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Illustrating Rotating Principal Stresses in a Materials Science Course

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2013 ASEE Annual Conference & Exposition


Atlanta, Georgia

Publication Date

June 23, 2013

Start Date

June 23, 2013

End Date

June 26, 2013



Conference Session

Interactive Approaches to Teaching Materials Fundamentals

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Page Count


Page Numbers

23.678.1 - 23.678.12



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Paper Authors

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Somnath Chattopadhyay Georgia Southern University


Rungun Nathan Penn State Berks Orcid 16x16

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Dr. Rungun Nathan is an associate professor in the division of engineering at Penn State Berks. He got his B.S. from University of Mysore, DIISc from Indian Institute of Science, M.S. from Louisiana State University and Ph.D. from Drexel University. He has worked in the area of Electronic Packaging in C-DOT (India) and then as a Scientific Assistant in the Robotics laboratory at Indian Institute of Science, Bangalore, India. He worked as a post-doc at University of Pennsylvania in the area of Haptics and Virtual Reality. His research interests are in the areas of unmanned vehicles particularly flapping flight, mechatronics, robotics, MEMS, virtual reality and haptics, and teaching with technology. He has active research in the area of lift in Porous medium with Dr. Qianhong Wu (Villanova University). He is an active member of ASEE and ASME and reviewer for several ASME, IEEE and ASEE, FIE conferences and journals.

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Illustrating Rotating Principal Stresses in a Materials Science Course Somnath Chattopadhyay Georgia Southern University Rungun Nathan Pennsylvania State University ABSTRACTThis work constitutes a laboratory component with a junior level materials science course andillustrates the importance of rotating principal stresses in design of components such as theautomotive crankshaft. The activity is centered on Mohr’s circle for a biaxial stress situationsinvolving time varying normal and shear stresses. A number of dynamic situations have beenconsidered, namely, (a) sinusoidally varying normal and shear stresses that are in phase, (b)sinusoidally varying normal and shear stresses that are 90° out of phase, (c) constant normalstress and sinusoidally varying shear stress, and (d) sinusoidally varying normal stress andconstant shear stress. Employing a graphical approach, the diameter of Mohr’s circle (theabsolute difference between the two principal stresses) as well as the principal stress directions ismonitored. The students see that for certain stress situations the principal stress directionsremain unchanged while for others the principal stress directions keep changing with time(rotating principal stresses). In general, the size of Mohr’s circle changes with time. The plottingoption of the Matlab code has been employed to construct three-dimensional plots for theindicated stress situations with the normal and shear stresses respectively in the x and ydirections and the time in the z-direction. The plots show how the principal directions changewith time, along with the size of Mohr’s circle. The students are made aware of the fact thatrotating principal stresses play a very important role in designing components that are subjectedto biaxial or mutiaxial fatigue, such as the crankshaft. Also the diameter of Mohr’s circle can bedirectly related to the Tresca or von-Mises theory of failure.

Chattopadhyay, S., & Nathan, R. (2013, June), Illustrating Rotating Principal Stresses in a Materials Science Course Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19692

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