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{live-template:Test Problem}

h2. Purpose

* Demonstrate [acceleration-load|kb:Acceleration load] application
* Demonstrate [absolute/relative|kb:Acceleration FAQ#Difference between relative and absolute acceleration] acceleration, velocity, and displacement
* Verify SAP2000 results with those obtained from 'Acceleration to displacement record' spreadsheet
* Check ALTADENA-1 acceleration record
* Check one 10-cycle sinusoidal acceleration record

h2. Model Overview

This test problem is based on the attached [SAP2000|sap2000:home] file. This file features a massless cantilever subjected to a vertical force which represents a mass source at its end. The acceleration [time history|kb:Time-history analysis] applied to this system is of sinusoidal variation. It is therefore defined as the 'SINE' time-history [load case|kb:Load case].

By plotting absolute acceleration, absolute velocity, and absolute displacement at a restrained joint, users may 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:

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!Acceleration_plot_functions.png|align=center,border=1!

{center-text}Figure 1 - Sinusoidal acceleration, velocity, and displacement plot{center-text}

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These plots match the values obtained through manual calculation, displayed in the Excel file attached. This manual calculation follows formulation J.2 of Appendix J in Dr. Edward L. Wilson’s text _Static and Dynamic Analysis of Structures_.

Further, 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.

h1h2. Attachments

* [Hand calculations|Acceleration loading^Hand calcs.pdf] in PDF format
* [SAP2000 V12.0.1 model|Acceleration loading^SAP2000 V12.0.1 model A.zip] in zipped SDB file
* [Spreadsheet calculation|Acceleration loading^Spreadsheet calcs.zip] in zipped Excel file

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h1. Previous page content:

h1. Purpose

* illustrate how acceleration load is applied to the model
* illustrate absolute/relative acceleration, velocity and displacements
* verify SAP2000 results against those obtained from spreadsheet ("acceleration to displacement record" SAP2000 tool)
* check one actual acceleration record (ALTADENA-1)
* check one sinusoidal acceleration record with 10 cycles

h1. Model Overview

The attached file contains a massless cantilever with 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 displacements. For the test model, these values are plotted in the graph below:

!Acceleration_plot_functions.png!

The values in the above graph match values calculated "manually" in the attached Excel file (as per Prof. Wilson: Static & Dynamic Analysis of Structures, Appendix J, Equation J.2). Our test problem shows that the displacement is not zero 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, it is recommended to make a correction to your input acceleration such the displacement is zero at the end of the record.

h1. Attachments

* [Hand calculations|Acceleration loading^Hand calcs.pdf] (PDF format)
* [SAP2000 V12.0.1 model A|Acceleration loading^SAP2000 V12.0.1 model A.zip] (zipped SDB file)
* [Spreadsheet calculations|Acceleration loading^Spreadsheet calcs.zip] (zipped Excel file)

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*To Do*: correct the acceleration record (by ok)
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