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Data Analysis Application Brief

Seismic Analysis

The Solution

Because PG&E's 34-story building was not equipped with an accelerograph back in 1989, Tsai used more recent accelerograms and those from nearby buildings to reconstruct his own accelerogram in DADiSP for the Loma Prieta earthquake. Earthquake Accelerogram

Seismic Transfer Function

The accelerograms recorded during a small earthquake for the 34th floor and the adjacent building's basement are shown in Windows 1 and 3 respectively, showing peak accelerations (PAs) of 0.008g in W1 and 0.025g in W3. A g is a unit of force equal to the gravity exerted on a body at rest. In Windows 2 and 4, the FFTs of these accelerograms are displayed and Window 5 shows the ratio of these two FFTs. This ratio represents the seismic transfer function for the high-rise building. The amplitude function of the FFT ratio in W5 was calculated and displayed in Window 6, showing the first three vibrational modes of the high-rise at 0.27 Hz, 0.78 Hz, and 1.39 Hz. Earthquake Accelerogram

Reconstructing Accelerograms

The third accelerogram (from the basement of the adjacent two-story building during the Loma Prieta earthquake) is displayed in Window 7, showing a PA of 0.13g. The FFT of this accelerogram was then calculated and displayed in Window 8. The product of the seismic transfer function (Window 5) and the FFT (Window 8) was calculated and displayed in Window 9. The inverse FFT of this product is shown in Window 10. The real part of W10 was taken as the accelerogram for the 34th floor of the high-rise during the Loma Prieta earthquake and displayed in Window 11, showing a peak acceleration of 0.20g.

Peak Velocity Calculations

Further calculations were done on the accelerograms in Windows 7 and 11 to obtain the peak velocities (PVs) and peak displacements (PDs) for Earthquake Accelerogram the 34-story building and the adjacent building's basement during the Loma Prieta earthquake. The first 29 seconds of the accelerograms in W7 and W11 were extracted and displayed in Windows 15 and 12. The data in W15 and W12 was integrated to obtain the PVs ( W16 and W13).

Differential Displacement

The PV for the 34th floor of the high-rise was 21.5 cm/s during the Loma Prieta earthquake, while the basement of the adjacent building had a PV of 21.3 cm/s. A second integration was performed on Windows 16 and 13 and displayed in W17 and W14 to obtain the PDs of these two buildings during the earthquake. The basement of the adjacent building had a PD of 5.7 cm while the 34th floor had a PD of 6.2 cm. Finally the differential displacement waveform at the 34th floor relative to the basement level of the building was calculated and displayed in Window 18. The waveform in W18 shows a PD of 6.8 cm.

A Handy Tool

In using DADiSP to recreate the high-rise office building's accelerogram, Yi-Ben Tsai was able to calculate the in-structure data for the 34-story office building. According to Tsai, "I have found DADiSP to be a handy tool for interactive analysis of earthquake strong-motion accelerograms to study the ground or structural response under seismic excitation."

The Problem