斜腹杆体外预应力结构杆索的耦合分析

Analysis of poles-cable coupling in externally prestressed structure with tilted belly poles

应用有限元理论,以斜腹杆体外预应力结构为对象,考虑杆与索的耦合作用,通过两结点直线只拉索单元模型的建立,得到求解索结点位移的斜腹杆体外预应力结构的刚度矩阵及腹杆伸缩列阵.首先从几何关系入手,分别求解由索结点位移列阵求索应变列阵与腹杆伸缩子列阵的转换矩阵;又用物理关系,分析由索应变列阵求索应力列阵的转换矩阵;再用变形体的虚功原理,求出由索结点位移列阵求索结点荷载列阵的转换矩阵;最后用腹杆的平衡条件,推导斜腹杆体外预应力结构的刚度矩阵及腹杆伸缩列阵.研究表明,斜腹杆体外预应力结构刚度矩阵的影响因素较为复杂,不仅与索单元的杨氏模量、长度、横截面面积等参量有关,也与腹杆的方向和长度有关.斜腹杆体外预应力结构杆索耦合的分析结果,为斜腹杆体外预应力加固设计提供了理论参考.

Using finite element theory, taking externally prestressed structure with tilted belly poles as object, taking account of coupling effect of pole with cable, and by means of setting up a cable unit model which has only-tension link elements, the stiffness matrix of the object and array of the telescopic poles are obtained for finding the displacement of the cable node. Firstly, starting the geometrical relation of the object, a conversion matrix is found for finding cable strain array and sub-array of telescopic poles, respectively. Then according to the physical relationship of the cable, the conversion matrix for finding the cable stress array from cable strain array is analyzed, further a according to the principle of virtual work of the deformed body, a conversion matrix for finding cable node load array from the cable nodal displacement array is obtained, and finally, according to the equilibrium condition of the poles, the stiffness matrix of the object and array of the telescopic poles are derived. It is shown by the investigation that the influencing factors of the stiffness matrix will be more complex, showing that it will be not only associated with parameters such as Young modulus, length, and cross-section area of the cable unit and also with the direction and length of the poles. The analysis result of the cable-pole coupling will provide a theoretical reference for reinforcement design of externally prestressed structure with tilted belly poles.