8.51 Drawing 1 of Figure P8.51 shows a counter shaft with helical gear ( B), bevel gear ( D), and two supporting bearings (A and C ). Loads acting on

the bevel gear are shown. Forces on the helical gear can be determined from equilibrium of moments about the shaft axis plus the given proportions of the helical gear force components. Shaft dimensions are given in drawing 2. All shoulder fillets(at points where diameter changes) have a radius of 5 mm. Note that the shaft is designed so that only bearing A takes thrust. The shaft is made of hardened steel, Su = 1069 MPa , Sy = 896 MPa.All important surfaces are finished by grinding. (a) Draw load, shear force, and bending moment diagrams for the shaft in the xy and xz planes. Also draw diagrams showing the intensity of the axial force and torque along the length of the shaft. (b) At points B, C ,and E of the shaft, calculate the equivalent stresses in preparation for deter-mining the fatigue safety factor. (Note: Refer to Table 8.2.) (c) For a reliability of 99% (and assuming a standard deviation of OO = 0.08Sn ), estimate the safety factor of the shaft at points B, C ,and E.