【作者】 唐毅；

【导师】 崔佳；

【作者基本信息】 重庆大学 ， 结构工程， 2005， 硕士

【摘要】 近年来大跨格构拱的应用越来越广。不论是单一的格构拱结构还是以格构拱为其重要组成部分的混合结构体系在工业建筑和公共建筑中都得到了广泛的采用,这使得格构拱的稳定计算问题变得更加重要起来。格构拱与实腹拱相比,其剪切变形不再是很小的了,因此格构拱的临界荷载的计算必须考虑剪切变形的影响。而剪切变形对临界荷载的影响程度决定于缀材的尺寸和结构布置等因素,本文最终目的就是研究这些因素对大跨格构拱平面内整体稳定的影响规律。而国内外关于大跨格构拱的稳定研究还很少。任意轴线拱的平衡微分方程是变系数的,难于直接求解而常常采用近似方法,如渐进法、有限差分法等。而本文研究格构拱的稳定问题还必须考虑剪切变形,前面所提近似方法便不太适用,于是本文在这种背景下作了以下主要研究工作: (1)　从拱的基本方程出发,结合CDC 法的基本原理,导出了计算拱挠度曲线的基本方程组,得到一种计算抛物线拱的临界荷载的新方法——拱的挠度曲线法(简称ADC 法);应用该法计算出了均布竖向荷载作用下等截面抛物线拱面内屈曲的临界荷载,其结果与现有文献和有限元法的结果吻合较好,验证了ADC 法的正确性,同时也展现了该法的诸多优势。(2)　在ADC 法的基础上顺利地引入的剪切变形,将ADC 法进一步发展成可以计算包括剪切变形在内的临界荷载的方法;在作了一些简化和假设后,将格构拱转化为等效的实腹拱,于是可用ADC 法进行近似分析;通过参数的单因素和多因素分析,得到了剪切变形对双肢缀条拱和三肢缀条拱的临界荷载的影响规律。(3)　为了简化格构拱临界荷载的计算,本文结合理论推导和数值回归分析, 提出了格构拱换算长细比的建议计算式,使格构拱的临界荷载可通过换算长细比转换成等效的实腹拱计算;最后本文还用有限元模拟了两铰拱和无铰拱的多个实际结构,并将有限元法的结果同ADC 法的结果和本文建议式的结果作了对比分析,结果表明按本文思路和方法分析是正确可行的。本文将CDC 法原理应用于拱的稳定分析当中,得到了求解拱临界荷载的ADC法还仅仅是个开始,该法还有很大的发展空间。像研究直线梁柱稳定问题的CDC法一样,ADC 法可以继续发展成为分析曲线梁柱稳定问题的通用方法。而格构式拱的稳定问题实践上还需要进一步的试验研究,理论上也有待更精确的二阶分析。更多还原

【Abstract】 The application of long-span lattice arches is becoming more and more popular in recent years. Both Simple lattice arches and mixed structural system get extensive adoption in industrial and public building. This makes the investigation on the stability of lattice arches very important. Compared with solid arch, the shear deformation of lattice arch is not small any more,so its effects on the critical load must be taken into consideration. Furthermore, to what degree the effect of shear deformation on the critical load is determined mainly by the dimension and arrangement of lacing bar. The purpose of this paper is to investigate how the shear deformation influences the overall buckling of the long-span lattice arch. However, there is a lack of researches on the stability of lattice arch both domestically and internationally. The coefficient of arbitrary axes arch’s equilibrium differential equation is variable, and this equation is so difficult to solve directly that usually approximate method have to be adopted, such as evolutionary method, finite difference method etc. Since shear deformation should be taken into consideration on the stability research of arch in this paper, and the above approximate methods neither work well nor can be adopted, the main research works are as follows: (1)Based on the basic equations for calculating the arch deformation curve derived from the basic arch equations and the basic principle of CDC method, a new method for calculating the critical load of parabola arch ——Arch Deflection Curve Method (ADC method for short) is obtained in this paper. With this method, the critical load of parabola arch under uniform vertical loads are worked out,and the value matches well with the results of current literature and of FEM. It has proved the ADC method to be accurate, also shows many advantages of the ADC method. (2)Through introducing the shearing deformation into the basic equations of the ADC method successfully,the ADC method develops further into a new method that can calculate critical load including shearing deformation; After making some simplification and tentative, the lattice arch is changed successfully into equivalent solid arch, hence the ADC method can be used to process an approximate analysis of lattice arch;Through the single factor and multi-factor analysis of the parameters, the laws of the shearing deformation’s influence on the critical load of two-legs or three-legs lacing arch are obtained. (3)For the sake of simplifying the calculation of the lattice arch’s critical load,combining the theoretical derivation and the numerical integration,a formula for equivalent slenderness ratio of the lattice arch is put forward in this paper. Hence the lattice arch can be converted into equivalent solid arch and critical load can be worked out simply;Finally,the simulation of actual lattice arch structure with finite element method is completed, and the contrast between the results of ADC method and the results of the formula is done. As a result, the analysis according to this paper’s thoughts and methods is right and reasonable. This paper applies the CDC method principles to the stability analysis of the arch, and gets the ADC method of calculating the critical load is just a beginning. The ADC method still can be further developed. Like the CDC method for the stability analysis of straight beam-column, the ADC method can continue to develop further into a general method to analyze stability problem of curve beam-column. Besides, the stability problem of the large-span lattice arch still needs further experimental studies and more accurate theoretical second-order analyses.更多还原