Abstract
If a bar is loaded by equal and opposite torques T on its ends, we anticipate that the relative rigid-body displacement of initially plane sections will consist of rotation, leading to a twist per unit length \(\beta \). These sections may also deform out of plane, but this deformation must be the same for all values of z.
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Notes
- 1.
See for example J. R. Barber, Intermediate Mechanics of Materials, Springer, Dordrecht, 2nd. edn. (2011), Chapter 6, A. P. Boresi, R. J. Schmidt and O. M. Sidebottom, Advanced Mechanics of Materials, John Wiley, New York, 5th edn., 1993, Chapter 6, W. B. Bickford, Advanced Mechanics of Materials,, Addison Wesley, Menlo Park, 1998, Chapter 3.
- 2.
This solution is approximate because the stress function is not independent of \(\theta \) in the curved region. Otherwise there would be a discontinuity at the curved/straight transition.
- 3.
See §38.1.
- 4.
If you want to impress your unsuspecting colleagues with your engineering expertise (or your immense strength), ask them to guess the answer to this question and then perform the experiment.
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Barber, J.R. (2022). Torsion of a Prismatic Bar. In: Elasticity. Solid Mechanics and Its Applications, vol 172. Springer, Cham. https://doi.org/10.1007/978-3-031-15214-6_17
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DOI: https://doi.org/10.1007/978-3-031-15214-6_17
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