# Joint Layout Design: Finding the Strongest Connections within Segmental Masonry Arched Forms
## 1 Introduction
### Innovative Design and Construction Methods for Masonry Curved Structures  
Contemporary manufacturing techniques, mostly developed based on the casting processes, facilitated fabrication of clay and concrete blocks with complex geometries. For example, most of the precast concrete panels have non-planar faces, allowing them to be simply interlocked to each other. Similarly, interlocking masonry blocks are commonly used to construct the contemporary masonry walls. Interlocking joints have usually one or several keys (locks) with, e.g., rectangular, trapezoidal, and circular cross-sections. Recently, several works have addressed the relationship between different joint shapes (keys' shape and number) and the load bearing capacity of structures, including simple flat walls [29; 30; 31; 32; 33], cylindrical assemblages [34], and arched form bridges with shear keys [8; 35].  
However, these works focused their investigation on the influence of a limited number of geometric parameters of the modular interlocking blocks, since the current manufacturing industry has been mostly developed based on casting processes using modular casts. On the other hand, recent transformations in digital manufacturing, including additive manufacturing techniques to print masonry blocks [36; 37] and concrete panels with parallel [38; 39] and non-parallel [40] layers, as well as cutting stones with CNC machines [41], have enabled us to construct segmental shells such that each of their constituent blocks has a unique shape [38; 39; 40; 41; 42; 43; 44; 45]. These promising manufacturing advancements have motivated architects and industrial designers, as well as civil, mechanical, and industrial engineers, both in academia and industry, to develop the design methods generating segmental assemblages composed of segments with complex shapes optimizing fabrication, construction process, etc. [1; 2; 3; 4; 5; 6].  
On the other hand, to date, very few research works have paved the way for the development of methods to design the specific shape and location for each individual joint with the aim to maximize the load an assemblage can bear. [PERSON] [46] showed that the bearing capacity of a compression-only, rigid, and frictionless body does not change after  
Figure 1: Three stereotomy techniques generating three different joint layouts with different load-bearing capacities: (**a**) false skew arch; (**b**) helicoidal method; (**c**) logarithmic method. Red arrows represent external loads applied to the arches beside their own weight.  
being tessellated by the joints normal to the flow of axial forces. The authors of this paper developed SiDMACIB, in the frame of a MCSA_IF [47], as one of the first efforts to design structurally sound interlocking blocks with finite shear and friction. In that project, the static approach of limit analysis was extended to the interlocking joints with orthotropic sliding behaviour governed by combined frictional and material shear strength properties. A method was developed to quantify the infeasibility of interlocking assemblages due to the sliding failure, namely the sliding infeasibility [48; 49]. Additionally, an optimization method was developed in which the shape of the interlocking joints was automatically adjusted to minimize the sliding infeasibility [50]. These results, however, remain limited to corrugated interlocking faces at this stage.