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A Study of Warping of Non-circular Shafts in Torsion

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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

Statics & Strength of Materials - A nice couple

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Page Count


Page Numbers

23.115.1 - 23.115.7

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Paper Authors

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Somnath Chattopadhyay Georgia Southern University

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A Study of Warping of Non-circular Shafts in Torsion Somnath Chattopadhyay Georgia Southern University ABSTRACTThis project is geared towards the study of warping as it takes place for non-circular shafts undertorsional loading. This constitutes a laboratory unit in the course of Mechanics of Materialstaught at the junior level. The students are first introduced to the fact that the torsional stressesand deformations are simplest for the circular cross section, where the plane sections remainplane before and after the application of torque. The set-up used for the experiment for circularshaft was employed to study torsion in a square cross-section. Strain gages were mounted on thesurface of the shaft to estimate the strains and stresses at various locations. The square crosssection was then further studied using the membrane analogy in which a thin homogeneousmembrane using a soap film was stretched over a hole in a closed box. The hole wasgeometrically similar to the shaft cross section. The film was bowed by air pressure, and theelevations of the resulting surface were measured. The students had to show that; (a) the torquecarried by the shaft was proportional to twice the v volume enclosed between the membrane andthe plane of its base. The stresses obtained by the experiment were compared with some existingsolutions for square cross sections under torsion.

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