For the solution of the conical shaft given in Example 9.7, compare the maximum shearing stress τ_θz with the corresponding result from strength of materials theory. Specifically, consider the case with a cone angle φ = 20^ᵒ with z = l, and compare dimensionless values of τ_θzl³/T.

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