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张弦梁结构(简称BSS)具有体系简单、充分发挥刚柔两种材料的优势等特点,在大跨度结构中得到了越来越广泛的应用。下弦索预应力值的确定和张弦梁零状态几何形态的解析解是求解常温荷载态下,以及高温荷载态下结构力学特征量解析解的基础。目前主要采用的做法是先行给定下弦索预应力值,然后通过数值模拟得到张弦梁零状态几何形态,但是,这种方法对结构设计人员可操作性不强。针对工程中常用的抛物线形张弦梁,通过对其预应力态下梁单元及索单元的微分平衡方程进行求解,以预应力态下张弦梁的几何形态为目标态,建立下弦索的预应力值与结构零状态几何函数间的关系,得出单榀张弦梁结构找形的简便计算方法。并将该方法的计算结果与基于有限元ANSYS软件模拟结果进行对比,误差不超过3%。结构工程师可以用这种简便计算方法设计零状态下张弦梁几何形态,从而得到满足建筑要求的抛物线形张弦梁几何形态。该方法的求解思路,也可为其它形状函数的张弦梁找形与分析提供参考。
The beam string structure (BSS for short) has the advantages of simple system, giving full play to the advantages of both rigid and flexible materials, and has been applied more and more widely in long-span structures. The determination of the prestressed value of the lower chord and the analytic solution of the zero-state geometry of the beam are the basis for solving the analytic solution of the structural mechanics characteristic quantities under the normal temperature load condition and the high temperature load condition. At present, the main method is to pre-set the pre-stress value of the lower chord, and then obtain the zero-state geometry of the beam by numerical simulation. However, this method is not feasible for structural designers. Aiming at the parabolic tensioned beam commonly used in engineering, by solving the differential equilibrium equation of beam element and cable element in prestressed state, the prestressing state of the beam is taken as the target state, and the prestress value and structure of the bottom chord are established Zero-state geometric function of the relationship between the singular string-beam structure obtained a simple method of finding the shape. The results of this method are compared with those of ANSYS based on finite element software. The error is less than 3%. Structural engineers can use this easy-to-calculate method to design the geometry of the string beam at zero conditions, resulting in a parabolic beam string geometry that meets the architectural requirements. The idea of this method can also provide a reference for finding the shape and analyzing the other shape functions of the beam.