考虑剪切变形影响的开口薄壁梁约束扭转研究

发布时间：2018-01-10 14:03

本文关键词：考虑剪切变形影响的开口薄壁梁约束扭转研究　出处：《长沙理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：开口薄壁梁在相同的横截面面积下可以获得更大的刚度,因而在各种建筑结构和桥梁工程中得到广泛的应用。为了确保其正常的工作,必须建立符合实际变形情况的开口薄壁梁力学模型,传统的符拉索夫理论由于抓住了其主要变形特征而在工程中广泛使用,但该理论忽略了二次剪应力对结构性能的影响,使其应用大受限制。为考虑剪切变形对开口薄壁梁约束扭转的影响,本文在符拉索夫开口薄壁梁理论的基础上发展了考虑剪切变形影响的开口薄壁梁约束扭转理论,主要研究内容如下:1、探讨了开口薄壁梁约束扭转的静力行为,对考虑剪切变形影响的开口薄壁梁约束扭转理论进行推导,给出了初参数法的一般解法,并推导了在不同扭矩荷载和边界条件下的位移及内力表达式。2、针对考虑剪切变形影响的开口薄壁梁约束扭转理论中出现的扭转剪应力不均匀系数,推导了几种常见的开口薄壁截面扭转剪应力不均匀系数的精确表达式,分析了扭转剪应力不均匀系数随高宽比、高厚比以及宽厚比等参数的影响规律。3、鉴于考虑剪切变形影响的开口薄壁梁约束扭转的解析解公式比较复杂,本文为得到与Timoshenko梁理论有类似的简化公式,探讨了圣维南扭矩可以忽略时的情形,阐述了简化方法与考虑剪切变形影响的解之间误差来源,定义剪切变形影响参数,给出了不同结构不同扭矩荷载下简化方法与解析解之间要达到5%的误差所需要的条件;分别对槽型截面和Z型截面梁进行了参数分析,定量的分析了各种理论与考虑剪切变形理论之间的误差大小随参数变化的趋势并得出了相关结论。4、对开口薄壁梁在横向、纵向偏心荷载作用下的约束扭转进行分析,将开口薄壁梁所受的偏心荷载作为一种外加双力矩考虑,推导了一些常见结构在偏心荷载作用下的变形及内力表达式;对槽型梁受纵向荷载进行了参数分析,定量地分析了各种理论与考虑剪切变形理论之间的误差大小随参数变化的趋势并得出了相关结论;同时分析了翘曲应力占总应力的百分比随参数变化的趋势并得出了相关结论。5、开口薄壁梁受轴向偏心弯矩荷载产生约束扭转时,按其弯曲中心的计算公式将不再适用。
[Abstract]:Open thin-walled beam can obtain greater stiffness under the same cross-section area, so it has been widely used in various building structures and bridge engineering, in order to ensure its normal work. It is necessary to establish a mechanical model of thin-walled open beam in accordance with the actual deformation. The traditional Frasov theory is widely used in engineering because of its main deformation characteristics. However, the theory ignores the influence of secondary shear stress on the performance of the structure, so its application is greatly restricted. In order to consider the effect of shear deformation on the restrained torsion of thin-walled beam with openings. In this paper, the constrained torsion theory of thin-walled open beam considering the effect of shear deformation is developed on the basis of the theory of open thin-walled beam. The main research contents are as follows: 1. The static behavior of constrained torsion of thin-walled open beam is discussed. The constrained torsion theory of thin-walled open beam considering shear deformation is deduced, and the general solution of initial parameter method is given. The expressions of displacement and internal force under different torsional loads and boundary conditions are derived. The torsional shear stress inhomogeneity coefficient appears in the constrained torsion theory of thin-walled open beam considering the effect of shear deformation. In this paper, the exact expressions of torsional shear stress inhomogeneity coefficient of thin-wall section are derived, and the influence of the parameters such as aspect ratio, ratio of height to thickness and ratio of width to thickness on torsional shear stress inhomogeneity coefficient is analyzed. 3. In view of the complexity of analytical solution formula for constrained torsion of thin-walled beam with shear deformation, the simplified formula is obtained in this paper, which is similar to that of Timoshenko beam theory. In this paper, the case of San Venan torque can be neglected is discussed. The error source between the simplified method and the solution considering the influence of shear deformation is expounded, and the influence parameters of shear deformation are defined. The conditions for the error of 5% between the simplified method and the analytical solution under different torsional loads are given. The parameter analysis of grooved section and Z section beam is carried out, and the trend of error between various theories and considering shear deformation theory is analyzed quantitatively, and the relevant conclusion is drawn. 4. The restrained torsion of thin-walled open beam under transverse and longitudinal eccentric loads is analyzed. The eccentric load of thin-walled open beam is considered as a kind of external double moment. The expressions of deformation and internal force of some common structures under eccentric load are derived. The parameter analysis of slot beam subjected to longitudinal load is carried out, and the trend of error between various theories and considering shear deformation theory with parameter variation is quantitatively analyzed and the relevant conclusions are drawn. At the same time, the variation trend of the percentage of warpage stress to total stress with parameters is analyzed and the conclusion is drawn. 5. When the shedding thin-walled beam is subjected to axial eccentric bending moment load, the restrained torsion is obtained. The formula based on its bending center will no longer apply.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU392.1

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