Design and Project of Masonry Vaults by Software based in GeometryMethods

This paper reports on an investigation on vaulted ceilings aimed at seeking connections between the geometry of such architectonic elements and their structural behaviour. A search for the balance of forces acting through such elements is put forward, upholding on the Limit Analysis Theory. Graphically, the element's security limits are evaluated according to the forces’ trajectory distance through the vault or dome shapes. A simulation of the application of this graphical method on three equally dimensioned square-based types of vaults is presented (namely barrel, groin and dominical vaults). The groin vault is the lightest (1.514 N/m2) and that with the lowest Concavity Factor (1.14), while the dominical vault stands as the heaviest (2.244 N/m2) and shows the highest Concavity Factor (2.07). On another note, the barrel type is only supported by its sides (4.610 N horizontal thrust applied on each one), the groin vault on its four corners (horizontal thrust 3.102 N, diagonally directed) and the dominical type on its four sides (1.524 N horizontal thrust on each). Despite stress values on the three vault types are low, a couple of points ought to be accounted for. The maximum stress on the groin vault is 0.03 N/mm2 with a significant increase up to 0.34 N/mm2 as the edges are approached. The maximum radial stress –transmitted to the supporting elements- on the dominical vault is 0.03 N/mm2, although a parallel-to-the-supports ring stress appears (whose intensity depends on proximity to vertical position as related to the supports) ranging up to 0.17 N/mm2, quite higher than the radial stress. Maximum work stress is not the defining value in order to guarantee stability for this element.