## 3 Seismic Structural Response
### Results for 6-Story Building  
For the 6-story steel-frame structure the most critical plastic hinges are located at Floors 5 and 6 as shown in Figure 1. The W12 \(\times\) 14 beams in this structure has a yielding flexure moment My = 60.7 kN-m and a yielding rotation \(\theta\)y = 0.0109 rad. For brevity, H and V are used to denote the horizontal and the vertical component, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**1**} & \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Magnitud**} & \multirow{2}{*}{**Rrup (km)**} & \multirow{2}{*}{**Lat.**} & \multirow{2}{*}{**Long.**} & \multirow{2}{*}{**H (km)**} & \multirow{2}{*}{**PGA\({}_{\text{h}}\) (g)**} & \multirow{2}{*}{**PGA\({}_{\text{v}}\) (g)**} \\  & & & **(YYYY/MM/DD)** & & & & & & & \\ \hline NILT & NS & 2017/09/07 & 8.2 & 100.6 & 14.76 & 94.11 & 58 & 0.498 & 0.449 \\ CALE & EW & 1997/01/11 & 7.1 & 25.15 & 17.91 & 103.91 & 40 & 0.404 & 0.422 \\ JAMI & EW & 1999/09/30 & 7.4 & 48.74 & 16.03 & 96.96 & 47 & 0.256 & 0.292 \\ SCRU & NS & 2017/09/07 & 8.2 & 91.65 & 14.76 & 94.11 & 58 & 0.253 & 0.299 \\ LANE & NS & 1999/09/30 & 7.4 & 22.56 & 16.03 & 96.96 & 47 & 0.244 & 0.213 \\ HMTT & EW & 2017/09/19 & 7.1 & 48.99 & 18.33 & 98.67 & 57 & 0.147 & 0.094 \\ RABO & NS & 2017/09/19 & 7.1 & 14.51 & 18.33 & 98.67 & 57 & 0.132 & 0.120 \\ \hline \hline \end{tabular}  
* \({}^{1}\) Stations designations are somewhat arbitrary acronyms of names in Spanish from different accelerometric arrays.  
\end{table} 
Table 1: Mexican ground motions used for the frames in Figure 1.  
When the 6-story building is subjected to the earthquake recorded at station NILT, the rotations and equivalent values (as function of the yielding rotation) from the non-linear dynamic analyses are 0.0293 rad (2.699y) for H and 0.0348 rad (3.209y) for H&V (i.e., horizontal and vertical component acting simultaneously). This represents an increase of 18.9% if the two components are used instead of only H (Figure 7, NILT-5S-RS). As an exceptional response for NILT recording, the rotations and equivalent values considering one or the two components for the non-linear dynamic analysis are 0.0351 rad and 3.220y (H) and 0.0342 rad and 3.150y (H&V), respectively. In this case the change is \(-2.1\%\) (i.e., the structural response actually decreased for this earthquake when both components were considered). This last result indicates that consideration of both components simultaneously can lead in some cases to less critical results (Figure 7, NILT-5S-LS). This could be explained because in some cases the vertical demand counteracts the horizontal one, for certain elements and under certain excitations, albeit this is not frequent. For the recording of station CALE, the most critical beam is on the left side of the 5 th floor. When only the horizontal seismic component is considered for the analysis, the maximum rotation value is 0.0268 rad, equivalent to 2.460y. On the other hand, when both, the horizontal and the vertical, seismic components are considered, the maximum rotation results in 0.0407 rad, equivalent to 3.730y. This means that the maximum rotation increased 51.6% with respect to that calculated when only the horizontal component is taken into account (Figure 7, CALE-5S-LS). For the earthquake recording of station JAMI, this time the most critical beam is situated on the left side of the 6 th floor (6 th story--6S-LS). For the horizontal response, the rotations remain linear with a value of 0.0102 rad, equivalent to 0.940y. On the other hand, when both components are considered simultaneously, the rotation is 0.0134 rad, which is equivalent to 1.230y. This represents a 30.8% rotation increase, as compared to the horizontal component analysis alone (Figure 7, JAMI-6S-RS). For the earthquake recorded at station SCRU (Figure 8, SCRU-6S-RS), the most critical beam is located on the right side of the 6 th level. In this case for the seismic horizontal component, 0.0100 rad and 0.920y were obtained.