## 2 Methodology
### State of Loads in the Different Stages of the Process  
The criterion used to analyse the behaviour of the vaulted structure of the Refectory is the comparison of the state of loads and deformations in each of the defined stages [3,35] and in two different situations: on the one hand, we have considered the segmental arches (arches 1, 2, 3, and 4), which are stressed by vaults, walls, and floors of similar dimensions and construction solutions, and on the other hand, arch number 5, which receives the loads from a different floor and vault surface, since the span of the last span is greater. In the transverse arches, two different points have been considered: the keystone (K) in the centre of the arch and the salmeres (S) at the extreme supports. For this purpose, the weights of the elements involved in the construction system are taken into account, based on the data provided in the tables of Annex C, Basic Document SE-AE of the CTE [38]:  
* **Dead weight of the vault, built with two threads of solid brick taken with lime mortar and rendered on the top and bottom with the same mortar, with an average thickness of 12 cm, and the consideration that the dead weight of a solid brick masonry with lime mortar is 18 KN/m\({}^{3}\), which results in: Qvault = 0.12 m \(\times\) 18 KN/m\({}^{3}\) = 2.16 KN/m\({}^{2}\). A load band is considered in the keystone (Qk), of 2 m for the standard arch and 1.5 m for arch 5. In the salmeres (Qs) is not considered, given that the vault discharges on the former arches and the lateral wall;
* **Dead weight of the unidirectional slab** resting on the brick masonry in segmental arches, made up of timber beams, beamwork based on solid brick revolton and hydraulic tile paving on fillings and lime mortar. An average thickness of 15 cm and a density of 18 KN/m\({}^{3}\) has been considered, and for the timber an average density of 8 KN/m\({}^{3}\), so that we can estimate an initial slab weight of 3.30 KN/m\({}^{2}\) for the initial slab. A constant load band of 5 m is considered for the standard arch and 6 m for arch number 5;
* **The dead weight of the 1 foot brickwork** (Catalan format with approximately 30 cm of rope) on the segmental arches is Q \({}_{\text{bricktwork 1 foot}}\) = 5.4 KN/m\({}^{2}\)\(\times\) h. This load is variable, being minimum on the keystone Q \({}_{keystone}\) = 5.4 KN/m\({}^{2}\)\(\times\) 0.25 m = 1.35 KN/m and maximum on the starts Q \({}_{factory\ start}\) = 5.4 KN/m\({}^{2}\)\(\times\) 2 m = 10.8 KN/m, considering the studied points C and S, respectively;
* **Self-weight of the rib-arches** made of limestone with a cross-section of approximately 0.20 m \(\times\) 0.40 m would have a uniformly distributed linear load of Q \({}_{rib-arches}\) = 0.20 m \(\times\) 0.40 m \(\times\) 28 KN/m\({}^{3}\) = 2.24 KN/m, considered constant over the entire arch (Figure 9);
* **Overloading of partition walls. ** The floor above the refectory is very diaphanous, with a partition wall of hollow brick with a thickness of 10 cm, and for this purpose a uniformly distributed linear load of 5 KN/m is considered. This is why this situation is considered to be the standard arch. In arch 5, given its initial situation with less partition walls, a load of 2 KN/m is considered. Figure 8: Principal vault extrados on its different restoration states: (**a**) Original (**b**) Reinforcement application on nerves (**c**) Finished. In the first phase, the state of charge results about original materials and elements (Table 1, Figure 10):  
In the second phase considered, the initial slab and the partition walls have been demolished, and, therefore, the load state will correspond to the sum of the own weights of arches, walls over arches, and vaults (Table 2, Figure 11).