# Effectiveness of LRB in Curved Bridge Isolation:
## 7 Bi-Directional Loading Effects  
Figure 14 shows the peak response of the isolated bridge for various ground motions. The effect of bi-directional ground motion was found to be significant for the considered earthquake motions. The various cases are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cases Considered** & \multicolumn{2}{c}{**Isolated Bridge**} \\  & **Isolation Period (sec)** & **Damping Ratio (\%)** \\ \hline Case 1 & 1.5 & 10 \\ Case 2 & 1.5 & 15 \\ Case 3 & 1.5 & 20 \\ Case 4 & 1.5 & 25 \\ Case 5 & 2.0 & 10 \\ Case 6 & 2.0 & 15 \\ Case 7 & 2.0 & 20 \\ Case 8 & 2.0 & 25 \\ Case 9 & 2.5 & 10 \\ Case 10 & 2.5 & 15 \\ Case 11 & 2.5 & 20 \\ Case 12 & 2.5 & 25 \\ Case 13 & 3.0 & 10 \\ Case 14 & 3.0 & 15 \\ Case 15 & 3.0 & 20 \\ Case 16 & 3.0 & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Different cases considered for the Isolated Bridge.  
The maximum effect of bi-directional motion was found for the Turkey earthquake. Therefore, the amplification of responses, to a significant extent, can be explained due to the Forward Directivity effect, which should be given prime importance in the seismic design of isolated bridge structures.  
Compared to uni-directional Turkey ground motion, the deck acceleration, the force transmitted to the pier, pier torsional moment, and deck displacement increased by about 98%, 95%, 90%, and 102%, respectively, for the bi-directional ground motion.  
The increase in maximum responses due to bi-directional ground motion is less for the Kobe earthquake, which is about 10%, 17%, 14%, and 15%, respectively, corresponding to deck acceleration, the force transmitted to the pier, pier torsional moment, and deck displacement. However, as compared to a uni-directional motion, the same responses are enhanced by 16%, 53%, 29%, and 54% for bi-directional Imperial Valley earthquakes.  
Figure 15 represents the envelope (corresponding to a 2.5 s time period and 20% damping ratio) of bearing displacement and force transmitted to the pier for Imperial Valley, Kobe, and Turkey earthquake motions. It was noticed that the bi-directional response envelope (red line) surpassed the uni-directional envelope (black line) by a substantial amount. A similar response was observed by [PERSON] et al. [49; 50; 51]. This fact is very important for the design of isolated bridge structures as, in the traditional manner only the principal horizontal direction was considered. However, for actual consideration, the design should have been  
Figure 14: The isolated curved bridge response parameters (**a**) Deck Acceleration, (**b**) Force transmitted to Pier, (**c**) Pier Torsional Moment, (**d**) Deck Displacement for Uni-directional (Uni) and Bi-directional (Bi) Imperial Valley (IV), Kobe (Ko) and Turkey (Tur) Ground Motions.  
governed by the response contribution considering bi-directional loading. In Figure 15, the blue line represents the time history response due to bi-directional loading. As the red line has exceeded both the blue and black lines, the dominance of the response of the bridge structure to the bi-directional motion has been well established.  
Figure 15: Response envelopes of the isolated bridge for Imperial Valley (**a,b**), Kobe (**c,d**), and Turkey (**e,f**) ground motions.