中文摘要：

采用有限元方法分析几何参数对树状结构节点承载力的影响，得到节点尺寸参数的最佳取值范围，并拟合出树状结构节点的承载力公式。通过逆吊递推找形设计方法设计整体树状结构，计算分析屋面梁悬挑长度和树状柱间屋面梁跨度的相对大小对其内力分布的影响，得到两者最佳比值范围。同时验算树状结构节点的受力情况，拟定设计公式中安全系数的最佳取值。根据拟定的安全系数值设计整体结构并验算其力学性能及对应节点的受力情况。计算结果表明：若树状柱两侧局部刚度一致，除最上一级分枝外，按逆吊递推找形法得到的结构对应的安全系数应取4；需增加悬挑长度的结构，安全系数应取5；最上一级分枝的安全系数应较其余分枝大1。根据节点承载力公式设计得到的树状结构，具有较大的刚度，可用于实际工程。

英文摘要：

The influence that geometrical parameters of the tree-like structure joint have on the joint had been analyzed to find the most reasonable range of these parameters. On this basis, the formula of bearing capacity of the joint was obtained. The shape of the integral tree-like structure was designed through the inverse-hang recursive method. The most reasonable relative size between the cantilevered length of the roof beam and the span between tree-like columns were calculated while analyzing the influence which the change of this relative size had on the internal force distribution, and the safety factor K in the formula of bearing capacity had been proposed by verifying the force station of the joint. The mechanical characteristics of the integral tree-like structure and the relative joint were verified again after designing the integral structure according to the suggested safety factor.Results show that the safety factor of the formula of bearing capacity ought to be 4 for the structure based on the inverse-hang recursive analysis and it needs to be equal to 5 for the cantilever-increased structure, while the safety factor of the uppermost branch need supply 1, if the local stiffness on both sides of the tree-like column are equal.The designed structure have better stiffness and it can be applied in practical engineering.