Elasticity/Torsion of circular cylinders

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Torsion of Circular Cylinders[edit | edit source]

Torsion of a cylinder with a circular cross section

About the problem:[edit | edit source]

  • Circular Cylinder.
  • Centroidal axis thru the center of each cross section (c.s.)
  • Length , Outer radius .
  • Applied torque .
  • Angle of twist .

Assumptions:[edit | edit source]

  • 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 | edit source]

  • 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 | edit source]

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