Page 327 - Marks Calculation for Machine Design

P1: Shashi
15:4
January 4, 2005
Brown.cls
Brown˙C07
FATIGUE AND DYNAMIC DESIGN
Step 5. Using the given geometric shear stress concentration factor (K ts ) and the notch
sensitivity (q), calculate the reduced concentration factor (K f ) from Eq. (6.23) as 309
K f = 1 + q(K ts − 1) = 1 + (0.9)(1.65 − 1) = 1 + 0.585 = 1.585
Step 6. Using the reduced stress concentration factor (K f ) found in step 5, calculate the
miscellaneous effect factor (k e ) using Eq. (7.16) as
1 1
k e = = = 0.63
K f 1.585
Step 7. Using the given ultimate tensile stress (S ut ) and the guidelines in Eq. (7.1),

calculate the test specimen endurance limit (S ) as
e

S = 0.504 S ut = (0.504)(630 MPa) = 317.5MPa
e
Step 8. Using the test specimen endurance limit (S ) found in step 7, and the modifying

e
factors found in steps 1 through 6, calculate the endurance limit (S e ) for the solid shaft
using the Marin equation in Eq. (7.7) as
S e = k a k b k c k d k e S = (0.45)(0.83)(0.577)(1)(0.63)(317.5MPa)

e
= (0.136)(317.5MPa) = 43.2MPa
Step 9. Calculate the mean torque (T m ) and the alternating torque (T a ) as
T max + T min (3,300 N · m) + (2,700 N · m)
T m = =
2 2
6,000 N · m
= = 3,000 N · m
2
T max − T min (3,300 N · m) − (2,700 N · m)
T a = =
2 2
600 N · m
= = 300 N · m
2
Step 10. Calculate the polar moment of inertia (J) of the circular cross section as
1 4 1 4 4 −7 4
J = πR = π(1.9cm) = 20.47 cm = 2.05 × 10 m
2 2
Step 11. Calculate the mean shear stress (τ m ) and the alternating shear stress (τ a ) as
T m R (3,000 N · m)(0.019 m)
τ m = = = 278.0MPa
J 2.05 × 10 −7 m 4
T a R (300 N · m)(0.019 m)
τ a = = −7 4 = 27.8MPa
J 2.05 × 10 m
Step 12. Using the given ultimate tensile stress (S ut ) and Eq. (7.33), calculate the ultimate
shear strength (S us ) as
S us = 0.67 S ut = (0.67)(630 MPa) = 422.1MPa