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Measures may be taken to improve the accuracy of output acceleration generated during time-history analysis. This article provides guidelines for these measures, which involve damping, inertia, output time step, and possible Hilber-Hughes-Taylor alpha-method application. |
Measures should be taken to obtain accurate output acceleration from time-history analysis. Acceleration is the second derivative of displacement, and derivative values are less accurate than integrated quantities during numerical analysis.
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- Time steps. For either modal or direct-integration time-history analysis, sufficient output time steps are necessary for accurate representation of the periodic solution. A time increment of one-tenth of the shortest time period of interest should accurately capture response.
HHT alpha value. For direct-integration time-history analysis, it is often useful to set a non-zero Hilber-Hughes-Taylor (HHT) alpha value (0 ≤ alpha ≤ -1/3) to damp out response from periods shorter than can be captured by the output time step. As stated in the CSI Analysis Reference Manual (Time Integration Parameters, page 362), using alpha = 0 is most accurate, but may permit excessive vibrations in higher frequency modes. A value of alpha = -1/3 tends to remove noise from periods up to about 10 times the time step. Users are advised to experiment, starting with a slightly negative value of -1/24 or -1/48.
- Moving-load analysis. Bridge analysis and design may benefit from a step-by-step moving-load analysis. Automated step-by-step vehicle loading creates separate load patterns at discrete locations along the bridge, amplifying one load pattern while reducing the next. At any instant in time, either one pattern is fully applied, or else two patterns are interpolated. Otherwise, switching one pattern on, then suddenly off while switching the next pattern on, creates an impulse-type load (similar to that from hammer impact) which will excite higher frequencies and ruin acceleration response.
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