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{live-template:Test Problem}

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*To Do*: correct the acceleration record (by ok)
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h2h1. 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

h2h1. 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.

h2h1. 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