基于能量变分原理的薄壁箱梁剪力滞效应解析法研究

发布时间：2018-05-13 00:32

本文选题：薄壁箱梁 + 剪滞效应　；参考：《中南大学》2014年硕士论文

【摘要】：随着我国交通事业的迅速发展,薄壁箱梁被广泛应用于各种大跨度、大宽度的桥梁结构,其剪力滞问题不容忽视,若不认真对待这些问题,很可能会造成箱梁局部开裂、局部失稳甚至于更加严重的后果。因此对薄壁箱梁剪力滞效应进行深入研究具有重要的理论和工程意义,本文基于薄壁结构理论和能量变分原理对单室和多室箱梁进行了以下研究： (1)提出了考虑荷载横向作用位置影响的等截面单室箱梁剪力滞分析的能量变分法。纵向翘曲位移横向分布规律设为κ次抛物线以便于分析不同翘曲位移函数的精度,对箱梁顶板、悬臂板和底板分别设置不同的剪滞纵向位移差函数以便准确反映梯形截面不同翼板的纵向翘曲位移变化幅度,计算外力势能时考虑荷载横向位置的影响,并考虑弯曲、剪切和剪力滞的耦合作用,由能量变分法推导出梁段单元控制微分方程组及其闭合解,并通过简支梁和悬臂梁算例予以验证,最后给出了梯形和矩形截面简支、悬臂箱梁剪滞效应的推导过程及剪滞系数、有效宽度比的理论计算公式,完善了荷载不同横向作用位置时箱梁剪力滞效应的计算分析理论。 (2)研究了荷载横向变位下等截面单室薄壁箱梁剪力滞效应的影响参数。利用能量变分法计算简支和悬臂箱梁剪力滞效应,分析荷载横向变位下荷载形式、宽跨比、宽高比、腹板横向位置和腹板斜度等因素对箱梁剪力滞效应的影响规律,并与现行规范进行对比,认为规范将各翼板有效宽度比统一取成一条曲线是不合理且偏不安全的,应根据实际荷载横向作用位置参考本文结论来选择相应的曲线进行取值。 (3)提出了考虑荷载横向作用位置的变截面单室箱梁剪力滞分析的有限段法。采用荷载横向变位下剪滞控制微分方程组的齐次解作为梁段单元位移模式,形成单室梯形箱梁的位移场函数,并导出梁段单元刚度矩阵及结点荷载列阵,建立单室箱梁剪力滞分析的有限梁段模型,并编制相应计算程序,以变截面连续箱梁为例将计算结果与有限元解、试验结果进行对比,结果吻合良好,验证了该分析方法的正确性。 (4)提出了薄壁箱梁剪力滞效应的叠加原理。通过简单荷载形式下剪力滞效应解的叠加来求解复杂力状态下箱梁的剪滞效应,并与有限元结果进行对比来验证该方法的准确性,该方法可将所作理论研究进行推广应用于工程实际。 (5)提出了考虑全截面轴力自平衡的等截面多室箱梁剪力滞分析的能量变分法。对不同翼板分别设置不同剪滞纵向位移差函数,纵向翘曲位移横向分布规律设为κ次抛物线以便于分析不同翘曲位移函数的精度,同时考虑全截面轴力自平衡条件,由能量变分法获得多室梯形箱梁的控制微分方程组及其闭合解,并编制相应计算程序,计算结果与有限元解进行对比,结果吻合良好,验证了本文所作假定和理论推导的正确性。 (6)研究了纵向翘曲位移横向分布规律的抛物线次数对计算精度的影响。对于单室箱梁,当荷载作用于腹板顶部时,抛物线次数取3时比取2时更接近有限元解,当荷载作用于其他位置时,抛物线次数取2时比取3时更接近有限元解；对于多室箱梁,顶、底板抛物线次数取3时比取2时更接近有限元解,悬臂板抛物线次数取2时比取3时更接近于有限元解；抛物线次数虽然影响计算精度,但对于实际工程而言,精度均能满足要求。
[Abstract]:With the rapid development of transportation in China, thin-walled box girder is widely used in large span and wide span bridge structures. The shear lag problem can not be ignored. If we do not take these problems seriously, it is likely to cause partial cracking, local instability and even more serious consequences. Therefore, the shear lag effect of thin-walled box girder is deep. The study has important theoretical and engineering significance. Based on thin-walled structure theory and energy variational principle, single room and multi compartment box girder are studied as follows:
(1) the energy variation method is proposed to analyze the shear lag analysis of the single chamber box girder with the influence of the lateral loading position. The transverse distribution of the longitudinal warping displacement is kappa parabola to facilitate the analysis of the accuracy of the different warping displacement functions, and the different shear lag longitudinal displacement difference functions are set to the roof of the box girder, the cantilever plate and the bottom plate respectively. The variation amplitude of longitudinal warping displacement of the different wing plates of the trapezoid section is accurately reflected, the effect of the lateral position of the load is considered when calculating the external force potential energy, and the coupling effect of the bending, shear and shear lag is considered. The differential equations and its closed solutions are derived by the energy variational method, and it is verified by a simple supported beam and a cantilever beam. Finally, the deducing process of the shear lag effect of the trapezoid and rectangular section, the shear lag effect of the cantilever box girder, the shear lag coefficient and the theoretical calculation formula of the effective width ratio are given, and the calculation and analysis theory of the shear lag effect of the box girder when the load is different lateral action position is perfected.
