# Joint Layout Design: Finding the Strongest Connections within Segmental Masonry Arched Forms
## 1 Introduction  
### Segmentation of Masonry Curved Structures throughout History  
Curved structural forms, including shells, domes, vaults, and arches, are strong geometries [1] that can bear large amounts of external loads through the optimal distribution of materials. These complex shapes usually need to be segmented into smaller parts to simplify fabrication [2; 3], facilitate transport [4], and improve assembly [5; 6]. Historic segmental vaults and domes were composed of masonry tiles, bricks, or stone blocks and were frequently used in the built environments to span large spaces. Furthermore, historically, masonry (and particularly stone) arches were used to construct bridges in the challenging environmental conditions stayed functional in the transport networks for decades or even centuries [7]. Later, masonry arched forms evolved in the form of precast concrete shells widely applied in contemporary architecture, engineering, and construction (AEC) industry. Precise quality control during the manufacturing and fabrication process, rapid assembly, and a relatively low waste production during the construction are the main advantages of the precast concrete when compared to the one cast in situ [8]. Furthermore, advances in computational fabrication such as additive manufacturing with concrete or digital stereotomy of stones map a promising future for the sustainable design and construction of freeform segmental masonry arched forms. Basically, segmenting a structure can result in weakening its response to loads; e.g., the load that it bears may decrease since a continuum is broken up into segments. To remedythis situation, the constituent blocks of a segmental structure can be kept together, using fillers such as mortars usually applied in historic masonry vaults, and grouts and epoxy resins implemented between the precast concrete blocks. The fillers, however, can be eroded over time and reduce the tensile strength of masonry, as shown in [9]. Therefore, several analyses carried out on historic masonry buildings [10; 11] as well as precast concrete structures [8] simply consider zero tensile resistance at joints as if they are mortarless (dry) joints. Furthermore, the typical strategies to improve the masonry capacity are the consolidation techniques with tie-rods or strength anchors [12; 13] or the use of tie roads in particular to improve the stability of vaults or support walls [14]. The position of the joints in an assemblage of units and their shape can also significantly affect the structural behaviour. Apparently, finding the right place and shapes for the joints can improve the assemblage load-bearing capacity. In this case, even if the fillers between the joints or the tie rods connecting the segments are eroded, the joint resistance does not significantly change. As a result, finding the appropriate joint shape and layout can be considered a long-term strategy to segment a vault without considerable loss of its structural load bearing capacity. The influence of the joint shape and location on the mechanical behaviour of segmental assemblages has been widely considered in the literature. In the context of historic masonry vaults, it has been observed that different brick bond patterns determining the joint shape and location may have considerably different load-bearing capacities even when the joints are considered cohesionless [10]. One straightforward example is a hemispheric dome with stacked and running bond patterns. Carrying its self-weight, the former should have at least the minimum thickness-to-radius ratio of 0.0425 according to [15], while the latter can remain stable with a thickness close to zero if the friction coefficient at the joints is considered large enough [15; 16]. Along the same line, the structural performance of different types of masonry vaults, including cross-vaults, barrel vaults and domes, constructed by bond patterns such as running bond and herringbone patterns, have been extensively investigated in the literature, as reviewed by [PERSON] et al. [17].