(Solved): In the gear box shown below, shaft \( A B \) drives shaft \( E F \) via \( C D \). In this system, ...

In the gear box shown below, shaft \( A B \) drives shaft \( E F \) via \( C D \). In this system, two pairs of gears are in mesh for torque transmission. Shaft \( A B \) receives input power of \( 5 \mathrm{~kW} \) from an electrical motor at \( 1000 \mathrm{rev} / \mathrm{min} \). As a result of gear mesh, interaction forces \( \mathbf{P}_{1} \) and \( \mathbf{P}_{2} \) occur. Assuming no frictional losses and considering the bearings at \( \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E} \) and \( \mathrm{F} \) to be simple supports, determine \( a \) location of the highest shear and normal stresses on shaft \( C D \). \( [15] \)