$(35$ Points$)$ A shaft is fixed to the floor and carries the illustrated loading. Find the largest value of T to meet the following design requirements.

$({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_{\text{s}\text{t}\text{e}\text{e}\text{l}}=16$ksi,$G_{\text{s}\text{t}\text{e}\text{e}\text{l}}=12{10}^3$ksi

$({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_{al}=8$ksi,$G_{al}=4{10}^3$ksi

The angle of twist for the free end is not to exceed $3.$