Page 320 - Marks Calculation for Machine Design

P1: Shashi
January 4, 2005
15:4
Brown.cls
Brown˙C07
STRENGTH OF MACHINES
302
Step 2. Only the larger diameter region of the stepped rod experiences the fluctuating axial
force (F 1 ), so use diameter (d 1 ) in Eq. (7.10) to calculate the size factor (k b ) as
−0.1133 −0.1133

d 4.8 −0.1133
∼
k b = = = (0.630) = 1.05 = 1
7.62 7.62
Step 3. The stepped rod is axially loaded, so the load type factor (k c ) from the guidelines
in Eq. (7.13) is
k c = 0.923
Step 4. As the stepped rod is operating at room temperature, the temperature factor (k d )
from Eq. (7.15) and Table 7.2 is
k d = 1
Step 5. Using the given reduced stress concentration factor (K f ), calculate the miscella-
neous effect factor (k e ) using Eq. (7.16) as
1 1
k e = = = 0.87
K f 1.15

Step 6. Using the given test specimen endurance limit (S ) and the modifying factors
e
found in steps 1 through 5, calculate the endurance limit (S e ) for the stepped rod using the
Marin equation in Eq. (7.7) as

S e = k a k b k c k d k e S = (0.90)(1)(0.923)(1)(0.87)(455 MPa)
e
= (0.723)(455 MPa) = 329.0MPa
Step 7. Calculate the maximum axial force (F max ) and minimum axial force (F min ) as
max
F max = F + F 2 = (3,600 N) + (2,250 N) = 5,850 N
1
min
F min = F + F 2 = (−900 N) + (2,250 N) = 1,350 N
1
Step 8. Calculate the mean axial force (F m ) and the alternating axial force (F a ) as
F max + F min (5,850 N) + (1,350 N) 7,200 lb
F m = = = = 3,600 N
2 2 2
F max − F min (5,850 N) − (1,350 N) 4,500 lb
F a = = = = 2,250 N
2 2 2
Step 9. Calculate the area (A) of the larger diameter (d 1 ) for stepped rod as
π 2 π 2 2 −5 2
A = d = (0.48 cm) = 0.181 cm = 1.81 × 10 m
1
4 4
Step 10. Calculate the mean axial stress (σ m ) and the alternating axial stress (σ a ) as
F m 3,600 N
σ m = = = 198.9MPa
A 1.81 × 10 −5 m 2
F a 2,250 N
σ a = = = 124.3MPa
A 1.81 × 10 −5 m 2