针对混合梁斜拉桥的结构特点,提出基于有效约束集法的混合梁斜拉桥合理成桥状态优化方法.以混合梁斜拉桥主梁、桥塔的弯曲及拉压能量之和为目标函数,以钢箱梁段竖向位移、桥塔水平位移、主梁上下缘及桥塔两侧应力、斜拉索索力及其均匀性为约束条件,建立混合梁斜拉桥合理成桥状态的二次规划数学模型,采用有效约束集算法进行合理成桥状态的优化.实例优化及比较结果显示,优化所得成桥状态,主梁竖向位移-22~8 mm,桥塔塔顶水平位移为向主跨侧偏20 mm,结构整体线形平顺;钢箱梁上下缘及钢桥塔两侧应力为-84.43~16.38 MPa,混凝土主梁上下缘及混凝土桥塔两侧应力为-16.31~-0.003 MPa,结构内力及应力均与无约束最小弯曲能量法计算结果相近;斜拉索索力为2061~2457 kN,其分布比无约束最小弯曲能量法的计算结果更均匀,且边墩具有更大的压力储备,表明该方法的有效性和优越性.
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.
[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.
