Purpose
- Demonstrate [acceleration-load] application
- Demonstrate absolute/relative acceleration, velocity, and displacement
- Verify SAP2000 results with those obtained from 'Acceleration to displacement record' spreadsheet
- Check ALTADENA-1 acceleration record
- Check one 10-cycle sinusoidal acceleration record
Model Overview
This test problem is based on the attached SAP2000 file. This file features a massless cantilever subjected to a vertical force which represents a mass source at its end. The acceleration time history applied to this system is of sinusoidal variation. It is therefore defined as the 'SINE' time-history load case.
By plotting absolute acceleration, absolute velocity, and absolute displacement at a restrained joint, users may obtain the applied ground-acceleration time history, along with its corresponding velocity and displacement records. For the test model given, these records are plotted in Figure 1:
Figure 1 - Sinusoidal acceleration, velocity, and displacement plot
These plots match the values obtained through manual calculation, displayed in the Excel file attached. This manual calculation follows formulation J.2 of Appendix J in Dr. Edward L. Wilson’s text Static and Dynamic Analysis of Structures.
Further, this test problem yields non-zero displacement at the end of the time-history record. Correction using the base line correction algorithm is therefore necessary to establish zero absolute displacement at the unrestrained joint upon conclusion of the record.
Attachments
- Hand calculations in PDF format
- SAP2000 V12.0.1 model in zipped SDB file
- Spreadsheet calculation in zipped Excel file
