From your results in Prob. 17–32, show that to meet a fatigue factor of safety n1 the optimal solution is
m = 4bcn1/a2 ropes
Having a diameter of
d = a/2cn1
Solve Prob. 17–31 if a factor of safety of 2 is required. Show what to do in order to accommodate to the necessary discreteness in the rope diameter d and the number of ropes m.
Prob. 17–31, A 2000-ft mine hoist operates with a 72-in drum using 6 × 19 monitor-steel wire rope. The cage and load weigh 8000lbf, and the cage is subjected to an acceleration of 2 ft/s2 when starting.
(a) For a single-strand hoist how does the factor of safety n = Ff/Ft vary with the choice of rope diameter?
(b) For four supporting strands of wire rope attached to the cage, how does the factor of safety vary with the choice of rope diameter?