Page 353 - Marks Calculation for Machine Design

P1: Sanjay
15:14
January 4, 2005
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 335
solution solution
Step 1. Using the given stiffness of the bolt Step 1. Using the given stiffness of the bolt
and members, calculate the joint constant (C) and members, calculate the joint constant (C)
from Eq. (8.35) as from Eq. (8.35) as
k bolt k bolt
C = C =
k bolt + k members k bolt + k members
8
6
3.03 × 10 lb/in 4.66 × 10 N/m
= =
8
(3.03 × 10 + 9.04 × 10 ) lb/in (4.66 × 10 + 1.47 × 10 ) N/m
6
9
6
6
8
3.03 × 10 lb/in 4.66 × 10 N/m
= =
8
6
12.07 × 10 lb/in 19.36 × 10 N/m
= 0.25 = 0.24
8.2.5 Static Loading
If the total load on the bolt (F bolt ) given by Eq. (8.39) is divided by the tensile-stress area
(A T ) then the following expression is obtained.
F bolt CP F preload
= + (8.42)
A T A T A T
The maximum value of the left-hand side of Eq. (8.42) is the proof strength (S proof ).Ifa
load factor (n load ) is used, which will act like a factor-of-safety for the bolt, then Eq. (8.42)
becomes
n load CP F preload
S proof = + (8.43)
A T A T
Solve for the load factor (n load ) in Eq. (8.43) to give
S proof A T − F preload
n load = (8.44)
CP
Using Eq. (8.25), Eq. (8.44) can be written as
F proof − F preload
n load = (8.45)
CP
In Eq. (8.41) it was stated that the total force in the members (Fmembers) must always
be negative, or compressive, to ensure that the joint will not separate, thereby placing the
entire load (P) on the bolt. Therefore, a factor-of-safety against separation (n separation ) can
be defined for when the total force in the members goes to zero. Setting (F members ) equal
to zero in Eq. (8.40) gives
F members = 0 = (1 − C)P o − F preload (8.46)
where (P o ) is the value of the external load for separation of the joint. Solving for (P o ) in
Eq. (8.46) gives

F preload
P o = (8.47)
(1 − C)