# Structural Identification of a Single-Story Building - Mass, Stiffness and Damping

Initial Publication Date: September 11, 2021

## Summary

Students will preform a set of two dynamics tests on a single-degree of freedom model. Using the acceleration time history response information collected from these tests students will be able to identify the model's mass, stiffness and damping coefficient. In practice, being able to determine the dynamics properties of an existing building or other structural system is critical in predicting the building's response to natural and man-made hazards and in identifying if damage occurred during an event.

To help with understanding the behavior of a single degree of freedom system, an app was developed in MATLAB. The app allows students to test out different mass, stiffness and damping scenarios and the effect that changing these variable values has on the behavior of the system modeled. The app also allows students to view the log decrement of the amplitude peaks of the motion. Students use the app to help prepare for the in-class lab and to also investigate the model they are testing during the lab.

## Learning Goals

Students will be able to determine the structural frame weight, W, in lb and the frame stiffness, k, in lb/in/m for the one-story frame model using the acceleration time histories collected experimentally from the model. Also, students will determine the structural damping ratio, Î¾, using the log decrement method discussed in class.

## Context for Use

This lab is run as part of a structural dynamics elective course for college juniors or seniors. The in-class lab will require about 20 minutes for setup and data collection per team. Teams of two or three students are used and three test models are available for use during class.
Students only need to know how to run an app in order to using the developed MATLAB program. No experience with MATLAB is required.
Changes can be made to the MATLAB app but these would require an understanding of the MATLAB GUI development environment and basic programming skills.

## Description and Teaching Materials

Students will preform two system identification dynamic tests on a single-degree of freedom model. Using the acceleration time history response information collected from these tests students will be able to identify the model's mass, stiffness and damping coefficient. In practice, being able to determine the dynamics properties of an existing building or other structural system is critical in predicting the building's response to natural and man-made hazards and in identifying if damage occurred during an event.

Video of Behavior of System identification Test (Quicktime Video 28.3MB Sep11 21)

MATLAB Files ( 120kB Sep11 21)

## Teaching Notes and Tips

For those interested in developing an app in MATLAB (or have used GUIDE to develop GUIs in the past):

https://www.mathworks.com/products/matlab/app-designer.html

https://www.mathworks.com/matlabcentral/fileexchange/66087-guide-to-app-designer-migration-tool-for-matlab

## Assessment

Students turn in a lab report on the system identification trials they conduct.
Two exam questions are given to students that focus on system identification and log decrement topics.