【作者】 甘亚南；

【导师】 周广春；

【作者基本信息】 哈尔滨工业大学 ， 结构工程， 2008， 博士

【摘要】 剪力滞问题在很早以前就有学者对其进行研究,但学者们当时仅仅局限于航空领域的金属结构,自从20世纪60年代,由于忽略剪力滞后效应导致多座箱形桥梁破坏才引起各国学者的注意。经过几十年的发展,对剪力滞问题的研究取得了一些成果,可以部分地解决实际桥梁结构中的问题。但许多问题并没有得到完全解决,随着我国交通事业的发展,在一些新建桥梁中有关剪力滞的新问题不断出现。对于这些问题如不认真对待,可能会造成结构局部开裂、局部失稳,或更加严重的破坏。因而对剪力滞后问题的研究具有重要的理论和工程实际意义,本文就以下几个方面进行了研究。1、直线和曲线矩形截面箱梁的静力学特性分析以薄壁杆或薄壁曲杆理论为基础,根据实际情况对上下翼板、悬臂翼板设置了一个或两个剪滞纵向位移差函数,由能量变分原理获得了直线和曲线矩形截面箱梁的控制微分方程和边界条件,得到了广义位移的闭合解。系统分析了边界条件、荷载类型、悬臂翼板长度和曲率半径R等因素对直线和曲线矩形截面箱梁剪力滞后效应的影响,明确了上、下翼板的应力变化规律。2、直线薄壁箱梁自振特性和动力反应的分析对于直线矩形和梯形截面箱梁,根据其特点分别设置了一个、两个或三个剪滞纵向位移差函数,在考虑剪力滞后效应的前提下,获得了边界条件、跨宽比、箱梁高度和悬臂翼板长度等因素对矩形和梯形截面箱梁自振特性影响的规律。同时,本文以直接法为基础,推导出了矩形截面箱梁的强迫振动方程,明确了剪力滞后效应对矩形截面箱梁动力反应影响的规律,因而本文内容丰富和发展了现行剪滞理论。3、梯形截面曲箱梁的静力学特性分析设置了三个不同的纵向剪滞位移差函数以准确反映顶板( u1 ( x ))、底板( u 2( x ))和悬臂板( u3 ( x ))的纵向位移变化,考虑了曲箱梁的弯、扭、翘、剪滞效应和剪切变形的耦合作用,本文内容发展了符拉索夫的曲杆理论,明确了曲线梯形截面箱梁的力学特点。同时制作了曲线梯形截面箱梁的有机玻璃模型桥,设计了测点布置和加载方案,对梯形截面曲箱梁上下翼板剪力滞效应进行了试验研究,理论结果与试验值进行了比较,验证了本文理论分析的正确性。4、直线和曲线矩形截面箱梁腹板静动力特性分析将剪力滞后效应引入直线和曲线矩形截面箱梁腹板,根据应变—位移关系获得系统总势能,依据箱梁腹板振动特点求得总动能,利用最小势能原理和哈密顿原理分别获得直线和曲线矩形截面箱梁腹板静、动力特性分析的控制微分方程和自然边界条件,明确了跨宽比、悬臂翼板长度、梁高及腹板厚度对直线和曲线矩形截面箱梁腹板剪滞效应的影响,为矩形截面箱梁腹板的力学特性分析提供理论参考。5、宽翼薄壁直线工字形梁静、动力特性及曲梁静力特性的分析为了准确反映工字形梁上、下翼板剪滞效应变化,对直线和曲线工字形梁上、下翼板设置了两个不同的剪滞纵向位移差函数U 1( x )、U 2( x ),推导出了工字形梁的控制微分方程和自然边界条件,通过系统的力学分析,获得了该类结构静、动力特性规律。6、薄壁箱梁翘曲函数精确度选择的研究根据箱形结构纵向翘曲位移函数设置的基本原理,选择一系列符合薄壁箱梁基本翘曲模式的翘曲位移函数,依据固有频率方程求出特定边界条件下相应翘曲位移函数箱形结构的自振频率,借助自振频率的大小对所设置翘曲位移函数的精度做出评判,且静力分析结果进一步证明了翘曲位移函数精度选择的必要性。更多还原

