Torsion: Summary and Further Reading
Course subject(s)
3. Torsion
Summary of Key Equations
In this unit, we developed the following equations for stress and deformation of circular shafts subjected to torsion:
\[\tau=\frac{Tr}{J} \]
Angle of twist of a uniform circular shaft\[\theta=\frac{TL}{GJ} \]
Differential angle of twist in a general circular shaft\[d\theta=\frac{T(x)dx}{G(x)J(x)} \]
For thin walled shafts, we developed:
\[ q=\frac{T}{2A_m}\]
Angle of twist in a thin walled shaft:\[ \phi=\frac{TL}{2A_m^2G} \int_0^{L_m}\frac{1}{t}ds\]
Further Reading and Problems
3.1. Torsion of Circular Shafts
Supplementary textbook reading: Ch. 5.1-5.2, 5.4
Practice problems: 5.2, 5.5, 5.11, 5.19, 5.53, 5.70, 5.73
3.2 Statically Indeterminate Torsion Problems
Supplementary textbook reading: Ch. 5.5
Practice problems: 5.81, 5.87, 5.94
3.3 Torsion of non-Circular and Thin-Walled shafts
Supplementary textbook reading: Ch. 5.6 – 5.7
Practice problems: 5.109, 5.111, 5.114, 5.116
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