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Ground acceleration is idealized as linear within each time increment, as shown in Figure 1:
Figure 1 - Ground acceleration record
Acceleration and velocity are integrated at each time step to generate expressions for velocity and displacement, as shown in Figure 2:
Figure 2 - Expressions for a, v, and d, derived through integration
These expressions are evaluated at t = ∆t to produce the set of recursive equations shown in Figure 3:
Figure 3 - Recursive equations characterizing ground motion
An acceleration record is then translated into its corresponding displacement record using these expressions.
This double-integration procedure should produce zero displacement at either end of the displacement record. However, if nonzero displacement does exist, a base-line correction must be applied according to Figure 4:
Figure 4 - Algorithm for zero displacement at record ends
- Displacement ground motion is then input at specific support locations using the option for Ground Displacement Load. This process is described in the Multi-support excitation article.
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