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2003•International Journal of Mechanical Engineering EducationRequires access

The Centre of Twist for a Prismatic Bar under Free Torsion

Shuguang Li

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Abstract

This paper presents a proof that the centre of twist for a prismatic bar under torsion coincides with the centroid of the cross-section. The centre of twist has long been regarded as arbitrary, since the consequence of a differently chosen centre of twist amounts only to a rigid-body rotation. However, what has not been properly addressed is that an arbitrarily chosen centre of twist results in an inconsistency in the formulation of conventional torsion theory.

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What this paper is about

This paper presents a proof that the centre of twist for a prismatic bar under torsion coincides with the centroid of the cross-section. The centre of twist has long been regarded as arbitrary, since the consequence of a differently chosen centre of twist amounts only to a rigid-body rotation. However, what has not been properly addressed is that an arbitrarily chosen centre of twist results in an inconsistency in the formulation of conventional torsion theory.

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Available abstract

This paper presents a proof that the centre of twist for a prismatic bar under torsion coincides with the centroid of the cross-section. The centre of twist has long been regarded as arbitrary, since the consequence of a differently chosen centre of twist amounts only to a rigid-body rotation. However, what has not been properly addressed is that an arbitrarily chosen centre of twist results in an inconsistency in the formulation of conventional torsion theory.

Key concepts: Twist, Torsion (gastropod), Centroid, Torsion constant, Geometry, Mathematics, Structural engineering, Physics

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