A gear transmits 5000 lb-in of torque to a circular shaft having a diameter of 2.25 in. A...

A gear transmits 5000 lb-in of torque to a circular shaft having a diameter of 2.25 in. A square key 0.50 in on a side connects the shaft to the hub of the gear, as shown in Figure. The key is made from AISI 1020 cold drawn steel. Determine the required length of the key, L, to be safe for shear and bearing. Use a design factor of 2.0 based on yield for shear and the AISC allowable bearing stress.

Figure:

                                         FIGURE Key for Problem.