## 2 Structural Assessment. Limit States Calculation Methods, Design Situation, and Loads  
The assessment of existing structures is intended to quantify their safety factor and, subsequently, determine whether conservation and reinforcement works are in order. Whatever structural analysis based on limit state calculation methods is conducted, there is a set of variables that must be considered, such as geometric data, material properties, and loads, among others [13]. Depending on whether the parameters are considered fixed values or random ones, two approaches for structural assessment can be distinguished: probabilistic and deterministic [14; 15; 16]. Most of the structural design codes are based on the second approach, where the limit state surface is the boundary between the safe and unsafe domains. It should be noted that addressing this problem strictly in terms of probability could be extremely complex [17] so that it is common practice to simplify the structural assessment by using partial factors. Therefore, the use of safety coefficients is a key indicator for the verification of the structural condition of the buildings analyzed in this research.  
Mainly two limit states are proposed on structural and geotechnical assessment [18]: Ultimate Limit State (ULS), related to those situations that compromise people's life, either caused by the partial or total collapse of the structure (e.g., loss of overall stability, bearing capacity, sliding or overturning failure); and Serviceability Limit State (SLS), related with user comfort or the appearance of the construction (e.g., excessive settlements, unacceptable vibrations). Basically, state limits aim at ensuring the safety, serviceability and durability of the construction. This paper mainly focuses on analysing ultimate limit states since the collapse of the structure could occur in these cases.  
Based on previous research [19], the comparative study between the formulations provided by different international codes allows to obtain an appropriate mathematical basis for the verification of built structures. According to its representativeness and validity, the following documents have been selected for a comparative study as a basis for the developed tool. Due to a recent update in 2019, Basic Document Structural Safety of the Spanish Technical Building Code (CTE DB SE, v2019) [20], the 2019 version of Basic Document Structural Safety Foundations of the Spanish Technical Building Code (CTE DB SE-C, v2019) [21] and the 2009 version of Earthquake Resistant Construction Standard: General Part and Building (NCSE-02) [22], the Spanish regulation documents have been selected as remarkable samples from a national structural design code [23]. On the other hand, the last published versions of Eurocode constitute highly representative documents at the international level. For this study, there will be considered the following ones: EN1991-1-4 Eurocode 1: Actions on Structures. Part 1-4: General Actions- Wind actions (EC1-4, v2010) [24], EN 1990-7-1 Eurocode 7: Geotechnical design--Part 1: General rules (EC7-1, v2005) [25] and EN 1998-8-5 November Eurocode 8: Design of structures for earthquake resistance--Part 5: Foundations, retaining structures, and geotechnical aspects (EC8-5, v2004) [26]. These documents set a long list of ultimate limit states, but only three of them are considered: overturning, sliding, and bearing failures. In simple terms, the first limit state is verification of static equilibrium (EQU Limit State) of the structure, which is considered as a rigid body, whereas the two others are verifications based on ground resistance (GEO Limit State). The main formulations for determining equilibrium states are discussed in the next sub-sections.