Page 342 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
324
Similarly, the total length (L total ) of a nut and bolt assembly can be separated into three
lengths as given by Eq. (8.12). APPLICATION TO MACHINES
L total = L grip + L nut + L extra (8.12)
where the grip length (L grip ) is the sum of two lengths, (L T ) and (L UT ),asgivenin
Eq. (8.10), and where (L nut ) is the full length of the nut, and (L extra ) is the extra length of
the bolt past the nut that typically should be one to two threads after tightening.
However, the actual threaded length of the bolt (L threaded ) is also the sum of three lengths,
given by Eq. (8.13) as
L threaded = L T + L nut + L extra (8.13)
or solving for the threaded length (L T ) needed to determine the stiffness of the threaded
length(k T ) from Eq. (8.6) gives
L T = L threaded − (L nut + L extra ) (8.14)

Using Eq. (8.12), the sum (L nut ) plus (L extra ) in Eq. (8.14) can be replaced with
L nut + L extra = L total − L grip (8.15)

so that the threaded length (L T ) becomes
L T = L threaded − (L total − L grip )
(8.16)
= L threaded − L total + L grip
Therefore, solving for the unthreaded length of the bolt (L UT ) in Eq. (8.10), needed to
determine the stiffness of the unthreaded length (k UT ) from Eq. (8.7), gives

L UT = L grip − L T (8.17)
where the grip length (L grip ) will be known from the design drawings, and the total length
(L total ) and threaded length (L threaded ) of the bolt can be found from standard references
such as Marks’ Standard Handbook for Mechanical Engineers.
Also, the threaded cross-sectional area (A T ), which is the tensile-stress area, would be
found in these same standard references, such as Marks’, whereas the unthreaded cross-
sectional area (A UT ) would be simply calculated using the nominal bolt diameter.
Consider the following example for a bolted connection like that shown in Fig. 8.1, except
that no washers are used.

U.S. Customary SI/Metric
Example 1. Determine the stiffness of a high- Example 1. Determine the stiffness of a high-
strength diameter steel bolt and nut assembly, strength diameter steel bolt and nut assembly,
with no installed washers, where with no installed washers, where
d bolt = 0.5 in (nominal) d bolt = 12 mm = 0.012 m (nominal)
L total = 2.5 in L total = 60 mm = 0.06 m
L threaded = 1.25 in L threaded = 30 mm = 0.03 m
L grip = 1.75 in L grip = 45 mm = 0.045 m
2
2
A T = 0.142 in = 1.42 × 10 −1 in 2 A T = 84.3 mm = 8.43 × 10 −5 m 2
6
9
E = 30 × 10 lb/in 2 E = 207 GPa = 207 × 10 N/m 2