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:

Shear stress in a circular shaft 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:

Shear flow in a thin walled shaft:

$q=\frac{T}{2A_m}$

Angle of twist in a thin walled shaft:

$\phi=\frac{TL}{2A_m^2G} \int_0^{L_m}\frac{1}{t}ds$

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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