Page 363 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 345
Step 10. Substitute the middle stiffness Step 10. Substitute the middle stiffness
(k middle ) found in step 7, the stiffness (k 1 ) found (k middle ) found in step 7, the stiffness (k 1 ) found
in step 8, and the stiffness (k 2 ) found in step 9 in step 8, and the stiffness (k 2 ) found in step 9
in Eq. (8.18) to determine the overall stiffness in Eq. (8.18) to determine the overall stiffness
of the members (k members ) as of 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
= 7 = 9
4.49 × 10 lb/in 7.88 × 10 N/m
1 1
+ +
7
9
3.26 × 10 lb/in 5.80 × 10 N/m
1 1
+ +
8
1.73 × 10 lb/in 3.26 × 10 10 N/m
2.23 × 10 1.27 × 10
 −8   −10 
in m
=  + 3.07 × 10 −8  =  + 1.72 × 10 −10 
+ 5.78 × 10 −9 lb + 3.07 × 10 −11 N
1 −8 1 −10
= 5.873 × 10 in/lb = 3.300 × 10 m/N
k members k members
Therefore, Therefore,
1 1
k members = k members =
5.873 × 10 −8 in/lb 3.300 × 10 −10 m/N
7
9
= 1.70 × 10 lb/in = 3.03 × 10 N/m
= 17,000 kips/in = 3,030 MN/m
Step 11. Substitute the stiffness of the cap Step 11. Substitute the stiffness of the cap
screw (k T ) from step 2 and the stiffness of screw (k T ) from step 2 and the stiffness of
the members (k members ) found in step 10 in the members (k members ) found in step 10 in
Eq. (8.35) to determine the joint constant (C) as Eq. (8.35) to determine the joint constant (C) as
k cap screw k cap screw
C = C =
k cap screw + k members k cap screw + k members
9
6
6.38 × 10 lb/in 1.20 × 10 N/m
= 6 6 = 9 9
(6.38 × 10 + 17.00 × 10 ) lb/in (1.20 × 10 + 3.03 × 10 ) N/m
6
9
6.38 × 10 lb/in 1.20 × 10 N/m
= =
9
6
23.38 × 10 lb/in 4.23 × 10 N/m
= 0.27 = 0.28
Step 12. Use the given proof strength (S proof ) Step 12. Use the given proof strength (S proof )
and tensile-stress area (A T ) in Eq. (8.25) to and tensile-stress area (A T ) in Eq. (8.25) to
determine the proof load (F proof ) determine the proof load (F proof )
F proof = S proof A T F proof = S proof A T
6
2
3
2
2
2
= (85 × 10 lb/in )(2.26 × 10 −1 in ) = (600 × 10 N/m )(1.57 × 10 −4 m )
= 19,200 lb = 94,200 N