Analysis of connections in reciprocal frame structures

Abstract

The structural system known as reciprocal frames (R.F.), is one that is not common amongst most architects and engineers, however the system can be said to date back to the 12th century. The reason for the latter, is due to the inherent complexities of the structural system that lead to architects and engineers to avert form using them. The structural behaviour of reciprocal frames is defined by the configuration of the elements that mutually support each other. Several academic investigations have been carried to further the understanding of the behaviour of such a system. However, much of this research has not focussed on the connection of these structures. The present methodology has been based on Gustaffson (2016) which highlighted how the stiffnesses of the notched timber connection affected the structural behaviour of a planar reciprocal frame roof. His study only focused on a square configuration reciprocal structure. Due the fact that reciprocal frame structures may be formed of several element configurations, the study within this dissertation has extended the focus of the methodology and sought to assess the change in stiffnesses of these connections with the element configuration of reciprocal frame structures, both on plan (angle θ) and in elevation (angle α) and how in turn these stiffnesses affect the overall structural behaviour. Therefore, an analysis in the understanding of how the stiffnesses of the connection vary with the angle θ between elements was undertaken. In all the current research, the contact areas are assumed to be applying full pressure between the supporting and supported elements of the R.F. unit. An equation for all translational and rotational stiffnesses with varying θ was obtained. This equation was then validated with Gustaffson (2016) for θ = 90°. Consequently, the elements were inclined by an angle α to further represent the behaviour of the stiffness within the connection of any type of 3D configuration. The focus of this study is the proposal of a general analytical equation that defines translational and rotational stiffnesses in the orthogonal directions of all elements within a 3D configuration. This will aid architects and engineers to easily analytically calculate the stiffnesses of these connections without the need of any numerical analysis. Once calculated, the stiffnesses of each iteration were inputted into a parametric structural model of simple R.F. structures (units) in order to gain an appreciation of the effect of the stiffnesses that might have on the axial forces, bending moments and shear forces on a structure under a given load. Through the understanding of the connection on a local scale, it would be possible to extend the use of the general equation to compete tessellations (repeated R.F. units forming a structure).