薄壁箱梁剪力滞效应分析的多参数修正理论及其应用研究

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, the effects of the longitudinal variation of the shear lag warping mode and the different boundary restraint between the cantilever flange slab and top slab of thin-walled box girders are still not considered in the shear lag warping mode adopted at present, and some obvious deficiency exists in the research of the shear lag effect of curved box girders. Based on the flexural theory of thin-walled box girders and the analytical method in elasticity mechanics, the multi-parameter modified mode of the shear lag warping displacement function is established through analyzing the in-plane shear deformation of flange slabs and combing the spatial finite element simulation analysis for shear lag effect, which can consider the effects of the longitudinal variation of the shear lag warping mode and the different boundary restraint between the cantilever flange slab and top slab of thin-walled box girders. A rigorous one-dimensional analytical theory for analyzing shear lag effect of thin-walled box girders is further presented. The coupling relations between the shear lag deformation and the bending, torsion and distortion deformation of curved box girders are derived from the consideration of the geometric equations of the thin shell theory. A one-dimensional analytical theory for analyzing shear lag effect of curved box girders is also presented. The influences of the structural systems, geometric parameters and load conditions on the shear lag effect of curved box girders are studied in detail and the 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 bases for the design of curved box girders in considering shear lag effect and the compilation of the relevant provisions in bridge design specifications.

薄壁箱梁在现代桥梁工程中得到广泛应用，其剪力滞效应是近年来国内外许多学者关注的研究课题。然而，目前采用的剪力滞翘曲模式没有考虑其纵向沿程变化特点及悬臂翼缘板与顶板的不同边界约束影响，而且对曲线箱梁的剪力滞效应研究还存在明显不足。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，结合剪力滞效应的空间有限元数值模拟分析结果，建立能够考虑沿程变化特点及悬臂翼缘板与顶板不同边界约束影响的多参数修正翘曲位移函数模式，进一步提出一种较为严密的薄壁箱梁一维剪力滞解析理论。从薄壳的几何方程出发，建立曲线箱梁的剪力滞变形与弯扭变形之间的耦合关系，提出一种分析曲线箱梁剪力滞效应的一维解析理论。在分析不同结构体系、几何参数、荷载条件等对曲线箱梁剪力滞效应影响规律的基础上，编制翼缘板有效宽度系数的实用图表曲线，为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。

薄壁箱梁广泛应用于各种体系的桥梁结构中，其剪力滞效应是设计中必须考虑的力学性能。然而，已有剪力滞解析理论不能全面反映箱梁横截面的实际翘曲模式，现行桥梁设计规范中与剪力滞效应相关的条文仅适用于直线箱梁，对曲线箱梁的相关规定尚需以深入的理论研究为依据。因此，开展薄壁箱梁剪力滞效应的理论研究具有重要的科学意义和工程应用价值。本项目的研究内容主要包括：薄壁箱梁悬臂翼缘板与顶板的剪力滞翘曲分布规律研究；全截面剪力滞翘曲分布的多参数修正位移模式研究；薄壁直线箱梁和曲线箱梁的一维剪力滞解析理论研究；考虑剪力滞效应和空间性能的薄壁箱梁计算理论研究。.本项目研究取得的主要成果如下：基于总势能最小原理，结合薄壁箱梁应力分布的空间有限元模拟结果，提出了能够全面反映各板件不同位置、不同宽度以及悬臂翼缘板与顶板之间不同边界约束影响的多参数修正翘曲位移模式，建立了剪力滞效应分析的多参数修正解析理论，悬臂板的边界约束修正系数可取为1.2~1.4。通过引入轴力和弯矩自平衡修正系数，从挠曲变形状态中分离出剪力滞变形状态，进一步建立了剪力滞效应分析的一维分离解析理论，给出了各种常见结构体系的剪力滞附加位移、翘曲应力、翘曲广义力矩及剪力滞系数的具体公式。将腹板和翼缘板的剪切变形用一个综合剪切翘曲模式进行描述，建立了可以充分考虑弯扭耦合关系及二次剪切变形影响的曲线箱梁剪力滞效应一维解析理论，简支曲线箱梁全截面综合剪切变形对弯曲应力的影响可达15%。将多参数修正解析理论与有限元方法相结合，建立了薄壁箱梁剪力滞效应分析的一维梁段有限元列式，编制了一维梁段有限元分析程序系统，分析了不同结构体系、荷载条件、几何参数等对剪力滞效应的影响规律。从多参数修正理论的实际应用出发，导出了曲线钢束锚固损失的精确计算公式，提出了畸变角定义的新方法，为全面分析预应力混凝土箱梁在偏心活载作用下的剪力滞效应和空间受力性能奠定了基础。

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