Lecture #12

Reading: 5:6-7

 

Torsion of Noncircular Cross Sections

 

When the cross section was circular, we noted that cross sections remained planar after a torque was applied.  This does not happen when the cross section is noncircular.  The cross section will warp out of plane.

 

For solid noncircular cross sections, the theory is beyond the scope of this course.  The textbook presents some equations for 3 common solid cross sections.  See the table in the textbook for these equations.  Although the theory is beyond this course, there is no reason why we cannot use the results of that theory to solve problems.

 

Another type of noncircular cross section which we can analyze is the thin walled tube.  Although the wall must be thin (generally an order of magnitude smaller than the major in-plane dimensions), the thickness of the wall does not have to be constant.

 

 

 

 

 

 

 

 

 

 

Since the wall is thin, we will assume that the shear stress is constant through the thickness and tangent to the wall centerline.  Consider a piece of the tube wall

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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