Page 349 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 331
Therefore, Therefore,
lb N
(1.814) 30 × 10 6 (0.5in) (1.814) 2.07 × 10 11 (.012 m)
in 2 m 2
k 1 = k 1 =
1.17 in 0.029 m
ln 5 ln 5
2.17 in 0.053 m
7
9
2.72 × 10 lb/in 4.51 × 10 N/m
= =
0.992 1.006
9
7
= 2.74 × 10 lb/in = 4.48 × 10 N/m
Step6. Substitutethemiddlestiffness(k middle ) Step6. Substitutethemiddlestiffness(k middle )
found in step 3, the stiffness (k 2 ) found in found in step 3, the stiffness (k 2 ) found in
step 4, and the stiffness (k 1 ) found in step 5 in step 4, and the stiffness (k 1 ) found in step 5 in
Eq. (8.18) to determine the overall stiffness of Eq. (8.18) to determine the overall stiffness of
the members (k members ) as the members (k members ) as
1 1 1 1 1 1 1 1
= + + = + +
k members k 1 k 2 k middle k members k 1 k 2 k middle
1 1
= =
2.74 × 10 lb/in 4.48 × 10 N/m
7
9
1 1
+ +
7
9
1.42 × 10 lb/in 2.28 × 10 N/m
1 1
+ +
8
2.69 × 10 lb/in 4.98 × 10 10 N/m
 −8   −10 
3.65 × 10 2.23 × 10
in m
=  +7.04 × 10 −8  lb =  +4.39 × 10 −10  N
+3.72 × 10 −9 +2.01 × 10 −11
= 1.106 × 10 −7 in/lb = 6.821 × 10 −10 m/N
Therefore, Therefore,
1 1
k members = −7 k members = −10
1.106 × 10 in/lb 6.821 × 10 m/N
9
6
= 9.04 × 10 lb/in = 1.47 × 10 N/m
= 9,040 kip/in = 1,470 MN/m
Note that the stiffness of the members found in Example 2 is about three times the stiffness
of the bolt found in Example 1. Also, the stiffness (k middle ) could have been neglected as it
was over ten times the stiffness (k 1 ) and over 20 times the stiffness (k 2 ). Remember, in a
series combination of stiffnesses, the lowest stiffness governs, not the highest.
8.2.3 Bolt Strength and Preload
The bolt strength, denoted by (S proof ), is the proof load, denoted by (F proof ), divided by the
tensile-stress area (A T ) and given in Eq. (8.24) as
F proof
S proof = (8.24)
A T