A grade 5, 1-in. UNF bolt has rolled threads and is used to clamp two rigid members together so that kc = 4kb . In keeping with the fatigue treatment of ductile members given in Chapter 8, assume that the material has an idealized stress–strain curve, with a "square corner" at the yield strength (not the proof strength). There is a force tending to separate the members that fluctuates rapidly between 0 and 20,000 lb. The construction and pre- cision of manufacture are such that there is a possibility of slight bolt bending. Two val- ues of initial tension are to be investigated: (1) the normal value that a mechanic might tend to apply (Eq. e in Section 10.7) and (2) the theoretical limiting value of At Sy .

(a) Make a force-versus-time plot (like that in Figure 10.34a) showing the fluctu- ating external load, bolt force, and fluctuating clamping force for each of the two values of initial tension. Begin the plot with initial tightening, show about three load cycles, and conclude with load off.

(b) Estimate the safety factor corresponding to each of the values of initial tension, where failure is considered to be either eventual fatigue fracture or opening of the joint (the clamping force drops to zero).