Purpose

• illustrate how acceleration load is applied to the model
• illustrate absolute/relative acceleration, velocity and displacements
• verify SAP2000 results against those obtained from spreadsheet ("acceleration to displacement record" SAP2000 tool)
• check one actual acceleration record (ALTADENA-1)
• check one sinusoidal acceleration record with 10 cycles

Model Overview

The attached file contains a massless cantilever with a vertical force applied at the top of the cantilever. This vertical force was considered as a source of mass. Time history function "SINE" with sinusoidal variation of the applied acceleration was defined and used in a time history load case.

Plotting absolute accelerations, absolute velocities, or absolute displacements against time at a restrained joint enables you to obtain the applied (ground) acceleration and corresponding time history of velocities and displacements. For the test model, these values are plotted in the graph below:

The values in the above graph match values calculated "manually" in the attached Excel file (as per Prof. Wilson: Static & Dynamic Analysis of Structures, Appendix J, Equation J.2). Our test problem shows that the displacement is not zero at the end of the time history record and therefore the acceleration time history data would need to be corrected to have zero displacement at the end of the record.

Since the absolute displacement at an unrestrained joint is a sum of (1) input (ground) displacement, which is calculated from input acceleration, and (2) relative displacement calculated from the time history analysis, it is recommended to make a correction to your input acceleration such the displacement is zero at the end of the record.

Attachments

• Hand calculations (PDF format)
• SAP2000 V12.0.1 model A (zipped SDB file)
• Spreadsheet calculations (zipped Excel file)