两层框架整体稳定的实用计算法

发布时间：2018-01-29 05:45

本文关键词： 计算长度系数二阶位移法轴力面积比法临界力重分布法挠度法　出处：《昆明理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：由于钢材的高强,钢框架可以做的相对细柔,这样就使得结构的稳定问题变得突出。由于稳定问题属于二阶问题,即需要考虑变形后的平衡,而传统的。一阶强度问题则只考虑变形前的平衡,因此稳定问题比一阶强度问题复杂,属于几何非线性。稳定问题的核心是求解杆件或结构的稳定承载力(即临界力)。求解单个杆件临界力并不困难,但要求解整个结构的临界力就不容易了。在现行的《钢结构设计规范》(GB50017-2003)中虽有求解框架计算长度系数的表格(见附录D),但该表格隐含了一些假设,使其只能用于规则框架(各柱轴力相同),而对于不规则框架(各柱轴力不同)则不再适用了。针对这一现状本论文拟从两层框架入手,推导框架整体稳定的临界方程(超越方程)进而求解,经过几千次的求解之后,得到了大量的数据,制成了两个框架柱计算长度系数的诺模图,用这些诺模图可快速的计算出柱子的计算长度系数。由于推导和求解是从框架整体失稳出发的,计算得到的各柱的临界力完全满足同时失稳的条件。本论文最有价值的成果是表4.2和表4.3中的诺模图,这些诺模图的正确性和可靠性是经过了有限元计算的验证,且计算精度很高,是快速计算不规则框架柱的临界力很好的工具,面对《钢结构设计规范》目前还没有该方面的计算表格,也算是一种补充。由于是整体稳定求解,未知量的数目随着层数的增加而增加,要得到最终的临界方程难度增大,所以目前仅做到了两层单跨的框架,但也可用于两层多跨框架,只需计入多跨框架梁的刚度即可。本论文也探索了求解临界力的新的近似方法,如轴力面积比法(第5章)、临界力重分布法(第6章)、挠度法(第7章)等。并获得了一些成果。
[Abstract]:Because of the high strength of steel, the steel frame can be relatively fine and flexible, so the stability problem of the structure becomes prominent. Because the stability problem belongs to the second order problem, it is necessary to consider the balance after deformation. However, the traditional first order strength problem only considers the balance before deformation, so the stability problem is more complicated than the first order strength problem. The core of the stability problem is to solve the stable bearing capacity of the member or structure (i.e. critical force). It is not difficult to solve the critical force of a single member. However, it is not easy to solve the critical force of the whole structure. In the current Code for Design of Steel structures (GB50017-2003), there is a table for calculating the calculated length coefficient of the frame (see Appendix D). However, the table contains some assumptions that can only be used in a regular frame (the axial force of each column is the same). But it is no longer applicable to irregular frames (different axial forces of columns). In view of this situation, the critical equation (transcendental equation) of global stability of frame is deduced and solved in this paper. After thousands of solutions, a large number of data are obtained, and two frame columns with calculated length coefficients are made into a Norm diagram. The calculated length coefficients of the columns can be calculated quickly by using these Norm diagrams, because the derivation and solution are based on the overall instability of the frame. The calculated critical forces of each column completely satisfy the condition of simultaneous instability. The most valuable results of this paper are the Norm graphs in Table 4.2 and Table 4.3. The correctness and reliability of these Norm diagrams are verified by the finite element calculation, and the calculation accuracy is very high. It is a good tool to calculate the critical force of irregular frame columns quickly. In the face of the steel structure design code, there is no calculation table for this aspect, which is a supplement. Because of the overall stability of the solution, the number of unknown quantities increases with the increase of the number of layers. To obtain the final critical equation is more difficult, so at present only a two-story single-span frame, but also can be used for two-story multi-span frame. The stiffness of multi-span frame beam can only be taken into account. In this paper, a new approximate method to solve the critical force, such as the axial force area ratio method (Chapter 5, critical force redistribution method), is also explored in this paper. Deflection method (Chapter 7) and some results are obtained.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU391

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