箱形梁剪力滞效应分析中的合理翘曲位移模式及其应用研究
发布时间：2019-05-09 13:18
【摘要】：随着我国桥梁建设的蓬勃发展，在众多的桥梁截面形式中，箱形截面梁，顾名思义截面形状犹如“箱子”有其优越的截面特性，受到桥梁设计师的青睐。而其中大悬臂板、宽体箱梁成为主要的发展趋势，由此剪力滞效应问题将被重点考虑。在以往的理论研究中，箱形梁剪力滞效应的分析方法众多，各自有其自身的适用条件和优缺点，基于最小势能原理的能量变分法最为经典和有效。但是传统的能量变分法分析剪力滞效应还是有一定的不足和缺陷，比如无法满足轴力自平衡条件，所选取的剪力滞翘曲位移函数缺乏严密的理论论证，针对不同板宽的翼板没有合理的修正，，所推导的纵向应力计算式太过于繁琐复杂等。本文就这些问题做出较详细的理论分析和修正，并建立ansys数值算例模型验证本文提出的分析方法，具体工作包括以下几个方面： 1.归纳出以往文献中对剪力滞翘曲位移函数定义的类型，主要有抛物线型和余弦曲线型，给出它们各自的假设条件和优缺点。并从控制剪力滞效应的翼板剪切变形规律出发，提出定义剪力滞翘曲位移的新方法。 2.以薄壁箱形梁的弯曲计算理论为基础，分析各翼板的剪切变形规律，给出剪力流计算式，并假定翼板横向位移对纵向坐标的导数很小可忽略不计，从理论上证明二次抛物线是较为合理的剪力滞翘曲位移函数。通过对全截面增加一个常数使翘曲应力满足轴力自平衡条件，对悬臂板和底板以不同板宽和水平形心轴不同距离作出修正，定义新的剪力滞翘曲位移函数。 3.将剪力滞效应引起的附加挠度作为剪力滞广义位移，定义剪力滞广义力矩作为对应剪力滞翘曲应力的广义力。这样所得到的考虑剪力滞效应后的纵向应力表达式和相应初等梁理论计算式形式一致，且物理意义更为明确。 4.以变分法原理建立控制微分方程，并通过边界条件求解得到简支箱形梁、悬臂箱形梁作用集中荷载和分布荷载的剪力滞附加挠度表达式，进而与初等梁弯曲理论结果叠加可得到考虑剪力滞效应后的箱形梁纵向应力和竖向挠度。 5.通过简支梁和悬臂梁两个计算算例，依据本文的理论方法分别求解在选取不同翘曲位移函数时的纵向应力，并建立ansys数值模型，验证本文的分析方法和建立的公式是否合理。 6.对一作用对称集中荷载的预应力混凝土简支梁算例的计算表明，实际的桥梁设计中，如若不考虑剪力滞效应时，对竖向挠度的影响可忽略不计，但纵向应力则相差较大，无法忽略。
[Abstract]:With the vigorous development of bridge construction in our country, among many bridge cross section forms, box section beam, as the name implies, has its superior section characteristics and is favored by bridge designers. Among them, large cantilever plate and wide-body box girder become the main development trend, so the shear lag effect will be taken into account. In the previous theoretical research, there are many methods to analyze the shear lag effect of box beams, each of which has its own applicable conditions, advantages and disadvantages, and the energy variation method based on the principle of minimum potential energy is the most classical and effective. However, the traditional energy variation method still has some shortcomings and defects in the analysis of shear lag effect, such as unable to meet the self-balance condition of axial force, and the selected shear lag warping displacement function is lack of rigorous theoretical demonstration. The calculation formula of longitudinal stress is too cumbersome and complex for different width airfoils without reasonable correction. In this paper, the theoretical analysis and correction of these problems are made in detail, and a numerical example of ansys is established to verify the analytical method proposed in this paper. The specific work includes the following aspects: 1. The definition types of shear lag warpage displacement function in previous literatures are summarized, mainly parabola and cosine curves, and their hypotheses, advantages and disadvantages are given. A new method to define the shear lag warping displacement is proposed based on the shear deformation law of the wing plate which controls the shear lag effect. 2. Based on the bending calculation theory of thin-wall box girder, the shear deformation law of each wing plate is analyzed, and the formula for calculating shear flow is given, and it is assumed that the derivative of transverse displacement of wing plate to longitudinal coordinates can be ignored. It is proved theoretically that quadratic parabola is a reasonable function of shear lag warping displacement. A new shear lag warping displacement function is defined by adding a constant to the whole section to make the warpage stress satisfy the self-balancing condition of axial force and modifying the cantilever plate and bottom plate with different width of plate and different distance of horizontal center axis. 3. The additional deflection caused by shear lag effect is regarded as the generalized displacement of shear lag, and the generalized moment of shear lag is defined as the generalized force corresponding to the shear lag warping stress. In this way, the expression of longitudinal stress after considering shear lag effect is in agreement with the corresponding theoretical formula of elementary beam, and the physical meaning is more clear. 4. Based on the principle of variation method, the governing differential equations are established, and the expressions of shear lag additional deflection of simply supported box beams and cantilever box beams acting on concentrated load and distributed load are obtained by solving the boundary conditions. Furthermore, the longitudinal stress and vertical deflection of the box beam with shear lag effect can be obtained by superposition of the results of the bending theory of the primary beam and the results of the bending theory of the primary beam. 5. Based on the calculation examples of simply supported beam and cantilever beam, the longitudinal stress in selecting different warping displacement functions is solved by the theoretical method in this paper, and the ansys numerical model is established to verify the rationality of the analytical method and the formula in this paper. 6. The calculation of a prestressed concrete simply supported beam with symmetric concentrated load shows that if shear lag effect is not considered in the actual bridge design, the influence on vertical deflection can be negligible, but the longitudinal stress is quite different from each other in the actual bridge design, if the shear lag effect is not considered, the influence on the vertical deflection can be negligible, but the longitudinal stress is quite different. You can't ignore it.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U448.213
