Page 355 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 337
Step 4. Substitute the bolt preload (F preload ) Step 4. Substitute the bolt preload (F preload )
found in step 2, and the given joint constant found in step 2, and the given joint constant
(C) and external load (P) in Eq. (8.49) to (C) and external load (P) in Eq. (8.49) to
determine the factor-of-safety against separa- determine the factor-of-safety against separa-
tion (n separation ) as tion (n separation ) as
F preload F preload
n separation = n separation =
P (1 − C) P (1 − C)
9,150 lb 37,950 N
= =
(2,500 lb)(1 − 0.25) (11,000 N)(1 − 0.24)
9,150 lb 37,950 N
= = 4.9 ∼ 5 = = 4.5
=
1,875 lb 8,360 N
Notice that the load factor (n load ) and the factor-of-safety against separation (n separation )
are very similar. This is not unexpected.
Examples 1 through 4 summarize the steps to determine if a design is safe under static
loading conditions. In list form, they are:
Example 1: Determine the stiffness of the bolt (k bolt ), or cap screw.
Example 2: Determine the stiffness of the members (k members ).
Example 3: Determine the joint constant (C).
Example 4: Determine the load factor (n load ) and factor-of-safety against separation
(n separation ).

The development of the formulas needed to determine these design parameters might
have seemed at times to be excessive. However, it is important for the design engineer to
feel comfortable with the formulas in a design analysis, and if only a few basic principles
and simple algebra are required to show how these formulas are obtained, it is believed
these developments were worthwhile.

8.2.6 Fatigue Loading
The following discussion on fatigue loading applies only to the bolt or cap screw in a
connection, not the members. As the bolt or cap screw will always have a bolt preload
(F preload ), the bolt or cap screw will experience fluctuating loading, as was discussed in
Chap. 7. The maximum load on the bolt is the total bolt load (F bolt ) given by Eq. (8.39)
and the minimum load is the bolt preload (F preload ) given by the guidelines of Eq. (8.26).
Therefore, the mean force on the bolt (F m ) is given by Eq. (8.50) as
F bolt + F preload
F m = (8.50)
2
Substitute the total bolt load (F bolt ) from Eq. (8.39) in Eq. (8.50) to give
CP
(CP + F preload ) + F preload CP + 2 F preload
F m = = = + F preload (8.51)
2 2 2
Similarly, the alternating force on the bolt (F a ) is given by Eq. (8.52) as
F bolt − F preload
F a = (8.52)
2