## 2 Materials and Methods
### Structural Design
Its design is based on fulfilling the requirements presented in Section 18.6: of the ACI 318-14 code \"Beams of special moment frames\" (the sections' dimensions were carried out). The required bending reinforcement was determined using the factored moments, mined using the factored moments, and the required anchoring length of the bending reinforcement in the outer column was calculated. It is also mentioned and verified that the transverse reinforcement is placed in a length 2 times the height of the beam to resist the shear, assuming that the shear resistance of the concrete is zero and that the shear resistance of the steel multiplied by a factor of 0.75 is greater than or equal to the design shear, calculated considering the maximum forces generated on the faces of the nodes using the probable flexural strength \(\big{(}M_{pr}\big{)}\), as shown below (Equation (1)):  
\[M_{pr}=A_{s}\big{(}1.25f_{y}\big{)}(d-\
icefrac{{a}}{{2}}) \tag{1}\]  
\(A_{s}=\) area of nonprestressed longitudinal tension reinforcement. \(f_{y}=\) specified yield strength for nonprestressed reinforcement. Figure 4: Structural analysis in SAP2000: (**a**) moment-resistant frame with reinforced concrete elements, (**b**) moment diagram obtained with load combinations. Figure 3: Maximum moments in beams: (**a**) option 1, (**b**) option 2. \(d\) = distance from extreme compression fiber to centroid of longitudinal tension reinforcement. \(a\) = depth of equivalent rectangular stress block. The pre-dimensioning of columns was carried out considering the most critical one, which has the largest area of influence (30 \(\times\) 30 cm for option 1 and 25 \(\times\) 25 cm for option 2), considering what is detailed in the NEC-SE-CG code: Loads (Non-Seismic) code [20] for the reduction of live load. The axial loads were obtained from the structural analysis in SAP2000; the required cross-sectional area to support the load was calculated with this value. Its design was based on fulfilling the requirements presented in Section 18.7: \"Columns of special moment frames\" of the ACI 318-14 code [18]. From the structural analysis, the axial force and design moment for the critical column of the two-story houses were obtained. Initially, a review of the dimensions of the sections was carried out, also considering the provisions of the NEC-SE-VIVIENDA code [21]. Assuming a longitudinal reinforcement of 4 bars of 18 mm for the column of the first option, and 4 bars of 14 mm for the second option (ensuring a permitted amount), the interaction diagrams (Figure 5) were generated where it was verified that the assumed longitudinal reinforcement would be able to withstand the axial force and design moment (Table 3). According to the strong column-weak beam criterion, the bending resistance of the columns must comply with the following (Equation (2)): the sum of the nominal bending moments of the columns reaching the node \((M_{nc})\) must be greater than or equal to 6/5 of the sum of the nominal bending resistant moments of the beams reaching the node \((M_{nb})\), through a compatibility analysis. \[\sum M_{nc}\geq(\sfrac{6}{5})\sum M_{nb} \tag{2}\]  
The length for which the reinforcement should be supplied for confinement and its maximum spacing, considering 12-mm stirrups, was determined. Finally, the equation that detailed that the sum of shear strength of concrete and steel multiplied by a reduction factor of 0.75 must be greater than the maximum probable shear resistance is satisfied for both designs. Figure 5: Interaction diagram: (**a**) option 1, (**b**) option 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Data** & **Option 1** & **Option 2** \\ \hline Axial Force – P\({}_{u}\) (Ton) & 11.66 & 13.23 \\ Moment – M\({}_{u}\) (Ton-m) & 2.33 & 1.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Axial force and design moment for columns. For the design of the foundations, an isolated square plinth was considered for 3 critical columns, located in the center, edge, and corner.