树状结构杆件计算长度系数研究

树状结构的杆件受力以轴压作用为主，稳定性是其结构设计中的控制因素。然而由于树状结构的复杂性，在现行规范中并未给出其杆件计算长度系数的取值建议。为解决该问题，首先从理论出发，利用位移法推导了简单平面树状结构杆件的计算长度系数解析式，确定了影响计算长度系数取值的关键参数；然后以有限元特征值屈曲分析法为基础，提出并改进了针对树状结构的1阶整体失稳法，研究了空间树状结构各级杆件计算长度系数随结构高跨比和相邻杆件刚度比的变化规律；最后，通过统计分析给出了空间树状结构树干和各级分支的计算长度系数的取值建议。研究表明，有侧移树状结构的1阶整体失稳模态与悬臂柱相近，而无侧移树状结构的1阶整体失稳模态与两端铰支柱相近，根据该特点可以快速确定树状结构的整体计算长度系数，并进一步确定树干和各级分枝的计算长度系数，以期为工程中高效开展树状结构的稳定性设计提供理论参考。

Effective length factors for branching structures

The members of branching structure are mainly subjected to compressive force under external loads, and the stability of the structure or its members is the governing factor in design. However, because of the complexity of branching structures, recommended values of the effective length factors are not covered in the current specification. To solve this problem, this paper starts with analytical studies. A displacement method is used to derive the analytical formulas of effective length factors for simple plane branching structures, and several influential factors of these recommended values are determined. Subsequently, an improved first-order global buckling method for branching structures is proposed. Effective length factors of the structural members of each level in the spatial branching structures are investigated by using eigen value buckling analysis. Moreover, the changing characteristics influenced by the height-span ratio and the stiffness ratio between two adjacent structural members are revealed. Finally, recommended values for the effective length factors for the trunk and branches of varying levels are obtained based on a statistic analysis. Based on the study above, it is found that the buckling modes of branching structures with lateral deformations are similar to free-stand columns, and the buckling modes of branching structures without lateral deformations are similar to simply-supported columns. According to this feature, the global effective length factors can be determined rapidly, then the effective length factors for the trunk and branches of each level can be calculated, which provides a basis for the stability design of branching structures.