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As an alternative, mathematical conversion is summarized in Appendix J of Dr. Edward L. Wilson’s text Wiki Markup
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- Ground acceleration is idealized as linear within each time increment, as shown in Figure 1:
- Acceleration and velocity are integrated at each time step to generate expressions for velocity and displacement, as shown in Figure 2:
- These expressions are evaluated at t = ∆t to produce the set of recursive equations shown in Figure 3:
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:
- 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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- Wilson, E. L. (2004). Static and Dynamic Analysis of Structures (4th ed.). Berkeley, CA: Computers and Structures, Inc.
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