基于缆-索-梁非线性耦合效应的大跨自锚式悬索桥合理成桥状态计算方法研究

For long-span self-anchored suspension bridges, the reasonable design state is of great significance to normal operation and structural safety of the bridges. As the long-span self-anchored suspension bridges exhibit more notable nonlinear effect, more details are required on the determination and calculation for the reasonable design state, as well as the existing problems in the original algorithm. Therefore, through theoretical analysis and experimental verification, this project intends to solve the unified model of reasonable design state considering the nonlinear coupling of main cable, cable and beam. First, based on the principle of minimum energy method, establish the mathematical expressions of reasonable design state, which will theoretically reveal the constitution mechanism and characteristics of reasonable design state. Then, find the discriminant method for finish bridge state shape matching of main cable and stiffening girder. Finally, based on the calculation model of cable-beam coupling and cable-main cable coupling, together with the deformation compatibility condition of main cable-beam coupling, establish the calculation model and iteration method for reasonable design state of main cable-cable-beam coupling, and verify them by experiment. Research results of this project will manifest important scientific significance and practical value on the determination and calculation for reasonable design state of long-span self-anchored suspension bridges.

大跨自锚式悬索桥的合理成桥状态对保障桥梁正常运营和结构安全至关重要。本项目针对非线性效应更加显著的大跨自锚式悬索桥对合理成桥状态确定和计算的更高要求，以及原有算法中存在的不足等问题，拟通过理论分析与试验验证的研究方法，解决考虑缆-索-梁非线性耦合的合理成桥状态统一模型计算等问题。首先，基于最小能量法原理，建立合理成桥状态的数学表达式，从理论层面揭示自锚式悬索桥合理成桥状态的构成机理和特征规律；然后，建立主缆与加劲梁成桥线形匹配判别方法；最后，基于索-梁耦合、缆-索耦合计算模型以及缆-梁耦合的变形协调条件，建立缆-索-梁耦合的合理成桥状态计算模型和迭代方法，并进行试验验证。本项目研究成果对大跨自锚式悬索桥合理成桥状态的确定和计算具有重要的科学意义和实用价值。

大跨度自锚式悬索桥对合理成桥状态的要求更高，能否达到合理成桥状态对保障桥梁正常运营和结构安全至关重要，由于缺乏对合理成桥状态本质的深入认识，且需要一种能综合考虑缆-索-梁耦合效应、效率更高的计算方法，本项目围绕大跨自锚式悬索桥合理成桥状态的关键科学问题，开展了系统的研究。分析了单一参数对自锚式悬索桥合理成桥状态的影响，揭示了主缆线形、刚度、加劲梁线形等对合理成桥状态的影响规律，构建了主缆、吊索、主塔及加劲梁关于吊索力的应变能表达式，推导出自锚式悬索桥合理成桥状态的数学表达式，揭示了自锚式悬索桥合理成桥状态的构成机理和特征规律。基于最小能量法原理，构建了考虑加劲梁轴向变形影响的梁-索耦合计算模型，推导出加劲梁线形误差对吊索力影响的雅克比矩阵，建立了梁-索耦合迭代的计算方法；基于主缆和加劲梁线形方程，建立了主缆与加劲梁线形匹配的判别方法。基于分段悬链线理论，揭示了主索鞍处主缆抗弯刚度对主缆线形的影响规律，建立了主缆线形的修正方法；基于牛顿-拉菲森数值算法，统一了包含缆-索-梁的自锚式悬索桥计算模型，建立了考虑缆-索-梁耦合的自锚式悬索桥合理成桥状态的计算方法。研究成果揭示了自锚式悬索桥合理成桥状态的本质，夯实了理论基础，为自锚式悬索桥向更大跨度的研究指明了方向；相关算法可用于索类结构的计算和分析，在拉吊桥梁、大跨拱桥的施工控制和长期安全监测中，也有广泛的应用前景。