Q$5.$ A rigid flange coupling as shown in the adjacent Figure connects two solid circular shafts and needs to transmit a maximum torque of $3kN-m.$ Proportionate dimensions are as shown in the Figure. The flanges are keyed to the shafts by parallel sunk keys. The shaft, the bolts and the keys are made of $30$ C $8(Su=500$MPa;$Sy=400$MPa $)$ steel. Assume that the yield strength in compression is $1\mathrm{.}5$ times of that in tension. Determine the dimeter of the shaft, and the key dimensions $($in mm $)$ to ensure factor of safety of $2\mathrm{.}5$ for each component. You may use $=\frac{16}{d^2}[2+3]$