(2) the influence parameters of shear lag effect of single chamber thin-walled box girder with lateral deflection are studied. Using the energy variational method, the shear lag effect of simple and cantilever box beams is calculated, and the influence of load forms, width to span ratio, width to height ratio, the lateral position of the web and the slope of the web and other factors on the shear lag effect of the box girder are analyzed by the energy variation method. Compared with the current standard, it is not reasonable and unsafe to draw the effective width ratio of each wing plate to a uniform curve, and the corresponding curve should be selected according to the horizontal action position of the actual load.
(3) a finite section method is proposed for the shear lag analysis of a single chamber box girder with variable cross section considering the lateral loading position. The homogeneous solution of the shear lag control differential equations under the lateral loading of the load is used as the displacement mode of the beam section element, and the displacement field function of the single chamber trapezoid box girder is formed, and the stiffness matrix of the beam section element and the node load array are derived. The finite beam section model of the shear lag analysis of single chamber box girder is made, and the corresponding calculation program is compiled. The calculation results are compared with the finite element solution and the experimental results. The results are in good agreement, and the correctness of the analysis method is verified.
(4) the superposition principle of shear lag effect of thin-walled box girder is put forward. The shear lag effect of box beam under complex force state is solved by superposition of shear lag effect under simple load, and the accuracy of the method is verified by comparison with the finite element results. The method can be applied to engineering practice.
(5) the energy variation method for the shear lag analysis of a multi compartment box girder with full section axial force self balance is proposed. The different shear lag longitudinal displacement difference functions are set to the different wing plates, and the transverse distribution of the longitudinal warping displacement is set as kappa parabola to facilitate the analysis of the accuracy of different warping displacement functions, and the axial force self leveling of the full section is considered. The control differential equations and the closed solutions of the multi compartment trapezoid box girder are obtained by the energy variational method, and the corresponding calculation program is compiled. The calculation results are compared with the finite element solution. The results are in good agreement, and the correctness of the hypothesis and theoretical deduction in this paper is verified.
(6) the influence of the number of parabola on the transverse distribution of the longitudinal warpage displacement is studied. For a single chamber box beam, when the number of parabola is 3 when the load acts on the top of the web, it is closer to the finite element solution when the number of parabola is taken 2. When the load acts on other positions, the number of parabola is more close to the finite element solution when the number of parabola is 2 than when it is 3. When the number of parabolic lines of the box girder, top and bottom plate is 3, it is closer to the finite element solution than when it takes 2. When the number of parabola of the cantilever plate is 2, it is closer to the finite element solution than when it takes 3. Although the number of parabolic lines affects the calculation accuracy, the precision can meet the requirements for the actual project.

【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441;U448.213

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