## 3 Simulated Models
### Frame Structure in 2D
#### 3.2.5 Analysis of the Results  
Figure 26 shows the results obtained from the different prototypes with the displacement applied at node 14 and the corresponding horizontal load. The highest energy absorption in frame B versus frame C is also observed in this figure. It resisted a comparable maximum value, but without the same ductility. The similarity of the curves in the frame B and frame D figures was remarkable given that the moment-curvature behavior of prototype frame B was simulated only in the joints to save material. Meanwhile, the rest of the bar was simulated with the behavior of frame C, which allowed for greater curvatures and bigger displacements than if joints were not reinforced, but with considerable savings in material. The maximum moments coincide with the moments introduced from the moment-curvature graphs of each prototype. The simulated SRC frame achieved the greatest displacements, a bigger load capable of support, and was able to absorb the most energy. Therefore, it behaved better when faced with horizontal seismic loads, but showed no difference when we embedded the reinforcement of the steel cross-sections in only the joints, which is where the strength was greater and the plastification was concentrated. Figure 26: Graph of the load at Node 14 in relation to the displacement of the different frames. Figure 25: Horizontal movement (m) of the simulated frame structure from the moment-curvature graph of frame D.  
The numerical model was obtained and a force-displacement graph from the simulated model with the moment-rotation graph was given. Once the non-linear simulation was carried out, the resulting force and the displacement of the most representative point of the gantry were obtained and the graph was drawn. When processing the non-linear calculation from the moment-curvature graph, a final result was obtained, from which, it was possible to extract the force-displacement values according to Figure 26. The force-displacement curve related to node 14 can be seen. The decreasing load starting from the maximum force the column was capable of, and the hardening at high displacements due to the strength mechanism change, with columns in tension are noticeable. The results in the frame B and frame D graphs are the same. The bending capacity of the steel cross-sections gave the structure a very high deformation capacity by maintaining major points of resistance until collapse took place due to a great energy absorption capacity and high ductility. From the strengths (\(F\)) and displacement (\(D_{max}\)) of each 2D frame up until collapse, the energy absorbed by the structure can be calculated. The energy absorbed by the vertical force is calculated using Equation (3):  
\[\text{Absorbed Energy}\ =\ \int_{0}^{D_{max}}F(u)du. \tag{3}\]  
Table 3 summarizes the results obtained, from which we can conclude that the reinforced concrete (frame A) structures absorbed less energy than the steel-reinforced concrete structures (frame B). All the bars of the steel-reinforced concrete structures (frame B) coincided with the behavior of the model containing steel-reinforced concrete only at the joints of frame D. The latter was more advantageous as it offered the greatest absorption capacity of displacements and its respective strength, as well as an important saving in steel, which was achieved by using sections only at joints. In the reinforced concrete structures, it would be convenient to explicitly consider the possibility of including reinforcements of reinforced concrete joints with embedded steel cross-sections as a solution for creating very high ductility according to Eurocode 4 [22] as the current regulation for designing structures with mixed steel and concrete. Either a unidirectional or bi-directional reinforced concrete structure with flat beam slabs, which has a low ductility according to Eurocode 8 [23], can be improved by embedding steel cross-sections in the three spatial directions in all the structure's reinforced concrete joints to offer very high ductility.