薄壁箱梁剪力滞翘曲位移函数的合理模式及其应用研究

Thin-walled box girders are widely used in modern bridge engineering due to their advantageous behavior. In recent years, scholars at home and abroad have been paying a great deal of attention to the shear lag effect in thin-walled box girders. However, no reasonable mode of displacement function for shear lag warping is proposed, and research work on the shear lag effect of special box girders such as skew curved box girder is still deficient..This research project concentrates on the reasonable displacement function for shear lag warping of thin-walled box girder and shear lag effect analysis in skew curved box girder. Based on the flexural theory of thin-walled box girder and elasticity mechanics, a rigorous mode of displacement function for shear lag warping is established through analyzing shear deformation of flanges. A method suitable for analyzing the shear lag effect in skew curved box girder is proposed, in which substructure is applied to describe the non-radial configuration at the ends of skew curved box girder and the rest regular segments are simulated by box beam element with generalized displacement field. The influence of non-radial configuration inclination, skew angle on top of pier, eccentric ratio of support, ratio of radius and span, ratio of span and width on the shear lag effect of skew curved box girder is studied in detail and practical graphic curves for the coefficient of flange effective width are compiled on the basis of numerical analysis. The implementation of the research project can provide scientific basis for the design of skew curved box girder considering shear lag effect and compilation of relevant items for bridge design specifications.

薄壁箱梁广泛应用于现代桥梁工程中，其剪力滞效应是近年来国内外学者关注的研究课题，然而，目前尚未提出剪力滞翘曲位移函数的合理模式，而且对特殊型式箱梁如斜交曲线箱梁的剪力滞效应研究还极为欠缺。.本项目拟研究薄壁箱梁剪力滞翘曲位移函数的合理模式及斜交曲线箱梁的剪力滞效应。基于薄壁箱梁的挠曲理论及弹性力学方法，从分析翼缘板的剪切变形出发，建立力学意义上严密的剪力滞翘曲位移函数模式。用子结构描述斜交曲线箱梁的端部非径向几何构形，用基于广义位移场的箱梁单元描述规则区域的梁段，提出一种适用于斜交曲线箱梁的剪力滞效应分析方法。在详细分析梁端非径向几何构形斜度、墩顶斜交角度、支承偏心率、径跨比、跨宽比等特征参数对斜交曲线箱梁剪力滞效应影响的基础上，编制翼缘板有效宽度系数的实用图表曲线，为斜交曲线箱梁考虑剪力滞效应的设计计算及制订桥梁设计规范中相关条文提供科学依据。

剪力滞效应是薄壁箱梁设计中必须考虑的问题，但现行桥梁设计规范中的处理方法非常粗糙，本项目拟开展薄壁箱梁剪力滞效应分析的解析理论研究。通过引入横截面整体位移调节系数，构建了薄壁箱梁剪力滞翘曲位移函数的二次抛物线型合理模式，使剪力滞翘曲应力在箱梁横截面上同时满足纵向自平衡条件和弯曲自平衡条件。以剪力滞挠度作为描述剪力滞变形状态的广义位移，应用能量原理及虚位移原理，得到了与剪力滞挠度相应的剪力滞双力矩。提出了基于新型翘曲位移模式的薄壁箱梁剪力滞效应解析理论。应用弹性力学基本原理，建立了关于剪力滞挠度的控制微分方程，在定义剪力滞翘曲相关几何特性的基础上，提出了剪力滞翘曲应力的简便公式，使薄壁箱梁的剪力滞效应分析与约束扭转和畸变效应分析相统一。以剪力滞控制微分方程齐次解作为单元剪力滞位移函数，提出了以剪力滞挠度和剪力滞挠曲转角为新增自由度的箱梁梁段有限元模型，建立了单元剪力滞刚度矩阵和等效节点力向量，编制了考虑剪力滞、约束扭转及畸变效应的梁段有限元程序系统，可用于斜交曲线箱梁剪力滞效应的耦合分析。详细分析了荷载类型、约束条件、结构几何特征参数等对箱形梁剪力滞效应的影响，揭示了各特征参数对箱形梁剪力滞效应的影响规律。