Advancing thin-tile vaults: structural analysis and robotic construction

Abstract

Thin-tile vaults are a a type of vaults that went out of fashion in the early twentieth century. Its origins are around the Mediterranean, but modern interest is mostly due to Guastavino, and the research done at MIT and ETH. The thin-tile vaults have a unique construction method without any temporary support. Eventually the increase in labour costs and the advancements in concrete and steel made the structure non-competitive.Robotics are a type of machines that can perform (semi)-automated tasks. In the past decades the development of robots have led to their implementation in the construction industry. Robots developed specifically for masonry show a high promise where they're able to lay much more bricks than even the most skilled mason.This research aims to investigate the time it takes for a robot to construct a thin-tile vault, and thereafter to advance the possibilities of research into and construction of the thin-tile vault. This is researched by answering the following question:How does a robotic construction of a parametrically designed thin-tile vault perform based on step-wise structural analyses?To answer this question a parametric model has been made to include the design of the thin-tile vault, the structural analysis and the robotic construction. This model is made in Grasshopper, but is supported by Python and RoboDK. Python performs any calculation necessary and analysis of this output. RoboDK is a robotic simulation program aimed to give users a tool to translate their design to robotic instructions. The structure of this report is based on the three aspects of the parametric model.In the first part the state of the art and the relevance of this research is stated. Thereafter the objectives, questions and methodology are noted.The first part of the model is related to the design. In the first chapter a literature review is provided on thin-tile vaults and similar vault structures. The second chapter of this part describes how the design model has been made. First the global shape of the vault is set as a barrel vault formed as a catenary arch. Then the bricks are placed on this vault surface using a similar approach as map projection. This is done with the introduction of the centre point approach. This ensures that proper information is maintained, like the course and the position within the course per brick. With this approach it is possible to fill this surface even with courses misaligned to the primary curvature. Bricks at the edge of the vaults surface are cut to fit within its domain. The last step is to thicken the bricks, which thus far had been represented as surfaces, into volumes.The structural analysis consists of three major parts. In the first chapter literature is shown to justify the use of a linear elastic analysis on masonry. Additionally the behaviour of this uncommon type of masonry is tried to be found in literature. The materials brick, mortar and epoxy are looked into as well. Bricks have time-independent properties, making these similar as found in the Eurocode, by manufacturers and in research. Mortar and gypsum plaster especially (also known as Plaster of Paris), are described in their material properties as well. Due to uncertainty in these properties, epoxy is investigated as well and found to have more theoretical values useful for this research. A small-scale experiment with bricks and epoxy has been done to verify what values from epoxy should be used.After the literature review on material properties, the structural analysis is done. The flow of this chapter starts with the form from the design model, through the forces of a cantilever, to the stresses occurring in the structure. The vault has been simplified to an arch during construction. Thrust is not present. The sectional forces are found by first considering the (partial) arch as a cantilever with a vertical shear force and rotational moment. Next this shear force is converted into the normal and shear force in the cross-section of the arch. This calculation has been worked out in a Python script.In the last chapter a possible stress distribution is shown. The analysis is based on a phased structural analysis. Each time step is equivalent to the placement of one row of bricks, which have a similar cantilever length. The stresses of the bottom and top side are shown, as well as the stresses between the wythes of the vault. In a DIANA model it is shown these wythes behave more like a monolithic material than a layered one. The last part is related to the robotic construction. First literature is shown related to masonry robotics. In the second chapter the stations the robot visits, are described. At the pallet station three instructions are described. The adhesive station has a number of instructions which is dividable by four. The vault station again has three instructions. This is similar to a pick & place work order, but with the adhesive station in between. Two configurations are considered. The first is when the robot is outside the vault, where it is closer to the support than to the apex. In the second configuration the robot is placed within the vault, where it is positioned close to the apex. In the last chapter the robot is chosen. Additionally the path is described with boundary conditions.The results are shown for 8 computations: a basis computation; one with the robot changed; one with the shape of the vault changed; one with the orientations of the wythes changed; one with an increase of the adhesive hardening time; one with a small course length of the vault; one with a different work space configuration; and lastly one with a different preferred construction sequence.In conclusion the models and results show that the construction of a thin-tile vault is similar to other masonry robotics, if the hardening time is excluded. Included, the number of bricks built per day is similar to two masons building a thin-tile vault prototype. The hardening time is the primary influence of the total construction time and any reduction here is advised. Further optimisation of the movement of the robots is possible with a more in-depth optimization of the work space configuration and an optimization where the shortest movements are considered across instructions. The linear-elastic structural analysis has been found to be possible to use for the calculation of the thin-tile vault during construction. Additionally, two construction sequence preferences work well with the multiple wythes, but one preference shows better results when more bricks with more cantilever length need to be placed, due to reducing the stresses on the edge of the extrados wythe.Further research into thin-tile vaults is still required to fully understand and model the thin-tile vault. Related to the three models (design, engineering and robotics) each have been improved in the models made for this research, but are still a long way away from full implementation.