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A new twist on torsion: A connection between vector calculus and mechanics of materials.

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Title: A new twist on torsion: A connection between vector calculus and mechanics of materials.
Authors: Espinosa Maldonado, Alvaro A.1 (AUTHOR), Dolovich, Allan T.1 (AUTHOR) allan.dolovich@usask.ca
Source: International Journal of Mechanical Engineering Education. Jan2026, Vol. 54 Issue 1, p153-172. 20p.
Subjects: Torsion, Vector calculus, Torsional load, Mechanical behavior of materials, Engineering education, Strains & stresses (Mechanics)
Abstract: In engineering education, the topic of torsion is taught in both calculus and mechanics of materials, but using different definitions. Apparently, a clear connection between these two concepts is not currently found in the literature. In this paper, for the case of a homogeneous linear-elastic cylindrical shaft subjected to external torques, mathematical expressions are derived for relating torsional stress, strain and angle of twist to the torsion of a curve as taught in calculus. A physical connection is also presented, in that the curve torsion resulting from the deformation of a longitudinal line close to the shaft axis is shown to be approximately equal to the mechanical twist per length in the shaft. Although some researchers have hinted at this connection, to our knowledge the full precise connection has not been previously established. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A new twist on torsion: A connection between vector calculus and mechanics of materials.
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  Data: <searchLink fieldCode="AR" term="%22Espinosa+Maldonado%2C+Alvaro+A%2E%22">Espinosa Maldonado, Alvaro A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dolovich%2C+Allan+T%2E%22">Dolovich, Allan T.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> allan.dolovich@usask.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Mechanical+Engineering+Education%22">International Journal of Mechanical Engineering Education</searchLink>. Jan2026, Vol. 54 Issue 1, p153-172. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Torsion%22">Torsion</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+calculus%22">Vector calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Torsional+load%22">Torsional load</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+behavior+of+materials%22">Mechanical behavior of materials</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+education%22">Engineering education</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink>
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  Label: Abstract
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  Data: In engineering education, the topic of torsion is taught in both calculus and mechanics of materials, but using different definitions. Apparently, a clear connection between these two concepts is not currently found in the literature. In this paper, for the case of a homogeneous linear-elastic cylindrical shaft subjected to external torques, mathematical expressions are derived for relating torsional stress, strain and angle of twist to the torsion of a curve as taught in calculus. A physical connection is also presented, in that the curve torsion resulting from the deformation of a longitudinal line close to the shaft axis is shown to be approximately equal to the mechanical twist per length in the shaft. Although some researchers have hinted at this connection, to our knowledge the full precise connection has not been previously established. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Journal of Mechanical Engineering Education is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Jan2026
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