Q$\mathrm{.}3$: A transmission shaft supporting a spur gears B and the pulley D is shown in Figure. The

shaft is mounted on two bearings A and C $.$ The diameter of the pulley and the pitch circle

diameter of the gear are $450$ mm and $300$ mm respectively. The pulley transmits $20$ kW power

at $500$ rpm to the gear. P$\_(1)$ and P$\_(2)$ are belt tensions in the tight and loose sides, while P$\_($t$)$ and P$\_($r$)$

are tangential and radial components of gear tooth force. Assume, P$\_(1)=3$P$\_(2)$ and P$\_($r$)=$P$\_($t$)$tan$(20\backslash$deg $)$S$\_($ut$)=700$

and S$\_($yt$)=460($N$)/($m$)$m$^(2),$ Endurance limit S$\_($e$)=100$MPa