# Analysis of Planar Double-Layer Timber Spatial Frames by Using Parametric Tools
## 1 Introduction
### Construction Systems
#### 1.2.2. Joints  
Depending on the type of bar used, the joint solution also varies. In timber construction, the critical part seems to be the connection between the timber bar and the (usually metallic) node. It is where the joining elements weaken the timber section and, at the same time, where the highest stress concentration occurs. In this regard, some of the research that has been developed (or is still in progress) is shown below:  
* Bamboo connectors (Figure 4a): [PERSON] and [PERSON] [13] developed a joint for the construction of double-layered bamboo space frames from octagonal plates welded to an octagonal base plate. During the research, the joint was tested on a double-layer bamboo space frame prototype with single supports every 4 m. The results were satisfactory. Currently, research is being continued with prototypes of larger spans.
* Solid wood log connectors (Figure 4b): One of the most well-known researchers in this field is Dr. [PERSON] [14]. Interested in the use of small-diameter logs, which, until then, had no use and were abundant in forestry waste, he developed a simple wire-tying method for attaching galvanized steel connector plates to the previously hollowed ends of roundwood poles. Without going into much depth, some other joints that have been proposed are the KT-W joint by [PERSON] (University of Osaka) and the 14 FTC-U joint by [PERSON] (University of Cape Town).
* Connectors in gluam sections (Figure 4c): In the same thesis [12] in which hollow sections of gluam are developed as bars, the appropriate joint solution for them is also uncovered. A hollow sphere is proposed with a screwed cover that allows access to the interior and incorporates unthreaded holes for inserting the threaded rods and fixing them inside the sphere by means of nuts. At the opposite end, the bar is threaded into an octagonal nut. To attach the node to the wood, casting plates are fixed to the inside of the wooden element.
* Connectors by CNC fabrication (Figure 4d): So far, metal-to-wood joints have been presented. The node is usually made of a high strength steel, since the stress concentration is very high at that point. Steel is a material easily shaped to the desired geometry (spherical, cylindrical, etc.) and strong enough to resist this punctual concentration of forces. A group of researchers from Victoria University of Wellington [15] proposed to work with plywood cut with the CNC router to create a wood-wood joint. The results of the tests performed on the prototypes showed that this solution works with deformations of about \(1/400\) when overloads of use type A1 (residential zone housing) and B (administrative zones) are applied to it. Although the structure was not at its ultimate limit (collapse), it was concluded that the joint should be further stiffened. Before moving on, we give one last note on the joints. Among the structures formed by bars, two subtypes can be distinguished: those in which the connection between bars is made through rigid nodes (that is, if the node undergoes a certain rotation, all the concurrent bars in it undergo the same rotation) or through articulated nodes (each concurrent bar can rotate independently of the others). This distinction, however, can often be overridden by the shape appearing when treating the nodes as rigid or as articulated, since the bending moments that necessarily appear in the first case are very small in comparison with the axial forces, which are of very similar magnitude in both cases. This consideration allows that it is not necessary to construct perfect articulated nodes and to use types of nodes that, in reality, are neither rigid nor articulated but are located, in general, in an intermediate zone [1,16].  
Figure 4: (**a**) [PERSON]’s bamboo frame connector; (**b**) [PERSON] solid wood log connector; (**c**) [PERSON]’s glualam hollow section joint; (**d**) [PERSON], Marriage, [PERSON] and Pelosi’s CNC fabrication frame with wood–wood joints.