{{Test Problem

Purpose

...

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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

  displacements

  displacement

• verify

  Verify SAP2000 results

  against

  with those obtained from

  spreadsheet ("acceleration

  the Acceleration to displacement record

  " SAP2000 tool)check one actual acceleration record (

  spreadsheet

• Check the ALTADENA-1

  )

  acceleration record

• check

  Check one 10-cycle sinusoidal acceleration record

  with 10 cycles

...

Overview

The attached SAP2000 file contains features a massless cantilever with subjected to a vertical force applied at the top of the cantilever. This vertical force was considered as a source of mass. Time history function "SINE" with sinusoidal variation of the applied acceleration was defined and used in a time history load case.Plotting absolute accelerations, absolute velocities, or absolute displacements against time at a restrained joint enables you to obtain the applied (ground) acceleration and corresponding time history of velocities and displacementswhich 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 values records are plotted in the graph belowFigure 1:

Image ModifiedThe values in the above graph match values calculated "manually"

Figure 1 - Sinusoidal acceleration, velocity, and displacement plot

These plots match the values obtained through manual calculation, displayed in the attached Excel file (as per Prof. Wilson: Static & . This manual calculation follows formulation J.2 of Appendix J in Dr. Edward L. Wilson’s text Static and Dynamic Analysis of Structures, Appendix J, Equation J.2). Our test problem shows that the displacement is not zero .

This test problem yields non-zero displacement at the end of the time-history record and therefore the acceleration time history data would need to be corrected to have zero displacement at the end of the record.

Since the absolute displacement at an unrestrained joint is a sum of (1) input (ground) displacement, which is calculated from input acceleration, and (2) relative displacement calculated from the time history analysis, I would recommend making a correction to your input acceleration such the displacement is zero at the end of the record.

To Do

{{To Do

See Also

• List of acceleration test problems

Attachments

...

. 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

  sapfile -

  model

  A

  (zipped SDB file)

• File | filename = Acceleration test problem spreadsheet.zip | title = spreadsheet calculations

  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