本文编号：2472798
[Abstract]:With the vigorous development of bridge construction in our country, among many bridge cross section forms, box section beam, as the name implies, has its superior section characteristics and is favored by bridge designers. Among them, large cantilever plate and wide-body box girder become the main development trend, so the shear lag effect will be taken into account. In the previous theoretical research, there are many methods to analyze the shear lag effect of box beams, each of which has its own applicable conditions, advantages and disadvantages, and the energy variation method based on the principle of minimum potential energy is the most classical and effective. However, the traditional energy variation method still has some shortcomings and defects in the analysis of shear lag effect, such as unable to meet the self-balance condition of axial force, and the selected shear lag warping displacement function is lack of rigorous theoretical demonstration. The calculation formula of longitudinal stress is too cumbersome and complex for different width airfoils without reasonable correction. In this paper, the theoretical analysis and correction of these problems are made in detail, and a numerical example of ansys is established to verify the analytical method proposed in this paper. The specific work includes the following aspects: 1. The definition types of shear lag warpage displacement function in previous literatures are summarized, mainly parabola and cosine curves, and their hypotheses, advantages and disadvantages are given. A new method to define the shear lag warping displacement is proposed based on the shear deformation law of the wing plate which controls the shear lag effect. 2. Based on the bending calculation theory of thin-wall box girder, the shear deformation law of each wing plate is analyzed, and the formula for calculating shear flow is given, and it is assumed that the derivative of transverse displacement of wing plate to longitudinal coordinates can be ignored. It is proved theoretically that quadratic parabola is a reasonable function of shear lag warping displacement. A new shear lag warping displacement function is defined by adding a constant to the whole section to make the warpage stress satisfy the self-balancing condition of axial force and modifying the cantilever plate and bottom plate with different width of plate and different distance of horizontal center axis. 3. The additional deflection caused by shear lag effect is regarded as the generalized displacement of shear lag, and the generalized moment of shear lag is defined as the generalized force corresponding to the shear lag warping stress. In this way, the expression of longitudinal stress after considering shear lag effect is in agreement with the corresponding theoretical formula of elementary beam, and the physical meaning is more clear. 4. Based on the principle of variation method, the governing differential equations are established, and the expressions of shear lag additional deflection of simply supported box beams and cantilever box beams acting on concentrated load and distributed load are obtained by solving the boundary conditions. Furthermore, the longitudinal stress and vertical deflection of the box beam with shear lag effect can be obtained by superposition of the results of the bending theory of the primary beam and the results of the bending theory of the primary beam. 5. Based on the calculation examples of simply supported beam and cantilever beam, the longitudinal stress in selecting different warping displacement functions is solved by the theoretical method in this paper, and the ansys numerical model is established to verify the rationality of the analytical method and the formula in this paper. 6. The calculation of a prestressed concrete simply supported beam with symmetric concentrated load shows that if shear lag effect is not considered in the actual bridge design, the influence on vertical deflection can be negligible, but the longitudinal stress is quite different from each other in the actual bridge design, if the shear lag effect is not considered, the influence on the vertical deflection can be negligible, but the longitudinal stress is quite different. You can't ignore it.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U448.213
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