**Test Problem**

Name: | Acceleration loading |

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

Program: | SAP2000 |

Version: | 12.0.1 |

Model ID: | na |

**On this page:**

# 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)