Introduction to Elasticity/Torsion of circular cylinders
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[edit] Torsion of Circular Cylinders
[edit] About the problem:
- Circular Cylinder.
- Centroidal axis thru the center of each cross section (c.s.)
- Length L, Outer radius c.
- Applied torque T.
- Angle of twist φ.
[edit] Assumptions:
- Each c.s. remains plane and undistorted.
- Each c.s. rotates through the same angle.
- No warping or change in shape.
- Amount of displacement of each c.s. is proportional to distance from end.
[edit] Find:
- Shear strains in the cylinder (γ).
- Shear stress in the cylinder (τ).
- Relation between torque (T) and angle of twist (φ).
- Relation between torque (T) and shear stress (τ).
[edit] Solution:
If γ is small, then
Therefore,
If the deformation is elastic,
Therefore,
The torque on each c.s. is given by
where J is the polar moment of inertia of the c.s.
Therefore,
and







