(Solved): Problem. The shaft for a pulley system is to be designed to support a 1000lb. load. The pulley ...

Problem. The shaft for a pulley system is to be designed to support a $$1000?\mathrm{lb}$$. load. The pulley system configuration is illustrated below (shaft not shown). Dimensions shown are fixed. The pulley rides on $$1/2$$-in. diameter ball bearings. Therefore, the shaft must be stepped and grooved to accommodate for the bearings. The pulley is the lead into a cable spool; therefore, the shaft is mounted on lubricated sliding bearings enabling the shaft to slide side-to-side between the two supports. The greater travel allowed between supports for the pulley, the better the design since this provides more uniform cable spooling. Uistance between bearing centers, $$a_b=3$$ in. Diagram not to scale. Design a shaft for this application such that the stress concentration factors for all stress raisers are equivalent. Report Format. The report should consist of only the following Sections: 1. Force analysis. Draw the free body diagram for the system. Show all work for the solution to all reactions. Additional equations necessary for the solution must be obtained using Castigliano's method. The equations for the reactions should be highlighted and should be a function of the distance $$a$$ that the load applied to the pulley is from the left end of the beam. 2. Moments. Plot the moments at the supports and at the pulley/load as a function of the location of the pulley/load. Provide a single computer-generated figure that graphs these functions. For this step in the analysis, assume that the load can transverse the entire 36-inch span between the supports. 3. Maximum stresses at supports. From moments calculated in part 2 above, determine the maximum stresses experienced at the supports (in psi). 5. The maximum stresses near and on the pulley. Determine the maximum stresses (in psi) experienced near and on the pulley. Provide all numerical values used in the calculations for these stresses including stress concentration factors, where the stress concentration factors are selected from and the dimension ratios used in the design in part 4 above (e.g., $$D/d,r/d)$$.