Make a comparison study of the torsion of a conical shaft given in Example 9.7 with corresponding results from mechanics of materials. First develop the τ _θz shear stress relations for each theory, and then make a comparison plot of the maximum section shear stress (normalized by the torque, T) for the case with cone angle φ = 30^ᵒ over the range 4≤z≤10.

Data from example 9.7

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As an example of a variable section problem, consider the torsion of a conical shaft with cone angle o, as shown in Fig. 9.18. We again have selected a problem whose boundary shape will help generate the solution. On the lateral sides of the conical boundary, z/ +2= coso, which is a constant. Thus, any function of this ratio will satisfy the boundary condition (9.7.7). It can be shown