A [4]. A rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150-mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20%. The shaft transmits a torque to point A of T = 340Nm. The shaft is machined from steel with S = 420MPa and Sut = 560MPa. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 250-mm section of the shaft based on (a) a static yield analysis using the distortion energy theory and (b) a fatigue-failure analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress-concentration factors (see Table 7.1 in text or in lecture 20 notes). (3 marks) y B 250 mm F 100 mm 20 D Use ASME Elliptic for fatigue analysis. Assume a size factor k = 0.85 for initial estimates. Assume a reliability of 99% for shaft failure. Bonus Problem Refer to figure below (left) in which a torsionally oscillating shaft of 1.25 in diameter has a 0.25 inch diameter hole all the way through it. By the way the shaft is loaded, it is subjected to a completely reversed torsional moment of 8300 lbf-in, and completely reversed cyclic bending moment, in the plane of the through-hole axis of 3700 lbf-in. The shaft is made of 4340 steel with S = 120,000 psi, Sut = 150,000 psi, elongation (e) of 15% in 2 in, and the actual fatigue properties of the shaft as shown below (right). How many torsional oscillations would you expect could be completed before fatigue failure of the shaft takes place. Assume that the critical point for bending and torsion coincide. Use Goodman failure criterion. y in. 12 in. d=0.25 T Alternating stress amplitude, perc Ultimate tensile strength 140 120 100 80 60 40 20 0 0.1 1 10 102 103 104 105 106 10 Cycles to failure