Investigate the issue of finding the location of ( z ) max for the torsion problem.

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Investigate the issue of finding the location of (τ θz)max for the torsion problem. First verify the results given by (14.6.17) and (14.6.18). Next apply these general relations to the specific gradation models given by (14.6.13)1,2, and develop explicit results for locations of the extrema.

Equation 14.6.17

' (r) < _M (r) re (0, a) a

Equation 14.6.18

To (ro) '(ro)

Equation 14.6.13

M(r) = Ho(1+zr)" a (r) = Moe-r

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