The machined shaft shown in figure supports two gears $($A & C$).$ Gear A receives power from another gear with the transmitted force $P_A=2500N$ applied at the $20$ pressure angle as shown. The power is transmitted through the shaft and delivered through gear $C$ through a transmitted force $P_C$ at the pressure angle $20$ shown. The yield strength for the shaft, which is made of cold$-$drawn steel, is $490$MPa and the ultimate strength is $580$MPa. The shaft is solid and of constant diameter. The safety factor is $3\mathrm{.}0.$ Assume the DET throughout. Also, for fatigue loading conditions assume completely reversed bending with a bending moment amplitude equal to that used for static conditions. The alternating torque is zero. Let $K_f=2\mathrm{.}0$ and $K_{fs}=1\mathrm{.}75.$

$****$ Tables$/$Charts can be found in the class activities or class lectures ${?}^{********}$

Perform the following:

What is the transmitted load $P_c$ on gear $C?$

Draw the FBD of the forces acting on the shaft.

Use MDSolids to draw the shear force and bending moment diagrams for the forces acting in $x-y$ plane and $x-z$ plane. Include screenshots from MDSolids to show your work.

Find the maximum bending moment at the critical location in the shaft.

Use the DET to determine the safe shaft diameter due to static loading, rounding your answer to the next highest convenient dimension.

Use the DE$-$ASME Elliptic fatigue criterion to determine the shaft diameter, rounding your answer to the next highest convenient dimension $($Note: Ignore all endurance limit modification factors except the surface finish factor$).$

One of the gears has been attached with a keyway, the other with a shrink fit. Which gear was attached with a keyway, and why?