10 Analytical and Experimental Analysis of Rocking Columns Subject to Seismic Excitation 81 10−3 10−2 0.005 0.01 0.05 0.1 0.25 0.5 0.75 0.9 0.95 0.99 0.995 Damping Coefficient Probability Fig. 10.9 Lognormal probability plot of the calculated damping ratios during the free rocking of the columns Time, (s) 5 5.5 6 6.5 7 7.5 8 8.5 −1 −0.5 0 0.5 1 Experimental Analytical Angular Dispalcement, (rad) Fig. 10.10 Comparison between the experimental and analytical results with an optimized coefficient of restitution 10.6 Conclusion The invention of motion tracking software has made the experimental verification of the analytical solutions of the rocking column possible. The speed and accuracy at which images can be processed has dramatically increased since Aslam et al. performed a few motion capture experiments using hand digitization. The data collected in this study confirmed the conclusions that the coefficient of restitution is not constant, is likely dependent on the angular velocity, and is significantly less than the theoretical derivation. The coefficient of restitution calculated for a steel column in this study is greater than that calculated by Aslam for their concrete blocks. The elastic properties of the two materials, and the geometry of the two columns, can account for the primary differences. Future research will continue to investigate the coefficient of restitution by further classifying the collected data by the relevant parameters at the start of the free rocking. More data will be collected to provide a larger statistical sample that can better accommodate the variation inherent to the experimental process. The analytical solution will be modified to account for the stochastic nature of the excitation phase. The modified analytical model, and its range of results, will be compared to all the collected data.
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