this paper, a smooth shape of the whole structure is obtained, with the vertical displacement of the main girder in the range of -22-8 mm, with the top of the pylon having a horizontal pre-deviation of 20 mm to the main span, and with the internal force and the normal stress in the whole structure all similar with what obtained from the unconstraint minimum bending energy method. The normal stresses in the steel girder and the steel pylon are in the range of -84.43-16.38 MPa, and the normal stresses in the concrete girder and the concrete pylon are in the range of -16.31-0.003 MPa, and the cable force is in the range of 2061-2457 kN, which are in a more uniform distribution than that obtained from the unconstraint minimum bending energy method, with the side piers having a more pressure reservation. Thus, the results show the great effectiveness and superiority of the method.
DAI Jie
,
QU Jun
,
QIAO Jiangang
,
QIN Fengjiang
. Optimization Analysis of Reasonable Completion State for Cable-stayed Bridge with Hybrid Girder Based on Active Set Method[J]. Science & Technology Review, 2014
, 32(34)
: 69
-77
.
DOI: 10.3981/j.issn.1000-7857.2014.34.010
[1] Gimsing N J, Georgakis C T. Cable supported bridges: Concept and design[M]. New York: John Wiley & Sons, 2011.
[2] Walther R. Cable stayed bridges[M]. London: Thomas Telford House, 1999.
[3] Wang P H, Tseng T C, Yang C G. Initial shape of cable-stayed bridges[J]. Computers & Structures, 1993, 47(1): 111-123.
[4] Chen D W, Au F T K, Tham L G, et al. Determination of initial cable forces in prestressed concrete cable-stayed bridges for given design deck profiles using the force equilibrium method[J]. Computers & Structures, 2000, 74(1): 1-9.
[5] 颜东煌, 李学文, 刘光栋, 等. 用应力平衡法确定斜拉桥主梁的合理成 桥状态[J]. 中国公路学报, 2000, 13(3): 49-52. Yan Donghuang, Li Xuewen, Liu Guangdong, et al. Deciding the reasonable finished dead state of the main beam of cable-stayed bridges using stress balanced method[J]. China Journal of Highway and Transport, 2000, 13(3): 49-52.
[6] 梁鹏, 肖汝诚, 张雪松. 斜拉桥索力优化实用方法[J]. 同济大学学报, 2003, 31(11): 1270-1274. Liang Peng, Xiao Rucheng, Zhang Xuesong. Practical method of optimization of cable tensions for cable-stayed bridges[J]. Journal of Tongji University, 2003, 31(11): 1270-1274.
[7] Lute V, Upadhyay A, Singh K K. Genetic algorithms-based optimization of cable stayed bridges[J]. Journal of Software Engineering & Applications, 2011, 4(10): 571-578.
[8] Hassan M M. Optimum design of cable-stayed bridges[D]. Canada Ontario: University of Western Ontario, 2010
[9] 陆楸, 徐有光. 斜拉桥最优索力的探讨[J]. 中国公路学报, 1990, 3(1): 38-48. Lu Qiu, Xu Youguang. Optimum tensioning of cable-stays[J]. China Journal of Highway and Transport, 1990, 3(1): 38-48.
[10] 颜东煌, 李学文, 刘光栋, 等. 混凝土斜拉桥合理成桥状态确定的分 步算法[J]. 中国公路学报, 2003, 16(1): 43-46. Yan Donghuang, Li Xuewen, Liu Guangdong, et al. Step-by-step arithmetic for the reasonable finished dead state of the concrete cablestayed bridges[J]. China Journal of Highway and Transport, 2003, 16 (1): 43-46.
[11] Kasuga A, Arai H, Breen J E, et al. Optimum cable-force adjustments in concrete cable-stayed bridges[J]. Journal of Structural Engineering, 1995, 121(4): 685-694.
[12] 肖汝诚, 项海帆. 斜拉桥索力优化的影响矩阵法[J]. 同济大学学报, 1998, 26(3): 235-239. Xiao Rucheng, Xiang Haifan. Influence matrix method of cable tension optimization for cable-stayed bridges[J]. Journal of Tongji University, 1998, 26(3): 235-239.
[13] Janjic D, Pircher M, Pircher H. Optimization of cable tensioning in cable-stayed bridges[J]. Journal of Bridge Engineering, 2003, 8(3): 131-137.
[14] Hassan M M. Optimization of stay cables in cable-stayed bridges using finite element, genetic algorithm, and B-spline combined technique[J]. Engineering Structures, 2013, 49(4): 643-654.
[15] Sung Y C, Chang D W, Teo E H. Optimum post-tensioning cable forces of Mau-Lo Hsi cable-stayed bridge[J]. Engineering Structures, 2006, 28 (10): 1407-1417.
[16] More J J, Wright S J, Pardalos P M. Optimization software guide[M]. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics, 1993.
[17] 陈宝林. 最优化理论与算法[M]. 2版. 北京: 清华大学出版社, 2005. Chen Baolin. Optimization theory and algorithm[M]. 2th ed. Beijing: Tsinghua University Press, 2005.
[18] 马昌凤. 最优化方法及其Matlab 程序设计[M]. 北京: 科学出版社, 2010. Ma Changfeng. Optimization method and its Matlab program design[M]. Beijing: Science Press, 2010.
[19] 黄侨, 吴红林, 杨大伟. 确定斜拉桥成桥索力多约束条件下最小能量 法[J]. 哈尔滨工业大学学报, 2007, 39(2): 288-291. Huang Qiao, Wu Honglin, Yang Dawei. Minimum energy method with multi-restrictions to decide the rational completed stage force[J]. Journal of Harbin Institute of Technology, 2007, 39(2): 288-291.