# Study of Lead Rubber Bearings for Vibration Reduction in High-Tech Factories
## 4 Parametric Study Using LRBs in High-Tech Factories  
### Earthquake Effect  
The base shears in the \(X\) and \(Y\) directions of the factory with and without LRBs are shown in Figure 7, where the PGA of the applied seismic load is 0.32 g, and \(T_{s}\) is 0.7 and 1.4 s for two cases, respectively. The base shear is determined from the summation of the shear forces at the top of all the piles, and it represents the total seismic loads changing with time for the superstructure of the high-tech factory. To simplify the time-dependent base shears in the \(X\) and \(Y\) directions, we first find the magnitude (\(S(t)\)) of the two-direction base shears using the following equation:  
\[S(t)=\sqrt{{S_{x}(t)}^{2}+{S_{y}(t)}^{2}} \tag{5}\]  
where \(S_{x}(t)\) and \(S_{y}(t)\), as shown in Figure 7, are the time-dependent base shears in \(X\) and \(Y\) directions, respectively. Then, we obtain the maximum base shear (\(Smax\)) of all the time steps during the finite element analysis. Finally, we define the base shear ratio (\(R=Smax_{LRB}/Smax_{NO-LRB}\)) as the maximum base shear of the structure with LRBs (\(Smax_{LRB}\)) over that without LRBs (\(Smax_{NO-LRB}\))), and this ratio can be used to understand the efficiency of the LRB used to structures during earthquakes. Figure 8 shows this base shear ratio changing with PGA under \(T_{s}\) of 0.6 s, and Figure 9 shows that changing with \(T_{s}\) under the PGA of 0.32 g. These figures indicate the following features:  
(1) Figure 8 shows that when PGA increases, the base shear ratio increases slightly. However, for the worse case, the ratio for the PGA of 0.4 g is still small, which means that the LRB can effectively reduce the seismic load regardless of the magnitude of earthquakes. Figure 9 shows that when the dominant period of the earthquake increases, the base shear ratio increases to a noted extent. For long period seismic loads, such as near fault earthquakes, this situation can lead to LRB disadvantages.  
(2) Usually, the high-tech factory requires thick floor slabs, big long trusses, and dense RC columns to reduce ambient vibration, but this arrangement will largely increase the building mass that causes large seismic loads during earthquakes. The high-tech factory with LRBs can decrease over 50% of the seismic base shear under \(T_{s}\leq 1.0\), which means that the high-tech factory can resist larger earthquakes  
Figure 6: Artificial time-history seismic acceleration for T\({}_{s}\) = 0.6 and peak ground accelerations (PGAs) of 0.36, 0.252, and 0.108 g in the local X, Y, and Z directions.  
using LRBs for not very long periods of seismic loads. The comparison of base shears, shown in Figure 7a,b, between the factory with and without LRBs indicates the above conclusion, where the time-history base shears of the factory with LRBs are much smaller than those without LRB.  
(3) For the earthquake with a very long dominant period, such as 1.4 s, the LRB efficiency to reduce the factory base shear may decrease a little, since the natural period of the factory, due to the full yield of the LRB, can approach the earthquake with a long dominant period. However, earthquakes with this long dominant period often occur in significantly soft soil, and the design of LRBs for the high-tech factory may avoid this condition. Nevertheless, the simulation results indicate that the LRB efficiency for the earthquake with a long dominant period is still in the acceptable range, as shown in Figure 7c,d.  
Figure 8: The base shear ratio changing with PGA under \(T_{s}\) of 0.6 s.  
Figure 7: Comparison of base shears between the factory with and without LRBs under the seismic load of PGA = 0.32 g and \(T_{s}\) = 0.7 s and 0.14 s.