Two‐dimensional (2D) funicular structures can be easily generated and controlled by means of simple geometric constructions. These geometric constructions derive from reciprocal relationships between the form and force diagrams of a structure, which form the basis of graphic statics. Unlike in 2D space, in 3D space, similar geometric constructions cannot always be established for the design of three‐dimensional (3D) funicular structures. In some specific cases though, purely geometric procedures requiring no numerical approximations can be defined. In particular, this contribution explores the geometric transformation of 2D funicular structures as a means to graphically generate 3D funicular structures in equilibrium with coplanar loads. A fully graphical method for the construction of such pairs of 3D skew funiculars in equilibrium with coplanar loads and with control over the position of the supports is presented. It is based on geometrical linear relationships between the original and the transformed structures. Ultimately, it is shown how such pairs of 3D skew funiculars can be applied to the design of bridge and roof structures for instance.

中文翻译：

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在共面载荷和支座位置平衡的情况下构造成对的3D倾斜缆索对的图形方法

二维（2D）缆索结构可以通过简单的几何构造轻松生成和控制。这些几何构造源自结构的形式图和力图之间的相互关系，这些关系构成了图形静力学的基础。与2D空间不同，在3D空间中，不能始终为三维（3D）缆索缆车结构的设计建立相似的几何构造。但是，在某些特定情况下，可以定义不需要数值逼近的纯几何过程。特别地，该贡献探索了2D缆索结构的几何变换，以图形方式在共面载荷的平衡下生成3D缆索结构。提出了一种完全图形化的方法来构造这种成对的3D偏斜缆车，它们在共面载荷和支撑位置的控制下处于平衡状态。它基于原始结构和变换后的结构之间的几何线性关系。最终，显示了如何将这样的3D倾斜缆索对应用于桥梁和屋顶结构的设计。