Page 352 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
334
APPLICATION TO MACHINES
then solve for (P bolt ) to give

k bolt
P bolt = P (8.34)
k bolt + k members
If a joint constant (C) is defined as
k bolt
C = (8.35)
k bolt + k members
then (1 − C) is therefore
k bolt k members
1 − C = 1 − = (8.36)
k bolt + k members k bolt + k members
Using the definition of the joint constant (C), the portion of the load carried by the bolt
(P bolt ) given in Eq. (8.34) becomes simply
P bolt = CP (8.37)
and using the definition of (1−C), the portion of the load carried by the members (P members )
given in Eq. (8.32) becomes simply
P members = (1 − C)P (8.38)
Therefore, the total load on the bolt (F bolt ) is the portion of the load (P) carried by the
bolt (P bolt ) plus the preload (F preload ) and given by Eq. (8.39) as
F bolt = P bolt + F preload = CP + F preload (8.39)
Similarly, the total load on the members (F members ) is the portion of the load (P) carried
by the members (P members ) minus the preload (F preload )and given by Eq. (8.40) as
F members = P members − F preload = (1 − C)P − F preload (8.40)
where the total force on the members (F members ) must remain negative to make sure the
joint does not separate, that is,
F members < 0 (8.41)
Experimental results indicate that the members can carry as much as 80 percent of the
external load (P), and therefore the bolt only carries 20 percent of the load.
Consider the following example using the stiffnesses of the bolt and members found in
Examples 1 and 2.

U.S. Customary SI/Metric
Example 3. Using the stiffness of the bolt Example 3. Using the stiffness of the bolt
(k bolt ) found in Example 1 and the stiffness of (k bolt ) found in Example 1 and the stiffness of
the members (k members ) found in Example 2, the members (k members ) found in Example 2,
determine the joint constant (C), where determine the joint constant (C), where
6
8
k bolt = 3.03 × 10 lb/in k bolt = 4.66 × 10 N/m
9
6
k members = 9.04 × 10 lb/in k members = 1.47 × 10 N/m