1
ME 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
d
t
b
d t
t d
A A E
k
A l
Al
=
+
The area of the unthreaded portion of the bolts, see Table (8-7), page 412, can be written as
2
4
d
d
A
π
=
Therefore, the area of the unthreaded portion of the bolts is given as
2
2
(12)
113 mm
4
d
A
π
×
=
=
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
2
84.3 mm
t
A
=
The length of the grip, see Figure for Problem (8-20), page 453, is given as
20
25
45 mm
G
L
=
+
=
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 mm
H
=

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