Example 1: Circular Cylinder
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Choose warping function
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Equilibrium ( ) is trivially satisfied.
The traction free BC is
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Integrating,
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where is a constant.
Hence, a circle satisfies traction-free BCs.
- There is no warping of cross sections for circular cylinders
The torsion constant is
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The twist per unit length is
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The non-zero stresses are
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The projected shear traction is
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Compare results from Mechanics of Materials solution
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and
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