Two solid steet thafts are joined by couplinges that are sorged integrailly with the shaft as shown. The diameter of the shaft and bolt circle are $d_B=5$ in$.$ and $D_{BC}=10ii{n}^2,$ the flange has a thickness $si{n}^2=\frac{5}{8}in$ nand there are eight $1-$ind.$-$diameter bolts. If the allowyble shear stress in the shat is $8000$ psio. $($a$)$ determine the full sorque capacity of the shafts based on shear stress. $($b$)$ What horsepower can the shafts transmit at $100$ rpm $($c$)$ What is the shear stress in the bolts? $($d$)$ Determine the bearing stress and maximum shear stress in the flanges.