$($a$)$ A steel tube has an outer diameter and thickness of $150mm$ and $35mm$ respectively. The maximum allowable shearing stress is $95$MPa.

i$.$ Calculate the maximum torque, $T$ that can be applied to the tube

$[4$ Marks$]$

ii$.$ Calculate the shear stress at the inner surface of the steel tube

$[4$ Marks$]$

$($b$)$ A combined circular shaft is made of three segments AB$,$ BC and CD consist of hollow shaft for segment $AB$ and solid shaft for segment $BC$ and $CD.$ The shaft is made of aluminium, copper and steel for segment $AB,BC$ and $CD$ respectively. Segment $AB$ has diameter $20mm$ and thickness of $5mm.$ The assembly is subjected to torques of $355Nm$ at $A,150Nm$ at $B,$ and $250Nm$ at $C.$ Given that the modulus of rigidity of aluminum, copper, and steel are $27$GPa,$48$GPa, and $80$GPa respectively

i$.$ Draw the torque diagram of the shaft

$[5$ Marks$]$

ii$.$ Determine the maximum torsional shear stress

$[5$ Marks$]$

iii. Calculate the angle or twist at the free end

$[7$ Marks$]$

ASSIGNMENT

T$23$II$/$RAA$1143$