分阶段施工桥梁无应力状态控制法的应用研究

发布时间：2018-05-06 04:00

本文选题：无应力状态控制法 + 几何非线性　；参考：《长安大学》2015年硕士论文

【摘要】：无应力状态控制法是一种解决分阶段施工桥梁结构计算的理论方法。它在世界上首次建立分阶段施工桥梁的力学平衡方程,第一次从理论上阐明桥梁构件单元的无应力状态量是影响分阶段施工桥梁内力和线形的本质因素,从而可以应用构件单元的无应力状态量控制分阶段施工桥梁施工过程和成桥状态的内力、位移。目前无应力状态控制法已形成一套系统的理论和方法,但是随着桥梁结构向着超大跨度发展,特别是斜拉桥,加劲梁一般采用钢箱梁的结构形式,梁高与跨径之比进一步减小,主梁变得更加纤细,这时结构体系的几何非线性问题更加突出地暴露出来。为了能将无应力状态控制法更好的运用在大跨径斜拉桥施工计算当中,具体的研究内容如下:1、无应力状态法的基本方程。首先基于势能驻值原理,推导了考虑几何非线性的分阶段成形结构无应力状态控制法一般静力平衡方程。根据一般静力平衡方程,分别得出了分阶段成形平面杆单元、梁单元结构的无应力状态控制法静力平衡方程。最后基于解析解得出了分阶段张拉平面索单元的无应力状态控制法静力平衡方程,对其非线性求解问题做了介绍。2、根据非线性有限元求解理论,分别得到了平面梁单元结构无应力状态控制法全量列式和增量列式的平衡方程;分别详细论述了运用TL列式、UL列式、CR-UL列式、CR-TL列式求解平衡方程的过程,并且通过实例验证了共转坐标法求解几何非线性问题的优越性。上述四种列式求解平衡方程的基本思路,对于杆单元和索单元来说也是适用的。3、通过数值算例,验证了分阶段成形结构无应力状态控制法静力平衡方程。分阶段成形结构的内力和位移与一次成形结构产生差异的本质原因不在于结构成形方式不同,而是因为分阶段成形结构的无应力状态量与一次成形结构不一致。4、对无应力状态控制法在斜拉桥施工仿真计算中的运用进行了理论分析,阐述了无应力正装分析的基本原理。以两个具体的钢箱梁斜拉桥工程为例,对一500m级斜拉桥,按线性无应力正装计算的结果与合理成桥状态相同,而且比倒拆-正装迭代分析方法更简单。对一600m级斜拉桥,分别取两种不同的成形方式,按非线性无应力正装计算,两种成形方式各索一次张拉索力不同,但施工过程索力变化趋势大致相同,且成桥阶段都收敛于合理成桥索力,且主梁最终状态的内力和位移计算结果都与合理成桥状态相差很小,验证了在大跨度斜拉桥施工阶段仿真分析中运用无应力状态控制法可靠性,进一步验证了无应力状态控制法的基本方程,为无应力正装计算的推广运用提供了理论基础和借鉴。
[Abstract]:The stress-free state control method is a theoretical method to solve the problem of bridge structure calculation. It is the first time in the world to establish the mechanical equilibrium equation of a phased construction bridge. For the first time, it is theoretically stated that the non-stress state of the bridge member element is the essential factor affecting the internal force and the linear shape of the bridge in the phased construction. Thus the non-stress state of the component element can be used to control the internal force and displacement of the construction process and the completed state of the bridge. At present, no stress state control method has formed a set of systematic theories and methods. However, with the development of bridge structure towards large span, especially for cable-stayed bridge, the stiffening beam generally adopts the structural form of steel box girder, and the ratio of beam height to span decreases further. As the main beam becomes more slender, the geometric nonlinearity of the structural system becomes more prominent. In order to apply the stress-free state control method to the construction calculation of long-span cable-stayed bridge, the concrete research contents are as follows: 1, the basic equation of the stress-free state method. Based on the standing principle of potential energy, the general static equilibrium equation of the non-stress state control method for stage-forming structures considering geometric nonlinearity is derived. According to the general static equilibrium equation, the static equilibrium equations of the non-stress state control method for the plane bar element and the beam element structure are obtained respectively. Finally, based on the analytical solution, the static equilibrium equation of the unstressed state control method for the tensioned plane cable element is obtained, and the nonlinear solution problem is introduced. 2. According to the theory of nonlinear finite element solution, In this paper, the equilibrium equations of the total and incremental equations of the stress-free state control method for plane beam element structures are obtained, respectively, and the process of solving the equilibrium equations by using the TL column and CR-UL and CR-TL respectively is discussed in detail. An example is given to verify the superiority of the corotating coordinate method in solving geometric nonlinear problems. The basic idea of solving the equilibrium equation by the above four formulations is also applicable to the bar element and cable element. The static equilibrium equation of the non-stress state control method for the stage-forming structure is verified by numerical examples. The essential reason for the difference between the internal force and displacement of the stage-forming structure and that of the primary forming structure is not the difference in the forming mode of the structure. But because the stress-free state of the stage-forming structure is not consistent with that of the one-stage forming structure, the application of the stress-free state control method in the simulation calculation of cable-stayed bridge construction is theoretically analyzed, and the basic principle of the stress-free dress analysis is expounded. Taking two concrete steel box girder cable-stayed bridges as an example, the calculation results of a 500m class cable-stayed bridge are the same as those of the reasonable bridge state, and are simpler than that of the inverted disassembly and normal load iterative analysis method. For a 600m class cable-stayed bridge, two different forming methods are taken. According to the calculation of nonlinear stress-free formwork, the tension of each cable is different in one time, but the change trend of cable force is roughly the same during construction. The final state of the main beam is calculated by the internal force and displacement, and the difference between the final state of the main beam and the reasonable state of the bridge is very small. The reliability of the stress-free state control method is verified in the simulation analysis of large-span cable-stayed bridge during the construction stage, and the basic equation of the stress-free state control method is further verified, which provides a theoretical basis and a reference for the popularization and application of unstressed dress calculation.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U445.4

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