1ME 452: Machine Design II Solution to Homework Set 12 Problem 1. (Problem 8-22, page 448). To determine the member stiffness use the approach outlined by Eq. (8-20), see page 415. Compare your result with the answer obtained from the finite-element study, see Eq. (8-23). To determine the length of the bolt use Table A-17, page 1015. To determine the height of the hexagonal nut use Table A-31, page 1035. Determine the preload using Eqs. (8-30) and (8-31), see page 427. Determine the load factor guarding against over-proof loading using Eq. (8-28), see page 425. Also determine the load factor guarding against joint separation using Eq. (8-29), see page 426. Solution: The stiffness of the bolt, see Equation (8-17), page 413 can be written as dtbd tt dA A EkA lAl=+The area of the unthreaded portion of the bolts, see Table (8-7), page 412, can be written as 24ddAπ=Therefore, the area of the unthreaded portion of the bolts is given as 22(12)113 mm4dAπ×==The tensile stress area for metric threads, see Table (8-1), page 398, for a diameter of 12 mm and assuming coarse pitch, is given as 284.3 mmtA=The length of the grip, see Figure for Problem (8-20), page 453, is given as 202545 mmGL=+=The height of the hexagonal head of the bolt, see Table (A-31), page 1035 , for a 12 mm size bolt and assuming regular hexagonal nut, is given as 10.8 mmH=
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