Test Problem


Acceleration loading


Demonstrate acceleration loading and validate relative/absolute acceleration, velocity, and displacement.





Model ID:


On this page:


The purpose of this test problem on acceleration loading is outlined as follows:

  • Check the ALTADENA-1 acceleration record
  • Check one 10-cycle sinusoidal acceleration record


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.