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It has already been briefly described how the principles from ‘Applied Structures I’ are carried out in the fabrication of the guide-work for the vault; however, this will be addressed again here so that the construction process, A-Z, can be contextualized in terms of structural behavior.
It is obvious now that Hooke’s 2nd Law enables the rapid construction of our efficient masonry geometry – “As Hangs the Flexible Line, so but Inverted will stand the Rigid Arch”. The hanging chain is set up with the corresponding span and rise of the full-scale vault, and is traced onto paper to create a template. This template, when flipped, is the most efficient geometry for a vault with this span and rise. Perhaps this seems a crude method, yet the accuracy and ease of the hanging chain lends itself to building in contexts with limited resources.
The guide-work is fabricated directly on top of the template and is installed – at opposite ends of the vault – to describe the curvature of the masonry surface. The guides must be installed so that they may be ‘dropped’ down and away from the vault after the masonry is completed; otherwise the guides may be accidentally pushed ‘up’ into the masonry, putting a very thin, compression-only structure into tension and risking collapse. Particularly as the first courses are being laid, motion of the guide-work can compromise the weaker bond of the first cantilevering masonry units, so it is critical that it is installed very securely. Since milled lumber is extremely expensive and limited in Ethiopia, Eucalypis branches are the primary multi-purpose construction material, serving as scaffolding and guide-stabilizer in our case.
Mason’s line (string) is tied to connect the guides, ‘lofting’ a surface with only string so the mason’s know where to lay the tiles in space. The first vaulted layer is set in plaster without formwork – cantilevering out into space while following the mason’s lines. Here, the masons must understand the accuracy required for this singly-curved geometry. Each line is spaced at roughly a half-meter, and the mason’s must develop the ability to see a continuous catenary surface, rather than building straight lines of masonry between each string. If only one tile is set too low over the mason’s line, pushing the entire length downwards, then each subsequent row will have an inaccurate geometry. Alternately, if straight courses are built from line to line, kinks will occur in the surface. Since our vault is so thin, and since it is only curved in one direction, there is no redundancy of the load paths – and such mistakes can have catastrophic effects, creating points at which stresses are collected and hinges can be formed which cause the structure to collapse.
The masons must understand how a single curved vault is weak (particularly when it is still only 1 layer with a 2 centimeter thickness), so they can understand how to load the surface without compromising the vault. A bucket, cut in half (which typically serves as the mixing vessel for the gypsum mortar), is appropriated as a teaching tool. It is a single-curved geometry which can be bent to be roughly the geometry of the SUDU. A since point load at the crown of the bucket vault shows how strong it is; hands wrapped over the surface show how well it performs with an evenly distributed load; but even one finger pushing at a quarter point demonstrates its deformation from an asymmetrical point load. Thus, workers are instructed to be careful with the first 2 cm layer, to wear hardhats when working below the worker scaffolding, and to be responsible for who is working beneath them.
The following layers of masonry are set ‘oblique’ to each other (generally rotated by 45 degrees) so that the joints between each layer are ‘broken’ (meaning, so that a joint does not overlap between multiple layers). This creates a very strong ‘sandwich’ of masonry, which gives us a reasonable assumption that ‘no sliding’ will occur in the material. Once the thickness of the vault – and thus its self-weight – is increased, it is more resilient against point loads.
Once a meter of the first and second course of masonry is laid, we may begin to build the stabilizing diaphragm walls that were described in the last post. The diaphragm walls are space 0.9 meters apart, creating regular stiffeners against asymmetrical loading. One the floor system fill has been added the diaphragms and the fill will work together to allow the load paths to travel through the floor system in the case of asymmetrical loading.
The sequencing of this whole series is important so that this single curved vault is not loaded – particularly asymmetrically – until these alternate load paths are provided for by the diaphragm and floor system fill. In our case, since the materials acquisition and testing of the semi-rigid fill was delayed, we had to continue construction while limiting access and loading to the unfinished floor system. Ideally, each section between diaphragms would have been filled, allowing on team to complete their work from the floor surface of the completed vault.
The tension ties must be specified with sufficient strength steel, at the proper gauge, and spaced accurately to tie the outward thrust of the single curved masonry shell. Special attention must be paid to the detailing of these members so that welded bonds with short overlaps – such as below – do not fail in shear at the connection.
This vault was designed so that all the load paths would be directed to the ring-beam, in the direction of the curvature of the vault. This will allow a funicular stair to cut up through the vault. Nevertheless, this detailing at the edge is important to insure that there is no critical lateral loading exerted upon the terminating wall of the vault.
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