Question $2$

A clamp$-$type coupling with $4$ bolts is used to connect two shafts of $50$ mm diameter and allowable shear stress of $70$ MPa $.$ The two shafts are also connected via a square cast iron$($C$.$I.$)$ key with a width of $12\mathrm{.}5$ mm ; and the coefficient of friction between the muff and the shaft is $0\mathrm{.}3.$ The brass bolts used have an allowable tensile strength of $140$ MPa $.$ The ultimate shear and crushing stress for C$.$I. is $140$ MPa $.$ The shaft, key and muff are made from different materials.

a$)$ Calculate the maximum allowable torque on the shaft.

$(2)$

b$)$ If the induced shear stress in the muff$/$sleeve is $6\mathrm{.}3\frac{N}{m}{m}^2,$ calculate the outside diameter$($D$).$

$(4)$

c$)$ If the induced shear stress in the key is $62\mathrm{.}5\frac{N}{m}{m}^2,$ determine the length of the key in shear.

$(2)$

d$)$ If the induced crushing stress in the key is $125\mathrm{.}5\frac{N}{m}{m}^2,$ determine the length of the key in crushing.

$(2)$

$(1)$

e$)$ Calculate the length of muff$/$sleeve$.$

$(2)$

f$)$ Determine the core diameter of the bolt $(d_c).$

$(3)$

g$)$ Calculate the pressure using the projected area of the shaft.

$[16]$

$2$