Name:  Acceleration loading 
Description:  Demonstrate acceleration loading and validate relative/absolute acceleration, velocity, and displacement. 
Program: 
SAP2000

Version:  12.0.1 
Model ID:  na 
Purpose
The purpose of this test problem on acceleration loading is outlined as follows:
 Demonstrate accelerationload application
 Demonstrate absolute/relative acceleration, velocity, and displacement
 Verify SAP2000 results with those obtained from the Acceleration to displacement record spreadsheet
 Check the ALTADENA1 acceleration record
 Check one 10cycle 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 timehistory load case, is applied to the system.
The absolute acceleration, velocity, and displacement of the restrained joint are plotted to obtain the applied groundacceleration 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 nonzero displacement at the end of the timehistory 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)