基于有效约束集法的混合梁斜拉桥合理成桥状态确定方法

Optimization Analysis of Reasonable Completion State for Cable-stayed Bridge with Hybrid Girder Based on Active Set Method

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 k N,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 cable- stayed 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 thenormal 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 unconsfraint 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.