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Purpose
The purpose of this test problem on acceleration loading is outlined as follows:
Demonstrate acceleration-load application
Demonstrate absolute/relative acceleration, velocity, and displacement
Verify SAP2000 results with those obtained from the Acceleration to displacement record spreadsheet
Check the ALTADENA-1 acceleration record
Check one 10-cycle sinusoidal acceleration record
Overview
The attached SAP2000 file features a massless cantilever subjected to a vertical force which represents a concentrated mass located at its free end. A sinusoidal acceleration time history, defined as the SINE time-history load case, is applied to the system.
The absolute acceleration, velocity, and displacement of the restrained joint are plotted to 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 attached Excel file . This manual calculation follows formulation J.2 of Appendix J in Dr. Edward L. Wilson’s text Static and Dynamic Analysis of Structures.
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
SAP2000 V12.0.1 model (zipped SDB file)
Spreadsheet calculation (zipped Excel file)
Hand calculations (PDF)
Metadata
Name: Acceleration loading
Description: Guidelines for acceleration-load application in an arbitrary direction. Applicable to static, modal, and buckling load cases.
Program: SAP2000
Program Version: 14.2.3
Model ID: na
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TO DO: Correct the acceleration record |