Introduction to Elasticity/Torsion of circular cylinders
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Torsion of Circular Cylinders [edit]
About the problem: [edit]
- Circular Cylinder.
- Centroidal axis thru the center of each cross section (c.s.)
- Length
, Outer radius
. - Applied torque
. - Angle of twist
.
Assumptions: [edit]
- 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.
Find: [edit]
- Shear strains in the cylinder (
). - Shear stress in the cylinder (
). - Relation between torque (
) and angle of twist (
). - Relation between torque (
) and shear stress (
).
Solution: [edit]
If
is small, then
Therefore,
If the material is linearly elastic,
Therefore,
The torque on each c.s. is given by
where
is the polar moment of inertia of the c.s.
Therefore,
and
, Outer radius
.
.
.
).