【Abstract】 Shear lag issues were studied by some scholars long before, but they were limited in the aviation structures only. Since 1960s, some scholars started to pay attention to shear lag problem because it resulted in the damage of bridges. Over the past several decades, the research outcomes solved the part of engineering problems relating to shear lag effect. However, the existing research achievements still do not handle the shear lag issues completely and accurately. With the development of communication, new problems about shear lag effect appeared continuously. If these problems are not treated seriously and properly, the local cracking and instability of structures from shear lag effect will appear so that it can cause serious damage of structures. Hence, the analysis of shear lag effect is more and more important and critical in theoretical and practical significances. This dissertation makes some contributions in the shear lag effect on the thin-walled beams which are commonly used in the modern bridges. The main contents of this dissertation are as follows:(1) The static analysis of straight and curved rectangle box beamsOn the basis of the thin-walled bars theory and the thin-walled curved bars theory, the governing differential equations and the natural boundary conditions of straight or curved rectangle box girders are established using an energy variation principle and the closed-form solutions of generalized displacement functions are obtained. The established governing differential equation applies one or two different longitudinal displacement difference functions to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs according to the practical configuration of the beam. The variation in the shear lag effects on straight and curved rectangle box girders, caused by the changes of factors such as natural boundary conditions, types of loading, lengths of cantilever flanges and curvature radius R , is discussed systematically. Meanwhile, an analysis is made for the change of stress in the top and bottom flanges.(2) The analysis of the natural frequency and dynamic response of straight thin-walled box beamsAccording to the structural features of straight rectangle and trapezoid box girders, one, two or three warping displacement functions are applied to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs respectively. In consideration of the shear lag effect, the natural frequency relating to the changes of factors such as natural boundary conditions, span-width ratio, height of thin-walled box girders, and length of cantilever flanges, is obtained. Also based on the direct method, the equation of dynamic response about rectangle box girders is deduced. The solution of the equation can rightly reflect the dynamic behaviour of thin-walled structures, which it develops and enriches the shear lag theory.(3) The static analysis of curved trapezoidal box beamsThree different longitudinal displacement difference functions are employed to accurately reflect the amplitude of change of shear lag in the thin-walled curved box girders with various widths of wing slabs respectively. Then, the governing differential equations and natural boundary conditions are proposed both using the minimum potential principle and taking into account of the curving, torsion, warping torsion (including secondary warping shear effect), shear deformation and shear lag effects. Thus, this dissertation develops Vlasov’s thin-walled curved bars theory and clearly reveals the mechanical performance of curved trapezoid box girders.A bridge model with continuous curved trapezoid box girder is designed and made in order to verify the proposed analytical techniques. Two loading cases, uniform and concentrated loads, are applied to study the shear lag effect on the top and bottom flanges of curved trapezoid box girder.(4) The analysis of static and dynamic characteristics of webs of thin-walled straight and curved box beamsIn consideration of shear lag effect on thin-walled box girder’s webs, the total potential energy stored in the box girders is obtained according to the relationship of strain-displacement. Also, the total kinetic energy of the box girders can be obtained based on web’s vibrating characteristics. Therefore, the web’s governing differential equations and corresponding natural boundary conditions can be obtained for the static and dynamic analysis of webs about thin-walled straight and curved box girders using the minimum potential principle and Hamilton principle. The web’s shear lag effect on straight and curved rectangle box girders is systematically discussed, involved in the factors such as span-width ratio, length of cantilever flanges, height of thin-walled box girder and thickness of webs. The research results provide a reference for the analysis of web’s mechanical characteristics.(5) The analysis on static and dynamic characteristics of straight and curved thin-walled I-beams with wide flangesTwo different longitudinal displacement difference functions ( U 1 ( x ), U 2( x )) are proposed in establishing the governing differential equations and corresponding natural boundary conditions, in order to accurately reflect the amplitude of change of shear lag in the thin-walled straight and curved I-beams with various widths of wing slabs. Then the mechanical analysis is conducted for the static and dynamic characteristics about straight and curved thin-walled I-beams.(6) An approach of accurately selecting longitudinal shear lag warping displacement function of thin-walled box girdersBased on the basic principle of longitudinal warping displacement function setting, this study selects a series of warping displacement functions that conform to basic warping mode of the box girder, in order to obtain the natural frequency equations corresponding to these proposed functions. Then, for the special boundary types, the natural frequency of the beam is determined under these given warping displacement functions. Finally, according to the magnitude of the natural frequency, the precision of warping displacement functions can be judged, and the static calculation examples indicate that the selection of warping displacement functions be necessary.更多还原