Page 347 - Marks Calculation for Machine Design

P1: Sanjay
15:14
January 4, 2005
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 329
where where
C 1 = (2 t tan α + D − d)(D + d) C 1 = (2 t tan α + D − d)(D + d)
∗
◦
= (2 t middle tan 30 + D − d bolt ) = (2 t middle tan 30 + D − d bolt )
◦
∗
∗
∗
×(D + d bolt ) ×(D + d bolt )

(2)(0.125 in)(0.577) (2)(0.0025 m)(0.577)
= =
+(1.62 in) − (0.5in) +(0.041 m) − (0.012 m)
×((1.62 in) + (0.5in)) ×((0.041 m) + (0.012 m))
= (1.26 in)(2.12 in) = (0.032 m)(0.053 m)
= 2.68 in 2 = 0.00170 m 2
and and
C 2 = (2 t tan α + D + d)(D − d) C 2 = (2 t tan α + D + d)(D − d)
◦
∗
◦
∗
= (2 t middle tan 30 + D + d bolt ) = (2 t middle tan 30 + D + d bolt )
∗
∗
×(D − d bolt ) ×(D − d bolt )

(2)(0.125 in)(0.577) (2)(0.0025 m)(0.577)
= =
+(1.62 in) + (0.5in) +(0.041 m) + (0.012 m)
×((1.62 in) − (0.5in)) ×((0.041 m) − (0.012 m))
= (2.26 in)(1.12 in) = (0.056 m)(0.029 m)
= 2.54 in 2 = 0.00162 m 2
Therefore, Therefore,

lb N
(1.814) 16 × 10 6 (0.5in) (1.814) 1.1 × 10 11 (.012 m)
in 2 m 2
k middle = k middle = 2
2.68 in 2 0.00170 m
ln ln 2
2.54 in 2 0.00162 m
9
7
1.45 × 10 lb/in = 2.39 × 10 N/m
= 0.048
0.054 10
8
= 2.69 × 10 lb/in = 4.98 × 10 N/m
Step 4. The remaining thickness of the cast Step 4. The remaining thickness of the cast
iron member is the thickness (t 2 ) minus the third iron member is the thickness (t 2 ) minus the third
thickness (t middle ), which from Eq. (8.19) is half thickness (t middle ), which from Eq. (8.19) is half
the grip length (L grip /2). Substitute this remain- the grip length (L grip /2). Substitute this remain-
ing thickness (L grip /2), the given bolt diameter ing thickness (L grip /2), the given bolt diameter
(d bolt ), and the modulus of elasticity (E 2 ) in (d bolt ), and the modulus of elasticity (E 2 ) in
Eq. (8.22) to find the stiffness (k 2 ) as Eq. (8.22) to find the stiffness (k 2 ) as
(π tan 30 ) Ed (π tan 30 ) Ed
◦
◦
k 2 = k 2 =
◦
◦
2 t tan 30 + 0.5 d 2 t tan 30 + 0.5 d
ln 5 ln 5
2 t tan 30 + 2.5 d 2 t tan 30 + 2.5 d
◦
◦
◦ ◦
(π tan 30 ) E 2 d bolt (π tan 30 ) E 2 d bolt
= =
ln 5 C 1 ln 5 C 1
C 2 C 2