(Solved): A constant-magnitude transverse load P= 1000 lb is applied as the shaft rotates subject to a time-va ...

A constant-magnitude transverse load P= 1000 lb is applied as the shaft rotates subject to a time-varying torque that varies from Tmin = 0 lb-in to Tmax = 2000 lb-in. Assume the following data: a = 16 in , b = 18 in , l = 20 in . Assume a shaft diameter of 1.75 in. The shaft is steel of Sut= 108 kpsi and Sy= 62 kpsi. The key is steel of Sut= 88 kpsi and Sy = 52 kpsi. The surface is machined, reliability is 90%, the shaft operates at a room temperature.

Determine the width and the length of the square key necessary to give a safety factor of at least 2 against both shear and bearing failure for the design shown in figure: