Problem $1(45$ pts$)$

A torque $T=100N*m$ is applied to the shaft EFG $,$ which is running at constant speed and contains gear $F.$ Gear $F$ transmits torque to shaft ABCD through gear $C,$ which drives the chain sprocket at $B,$ transmitting a force $P$ as shown. Sprocket $B,$ gear $C,$ and gear $F$ have pitch diameters of $a=150,b=250,$ and $c=125mm,$ respectively. The contact force between the gears is transmitted through the pressure angle $=20.$ Assume no frictional losses and considering the bearings at $A,D,E,$ and $G$ to be simple supports. The material is $1018$ CD steel.

a$)$ Determine bearing reactions $(5$ pts $)$

b$)$ Locate the point on shaft ABCD that contains the maximum tensile bending and maximum torsional shear stresses. $(5$ pts$)$

c$)$ Determine the bending and shear stresses at point $B.(5$ pts$)$

d$)$ Determine the maximum principal normal $(10$ pts$)$

e$)$ Determine the shear stresses in the shaft. $(10$ pts$)$

f$)$ Determine the minimum factor of safety for yielding using distortion$-$energy theory. $(10$ pts$)$

$y$

Fig. $1.$ Problem $1$