Lecture #9

Reading: 5:1-3

 

Torsion of members having a circular cross section

 

Consider a bar with a circular cross section.  First, we make a grid on the member of lines along the length and around the circumference.  Now, we place a torsional moment on the member and watch how the grid deforms.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We note a couple of things from the deformation.  First, the vertical lines which represent a cross section in the two dimensional view remain vertical.  This means that the cross section remains planar.  In other words, a cross section rotates as a rigid disk.  Secondly, if we consider the shape of a single element of the grid, we see the deformation gives the shape that we saw earlier caused by shear stress.

 

 

 

 

 

 

 

 

 

 

 

 

Now, consider a slice of the torsion member.  We will consider the left side of the slice as being fixed and the right side as having a torque applied.

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