PSI - Issue 55

Isabel Turbay et al. / Procedia Structural Integrity 55 (2024) 168–176 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3. Results 3.1. Simplification of the set of variables through PCA. Table 2 shows the input data matrix that contains 18 variables and was explained by the combination of 13 variables located between the axes F1 and F2.

Table 2. Principal components analysis.

Final variables / Output, in other components

Initial variables / Input

Final variables / Output, main components

Number of variables

Number of variables

Variables on other axes

Number of variables

F1 and F2 axis variables

Variables

Cataloguing, Level of use, Fire resistance, Roofs, Installations, Land use, Inadequate occupation of public space, Traffic, Simplicity of the construction solution, Seismic vulnerability, Inappropriate interventions, Physical chemical characteristics, Texture, Foundation, Structure, Construction system, Maintenance and Urban Landscape

Axis F1 (33.1%): Fire resistance, Roofs, Physical-chemical characteristics, Texture, Foundation, Structure, Construction system and Urban landscape Axis F2 (20.8%): Level of use, Land use, Inadequate occupation of public space, Traffic and Seismic vulnerability

Other axes (46.1%) Cataloguing, Installations, Simplicity of the construction solution, Inappropriate interventions and Maintenance

18

13

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3.2. Evaluation of the correlation between factors that affect vulnerability indices. Fig. 1 shows the vectors in red of the 18 variables (factors that have been defined in the vulnerability indices) and the vectors in blue represent the supplementary variables or vulnerability indices (VI, VIp, VIe1, VIe2). • Factors with positive correlation. The variables that define the state of conservation of the building, the materials and conservation are observed with positive correlation. That is, the vectors of foundation, structure, coatings, physical-chemical characteristics, texture and maintenance are close, they have the same direction and closed angles, which means that they influence each other positively. The alteration of materials affects the conservation state of the building as well as problems in the structure deteriorate the materials. In these cases, the way to stop deterioration in materials and structure depends on maintenance. The variables land use and inadequate occupation of public space also have a positive correlation. In the case studies, churches located in commercial sectors (high land use rating) also have a high level of inadequate occupation of public space. The correlation between seismic vulnerability, the simplicity of the construction solution and the roofs is also notable; churches that have a high seismic vulnerability tend to also be those with a complex construction solution, especially in their roofs. A final correlation to evaluate is between inappropriate interventions and the urban landscape, which could be related to interventions at the urban level that affect the shape, heights or colour of buildings. • Factors with negative correlation. The cover factor is located opposite the fire resistance. The churches that are less vulnerable to fire resistance generally correspond to the churches with the highest roof ratings, that is, roofs with the worst performance characteristics for water evacuation. This is explained since churches with coffered ceilings are particularly simpler (gabled), but they would be the least resistant to fire due to the wood of their roof structures. Moreover, the variables fire resistance and simplicity of the constructive solution has vectors in an opposite way. In general, the churches with the lowest fire resistance rating (less vulnerable) are the highest rated in constructive simplicity. Constructive simplicity is qualified according to the criteria of Macías (2012). Fig. 1