The torsion rod with variable cross$-$section

shown in Fig. $2\mathrm{.}1$ is clamped at A and

carries point torques at B $(4$ kN$.$m$),$ C $(8$

kN$.$m$)$ and D $($unknown value $7)$ with the

senses indicated in the figure. It is known

that the diameter of AB is $25$ mm$,$ the

diameter of BC is $50$ mm and the diameter

of CD is $20$ mm$.$ Furthermore, $6$LAB$=6$LBC

$=5$LCD $1200$ mm$.$ If the shear modulus of

the material is $80$ GPa, find:

a$)$ The value of T that would make the

angle of twist at point C with respect to A

equal to zero.

b$)$ The maximum value of T that can

applied with the sense shown such that

failure does not occur for an allowable

shear stress of $1\mathrm{.}1$ GPa. Can the condition

from part a be achieved without failure?