Problem $4.$ The figure shows a shaft used for transmitting power between two pulleys. The diameters of the pulleys are $6$ inches and $12$ inches, respectively. The diameter of the shaft is $4$ inches.

a$)(2$ points$)$ inve sman puney is connectea to an external driver such as an engine, and the large pulley is connected to a load such as a lathe, then which way is the shaft turning, when viewed from D$?$ Explain your answer briefly.

b$)(5$ points$)$ At which location is the shaft experiencing the highest stress? Present detail analysis. Note: Compute the bending moments and torsional moments at the different sections and choose the section that experiences the largest combination of the two. You do not need to compute the stresses in this step.

c$)(4$ points$)$ Compute all the stresses applied to an element on the surface of the critical section and draw the element with those stresses shown.

d$)(4$ points$)$ For the critical element, draw the Mohr's circle and report the principal stresses and the maximum shear stress.