The acceleration loads automatically calculated by the program are intended to apply ground acceleration. For example, translational acceleration loads are calculated as the negative translational joint mass at a joint times the input acceleration. CSI Analysis Reference Manual, chapter Load Patterns, section Acceleration Loads, has additional information on this.

To apply the acceleration load at the water level, you would need to convert the acceleration time history record to a displacement time history record. Once you have the displacement record, define a Load pattern in which you apply a unit value of joint displacements in the direction of acceleration at the affected joint. For this to affect the structure, you also need to restrain these joints in the direction of loading only. Then create a time history function that will describe a variation of these displacements in time. Finally, define a time history load case that will be specified using both the displacement and the time function.

FAQ

Converting acceleration time history records to displacement time history records

Would it be appropriate for this user to use equations J.2 (provided in Appendix J of the book Static & Dynamic Analysis of Structures by Prof. Wilson) to convert acceleration time history records to displacement time history records?

Yes, that equation can be used to generate displacement history from the ground acceleration history. However, it should be borne in mind that the double integration of ground acceleration records should produce zero displacements at the end of the record. If this does not happen then it may be necessary to apply a base line correction to the displacement record.

Is the base line correction the same procedure as the "Algorithm to Set Displacements at End of Records to Zero" summarized in Table J.1 of Prof. Wilson's book?

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When an acceleration record is specified for time-history analysis, the ground motion is automatically applied to all support restraints. CSI Software uses d’Alembert’s principle to then translate the time history into acceleration loads which are applied to structural joints. During formulation, since acceleration couples with mass, it is important that joints have mass. Acceleration loads are explained further in the CSI Analysis Reference Manual (Chapter XVII: Load Patterns, Acceleration Loads).

To manually input ground motion at specific supports, it is necessary to first convert the acceleration record into its corresponding displacement time-history record. During conversion, displacement is piecewise linear, velocity is piecewise constant, and acceleration is a series of impulse functions at each time step. Users should mind output accuracy by smoothing the displacement record. A smaller time step, possibly ¹/₁₀ that of the acceleration record, will refine the ground motion during conversion.

Experimental conversion

Two basic methods are available for conversion from Acceleration time history to displacement. First, an experimental approach is described as follows:

1. Create a simple SAP2000 model.
2. Apply the acceleration time history using the given time step (perhaps 0.02).
3. Set the output time step to ¹/₁₀ of this value (0.002).
4. Extract the displacement results from a support restraint.
5. Correct for zero initial and final displacement and velocity using a + bt.
6. Use this refined displacement function as the ground-motion input for the actual model.

Mathematical conversion

As an alternative, mathematical conversion is summarized in Appendix J of Dr. Edward L. Wilson’s text Static and Dynamic Analysis of Structures. The conversion is given in Figure 3, and its formulation is described as follows:

1. Ground acceleration is idealized as linear within each time increment, as shown in Figure 1:
   
   
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   Figure 1 - Ground acceleration record

   
   

2. Acceleration and velocity are integrated at each time step to generate expressions for velocity and displacement, as shown in Figure 2:
   
   
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   Figure 2 - Expressions for a, v, and d, derived through integration

   
   

3. These expressions are evaluated at t = ∆t to produce the set of recursive equations shown in Figure 3:
   
   
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   Figure 3 - Recursive equations characterizing ground motion

   An acceleration record is then translated into its corresponding displacement record using these expressions.

4. 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:
   
   
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   Figure 4 - Algorithm for zero displacement at record ends

   
   

5. 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.

See Also

• Ground motion at specific supports – Manual multi-support excitation

• Output accuracy – Time-history output-acceleration accuracy

References

• Wilson, E. L. (2004). Static and Dynamic Analysis of Structures (4th ed.). Berkeley, CA: Computers and Structures, Inc.
  Available for purchase on the CSI Products > Books page