圆形平面斜交式索桁架找力和找形方法研究

RESEARCH ON FORCE-FINDING AND FORM-FINDING METHOD FOR DIAGONAL CABLE-TRUSS WITH A CIRCULAR PLAN

  • 摘要: 空间索桁体系中单根上弦或下弦索均可看作为一次静不定和动不定体系,可基于平衡条件或其他已知条件分别求解其力和形的解空间。基于节点平衡关系,将结构自重和屋面荷载等效为节点荷载,推导了有内环索和无内环索的圆形平面斜交式索桁架考虑结构自重和屋面荷载的初始预应力分布的解析公式。给出了索桁架考虑结构自重和屋面荷载的找力和找形方法的计算流程。首先将上弦索外形作为已知条件,通过给定中心竖杆初始内力,可以求得所有上弦索和竖杆内力。然后将竖杆内力作为已知条件,通过给定下弦索中一根索的形状或内力,可以求得所有下弦索的形状和内力。分别以有内环索和无内环索的斜交式索桁架为算例,基于相同的中心压杆预应力水平,比较了有无考虑结构自重和屋面荷载时初始预应力分布的差异,分析了找力和找形方法的计算效率和精度。计算结果表明:本文找力和找形方法可精确地计算斜交式索桁架在结构自重和屋面荷载下的初始预应力和下弦索几何形状,并可推广应用于其他类型空间索桁体系的实际工程设计。

     

    Abstract: In a spatial cable-truss system, a single upper or lower chord cable can be considered as a first-order system that is statically indeterminate and kinematically indeterminate. The solutions for forces and shapes can be determined separately by the grounds of equilibrium conditions or other known conditions. Based on the nodal equilibrium relationship, an analytical formula for the initial prestress distribution in a circular plan diagonal cable-truss, both with and without an inner hoop, was derived by assuming the self-weight and roof loads as equivalent nodal forces. The calculation process of force-finding and form-finding for cable-truss under self-weight and roof loads is provided. First, by assuming that the shape of the upper chord cables is known and by providing the initial prestress of the central vertical strut, the initial prestresses of all upper chord cables and vertical struts can be calculated. Next, with the initial prestress of the vertical struts known, the shape and initial prestress of all lower chord cables can be determined by specifying either the shape or initial prestress of one cable. Based on the same level of prestress in the central strut, the differences in the initial prestress distribution with and without considering the self-weight and roof loads were compared by using two diagonal cable-trusses with and without an inner hoop as illustrative examples. The calculation efficiency and accuracy of the force-finding and form-finding method were analyzed. The force-finding and form-finding method outlined accurately calculates the initial prestress and lower chord geometry of diagonal cable-trusses under self-weight and roof loads. This method is applicable to the practical engineering design of other types of spatial cable-truss systems.

     

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