Introduction to Elasticity/Torsion of rectangular sections

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Sample homework problem[edit | edit source]

Torsion of a bar with a rectangular cross section[edit | edit source]

Given:

A cylinder with a rectangular cross sections under torison.

A bar with a rectangular cross section

Show:

Why a function of the form

cannot be used as a Prandtl stress function for this cross section.

Solution[edit | edit source]

For compatibility, we need

However, for the given ,

which is not constant. Hence, the given function cannot be used as a Prandtl stress function.