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- In a response history analysis, the displacement-velocity-acceleration relationships are defined by the step-by-step integration method. The most common is the “constant average acceleration” method (also known as the “trapezoidal rule” or “Newmark beta=1/4 method). The relationships are not simply d(displ)/dt = veloc and d(veloc)/dt = accn. If you look at the velocities in the text file that you sent, you will see that the average values are OK, but they oscillate. This is probably because the text files are for a time step of 0.02 seconds, which is too long. I would expect the velocities to vary more smoothly for the shorter time step that you considered (0.001 sec). Was that the case?
- The calculated accelerations can be very sensitive, and may oscillate wildly.
- The amount of damping that you assumed may be much too large. You may have used the same Rayleigh damping properties that you would use for a dynamic earthquake analysis. If so, those properties will be based on the long period vibration modes for lateral motion. The periods for vertical vibration, when a column is suddenly removed, are much shorter, so those modes may be very heavily damped. If you use Rayleigh damping, the properties should be based on the dominant vertical periods of vibration with a removed column. What type of damping did you use, and how did you choose the damping parameters?
- Incidentally, 5% damping is probably too large, for earthquake analysis as well as progressive collapse. For a tall building, a more reasonable value for earthquake analysis is 2%. For progressive collapse I suggest no more than 1% (based on vertical vibration periods), or even zero.
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