Page 456 - Shigley's Mechanical Engineering Design

bud29281_ch08_409-474.qxd 12/22/09 5:45 PM Page 431 epg Disk1:Desktop Folder:TEMPWORK:Don't-Delete Jobs:MHDQ196/Budynas:

Screws, Fasteners, and the Design of Nonpermanent Joints 431
Figure 8–17

Dimensions in inches.

1.437
0.75
0.095

1
2 0.6725
0.0775
3
4 0.6725

1.527

(a) (b)

The distance between the joint line and the dotted frusta line is 0.6725 − 0.5 −
0.095 = 0.0775 in. Thus, the top frusta consist of the steel washer, steel plate, and
0.0775 in of the cast iron. Since the washer and top plate are both steel with
6
E = 30(10 ) psi, they can be considered a single frustum of 0.595 in thick. The outer
diameter of the frustum of the steel member at the joint interface is 0.75 + 2(0.595)
tan 30° = 1.437 in. The outer diameter at the midpoint of the entire joint is 0.75 +
2(0.6725) tan 30° = 1.527 in. Using Eq. (8–20), the spring rate of the steel is

6
0.5774π(30)(10 )0.5 6
k 1 = = 30.80(10 ) lbf/in
[1.155(0.595) + 0.75 − 0.5](0.75 + 0.5)
ln
[1.155(0.595) + 0.75 + 0.5](0.75 − 0.5)
For the upper cast-iron frustum

6
0.5774π(14.5)(10 )0.5 6
k 2 = = 285.5(10 ) lbf/in
[1.155(0.0775) + 1.437 − 0.5](1.437 + 0.5)
ln
[1.155(0.0775) + 1.437 + 0.5](1.437 − 0.5)
For the lower cast-iron frustum

6
0.5774π(14.5)(10 )0.5 6
k 3 = = 14.15(10 ) lbf/in
[1.155(0.6725) + 0.75 − 0.5](0.75 + 0.5)
ln
[1.155(0.6725) + 0.75 + 0.5](0.75 − 0.5)
The three frusta are in series, so from Eq. (8–18)

1 1 1 1
= + +
6
6
6
k m 30.80(10 ) 285.5(10 ) 14.15(10 )