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Exploring the Relationship between Dynamics and Stability

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Conference

2015 ASEE Annual Conference & Exposition

Location

Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015

ISBN

978-0-692-50180-1

ISSN

2153-5965

Conference Session

Civil Engineering Division Technical Session 9

Tagged Division

Civil Engineering

Tagged Topic

Diversity

Page Count

9

Page Numbers

26.739.1 - 26.739.9

DOI

10.18260/p.24076

Permanent URL

https://peer.asee.org/24076

Download Count

117

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Paper Authors

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William G. Rosenblatt California Polytechnic State University, San Luis Obispo

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William Rosenblatt is a Graduate Assistant for the Architectural Engineering Department at California Polytechnic University, San Luis Obispo. He currently conducts research in the field of building damage detection through forced-vibration testing. He will be graduating in December 2015 with the intent of entering the field of forensic engineering.

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Peter Laursen P.E. California Polytechnic State University

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Dr. Peter Laursen, P.E., is an Associate Professor of Architectural Engineering at the California Polytechnic State University, San Luis Obispo (Cal Poly) where he teaches courses on the analysis and design of structural systems including laboratory courses.

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Graham C. Archer P.Eng California Polytechnic State University

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Dr. Graham Archer, P.Eng., is a Professor of Architectural Engineering at the California Polytechnic State University, San Luis Obispo (Cal Poly) where he teaches courses on the analysis and design of structural systems.

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Cole C. McDaniel California Polytechnic State University

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Dr. Cole McDaniel, P.E., is a Professor of Architectural Engineering at the California Polytechnic State University, San Luis Obispo (Cal Poly) where he teaches courses on the analysis and design of structural systems with a focus on seismic behavior.

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Abstract

Exploring the Relationship between Dynamics and StabilityStructural engineering students have long struggled, both at the undergraduate and graduatelevel, with structural dynamics and stability. The two topics are generally taught separately butwith a similar approach: first using a differential equation formulation; and then, as the problemsbecome increasingly complex, using a matrix-based eigen-analysis approach. Given that manystudents struggle with advanced mathematics, it’s no wonder that student comprehension in bothtopics is often lacking.This paper describes the development, implementation, and assessment of a simple laboratoryexercise in which students explore the interconnectivity between structural dynamics andstructural stability. The objectives are to demonstrate: 1) the effect of end restraints on columnbuckling; 2) the effect of end restraints on the natural frequency of vibration of a column; and 3)most importantly the effect of axial load on vibration frequency i.e. as the buckling load isapproached, the natural frequency drops to zero. Mathematically, the similarity betweenbuckling and stability is evident in the differential equation and eigen-analysis approach.However in the students’ minds, these topics bear little to no resemblance; after all, they weretaught in different courses.The experimental setup is shown in the attached photograph. Four different end conditions (fix-fix, fix-pin, pin-pin, pin-guided) are incorporated. Standard accelerometers placed at mid heightare used to determine the natural frequency of vibration. The entire setup can be constructedwith minimal cost. While the laboratory setup can easily be incorporated separately in both adynamics course (to demonstrate the concept of modes of vibration) and a stability course (todemonstrate buckled shapes and loads), in the current use the setup is employed after thestudents have been introduced to both concepts. Prior to the activity, the students’ understandingand interest of beam vibration and column buckling was assessed through a quiz-for-grade andfound to be typical for senior undergraduates; i.e. weak.During the laboratory, it rapidly becomes clear that the students’ interest level rises. Withoutany prompting, the students immediately start to play with the test setup by pressing down on thecolumns by hand and observing the different buckling shapes associated with the end restraints.Separately, they monitor the accelerometer output and take some delight in seeing the effects ofplucking the column (like a guitar string) and observing the motion on the computer screen. It iswhen the column loading and the plucking action are combined in a more formal laboratoryexercise that the learning is solidified. Observing the drop off in frequency as the column isloaded leaves them with no doubt that the column flexural stiffness is affected by the presence ofaxial loads. Assessments taken after the exercise confirm the learning objectives were realized.Not only has the students’ interest in the buckling and stability been greatly enriched, theirability to apply the concepts and relate them together has demonstrably improved.Buckling of a Fixed-Fixed Column

Rosenblatt, W. G., & Laursen, P., & Archer, G. C., & McDaniel, C. C. (2015, June), Exploring the Relationship between Dynamics and Stability Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24076

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