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A Tool For Teaching Stress Transformation By Mohr's Circle

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1997 Annual Conference


Milwaukee, Wisconsin

Publication Date

June 15, 1997

Start Date

June 15, 1997

End Date

June 18, 1997



Page Count


Page Numbers

2.47.1 - 2.47.5



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Paper Authors

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Amer Mokaddem

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James Moller

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 3266


James Moller, Amer Mokaddem Miami University, Oxford, OH


The determination of transformed and principal stresses is frequently a significant conceptual hurdle for Mechanics of Materials students. Mohr’s circle is commonly introduced as a tool ostensibly to make the transformation concept easier to understand and apply. Yet learning the Mohr’s circle conventions frequently introduces an additional challenge. A computer program to assist the learning of stress transformation and Mohr’s circle is introduced. It displays diagrams of the state of stress and the corresponding Mohr’s circle as transformation angle is varied. Results of student testing indicate it is most effective at improving ability to anticipate the variation of stress magnitude as transformation angle varies and for identifying principal stresses on the circle.


The transformation of stress, strain, moment of inertia among coordinate systems is important in static and structural analysis. Late in the last century, Mohr 1, 2 introduced a graphical construction to assist in the process. At Mohr’s time, the technology for graphical construction was drafting and any technology for computation was quite tedious compared with modern tools. His graphical approach to constructing his circle could be used to find approximate values for transformed stresses and thereby save what, at the time, would have been great computational effort. Indeed, as recently as 1972, the construction of Mohr’s circle was couched in drafting terminology 3.

Mohr’s circle is among the most difficult topics for students to comprehend, according to surveys of them and examination of their test results. Students in the Manufacturing Engineering department’s Strength of Materials course were surveyed at the end of both the Fall 1995 and Spring 1996 semesters. Among the questions posed to them was their level of confidence with each of the principal topics covered. In both semesters, stress transformation and Mohr’s circle ranked among the lowest. This was in spite of having spent two lectures on them each semester.

Based on student questions and comparison with the other topics covered in the course, there are several distinguishing features of the stress transformation concepts which make it more challenging to learn. First, the relation among the load on a member and the state of stress at a point for a single coordinate system takes some students the entire semester to master. Second, the parametric relation and stress axes become confused with the spatial coordinate axes. Third,

Mokaddem, A., & Moller, J. (1997, June), A Tool For Teaching Stress Transformation By Mohr's Circle Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6838

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