Abstract: Based on the varied expressions of reciprocal systems in the context of Eastern and Western cultures, this study investigated the basic features and principles of reciprocal systems from the perspective of structural composition and stresses. The unique reciprocal principles of the Bianshui rainbow-shaped bridge in Eastern tradition and the woven timber arch system in Fujian and Zhejiang Provinces were reviewed. In the up-pressed lock running through the crossing timber, two arch frames are used as independent structural units; this offers extra support and reinforcement. This is known as the Eastern "reinforcing reciprocal frame". With respect to the Western traditional reciprocal system, although the Da Vinci woven bridge has a similar outer layer to the Eastern reciprocal bridge, the stress principle differs greatly. For rainbow-shaped bridges, there is no reciprocal relationship among the components in the arch frame; a reciprocal relationship in circulating force transmission is only formed among the units. The structural units of the woven bridge are formed by horizontal and vertical combinations and overlapping of four unit components, achieving a reciprocal system in and among the structural units. The principles of the Western reciprocal floor structure and reciprocal dome are highly consistent with those of the woven bridge. On the one hand, a reciprocal relation exists among the units; the components in the unit achieve a stress balance for the whole structural unit through cyclic force transmission. On the other hand, a reciprocal system among structural units exists. The cyclic force transmission state is expanded to several units, thus achieving the overall stress balance of several unit combinations. In brief, the stress balance in the Western reciprocal system runs through the structural units and overall structure; this is known as a "balanced reciprocal system". On this basis, the similarities and differences in the principles of Eastern and Western reciprocal systems were analyzed. The similarities include the layer composition, small-sized components, and cyclic force transmission. In terms of the differences, the Eastern reciprocal system achieves reinforcement and stability through a reciprocal frame among structural units. There must be an angle between the unit components on the cross-section in order to insert the crossing timber and thereby reinforce the components of another unit. Further, the curvature of the surface has strong adaptation. In contrast, the Western reciprocal system establishes reciprocal frames among structural units and in each unit, maintaining a reciprocal mechanical balance; this is conducive to morphological expansion along the plane direction and expansion of the span. To sum up, the Western balanced reciprocal system is far superior to the Eastern reinforced reciprocal system in terms of span expansion. However, curvature changes can rely on relative positional changes between cumulative members and horizontal surfaces among components in multiple groups of structural units. Hence, the changes in the adaptive curvature of the surface are far smaller than the reinforcement structure. In a word, the reciprocal system of the Eastern traditional bridge is only applicable to a one-way hook surface. The Western balanced reciprocal system is difficult to fit to a large curved surface. To address their development bottlenecks, a new configuration that adapts to a free curved surface was designed and built based on the Da Vinci woven bridge. The span accessibility and stress accessibility were verified from the perspective of construction. These findings offer new directions and a theoretical foundation for the future development of contemporary reciprocal frame systems.

Key words: reciprocal structure, reinforced reciprocal frame, balanced reciprocal frame, reciprocal dome, woven arch, rainbow bridge

摘要： 基于东西方文明背景下互承框架的多样表现形式，从结构构成与受力出发探究互承体系的基本特征和原理要素，进而从其原理的倾向性差异中梳理出东方加固式和西方平衡式两种互承形式，并探讨了二者的原理差异、形态差异、构型差异与适用范围，主要结论有东方以结构单元之间的互承实现加固和稳定性，其曲面曲率适应性较强；西方则以在结构单元之间以及单元内部同时构建互承且均保持力学平衡实现了跨度的拓展。由此，针对东方传统桥梁互承体系仅可适应单向曲面以及西方平衡式互承难以拟合大曲率曲面的发展瓶颈，以达·芬奇编织桥为原理基底，设计并建造了一种可适应自由曲面的新构型，且从建造视角论证了其跨度可行性与受力可行性，这一实验性构想为当代互承框架设计的未来发展提供新的方向及相应理论基础。

关键词: 关键词　互承框架, 加固式互承, 平衡式互承, 编木穹, 编木拱桥, 虹桥