## 3 Seismic Response Spectra in Mexico
### Initial Inputs for the Elastic Design Spectrum According to MDOC Sismo CFE 2015  
For the seismic elastic design spectrum, it is required to know the importance of the structure, the reference spectrum ER in the rock layer, and the soil physical properties, which include the dynamic amplification factors due to the site effects. The first step would be defining the importance of the structure, assigning a group and/or subgroup according to Table 2, which depends on the occupancy of the building. Group A+ contains buildings of great importance that require a very high safety level in the presence of a strong earthquake, where the failure can be related to major environmental or economic disasters. Group A refers to structures of high importance that require a high safety level, and group B includes all other ordinary structures with moderate safety level. Buildings related to the energy sector are classified within groups A+ and A, while ordinary structures such as offices, houses, and industrial buildings are classified within group B. By selecting the group and/or subgroup according to the structure's importance, three variables can be defined: the structural importance factor, \(F_{IE}\), the seismic elastic design spectra procedure, and the soil dynamic properties data of the site. The structural importance factor, \(F_{IE}\), is applied directly to the spectrum by multiplying the acceleration values to ensure structural safety. The seismic elastic design spectra procedure can be classified into three types: constant acceleration spectra, regional spectra, and site-specific spectra. The soil dynamic properties of the site show the required data \begin{table}
\begin{tabular}{c c c c c} \hline
**Group** & **Description** & **Building Examples** & **Subgroup** & **Building Classification** \\ \hline A+ & Structures of great importance & Dams and nuclear plants & – & Energy or industrial sector of great importance \\  & & Electric power generators, bridges, water treatment & A1 & Belong to the energy or industrial sector \\  & & plants, and buildings & A2 & Do not belong to the energy or industrial sector \\  & & Industrial buildings, offices, houses, and other & B1 & Buildings with height \(H>13\) m or built area \(A>400\) m\({}^{2}\) \\ B & Structures with ordinary safety level & & offices, houses, and other common structures & Buildings with height \(H\leq 13\) m and Buildings with height \(H\leq 13\) m and \(H\leq 400\) m\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Importance of buildings and their requirements related to the elastic design spectrum, adapted with permission from [PERSON], Comision Federal de Electricidad Manual de Diseno de Obras Civiles; published by Comision Federal de Electricidad (CFE), 2015 [1]. \begin{table}
\begin{tabular}{c c c c c} \hline
**Zone** & \begin{tabular}{c} **Maximum Acceleration** \\ **in Rock**, \(a_{0r}\) (**cm/s\({}^{2}\)**)\({}^{1}\)** \\ \end{tabular} & \begin{tabular}{c} **Maximum Velocity** \\ **in Rock**, \(v_{r\_max}\) (**cm/s\({}^{2}\)**)\({}^{2}\)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum Displacement** \\ **in Rock**, \(d_{r\_max}\) (**cm\()\({}^{2}\)** \\ \end{tabular} &
\begin{tabular}{c} **Seismic** \\ **Intensity** \\ \end{tabular} \\ \hline A & \(a_{0r}\leq 50\) & \(4\leq v_{r\_max}<10\) & \(1\leq d_{r\_max}\leq 21\) & Low \\ B & \(50\leq a_{0r}<100\) & \(6\leq v_{r\_max}<18\) & \(6\leq d_{r\_max}<50\) & Moderate \\ C & \(100\leq a_{0r}<200\) & \(11\leq v_{r\_max}<27\) & \(6\leq d_{r\_max}<50\) & High \\ D & \(a_{0r}\geq 200\) & \(21\leq v_{r\_max}<62\) & \(35\leq d_{r\_max}<99\) & Very high \\ \hline \end{tabular}
\end{table} 
Table 1: Maximum acceleration, velocity, and displacement in the rock layer for each seismic zone, adapted with permission from [PERSON], Comision Federal de Electricidad Manual de Diseno de Obras Civiles; published by Comision Federal de Electricidad (CFE), 2015 [1]. from the soil layers to obtain different solutions, either numerically or mathematically.