Page 311 - Marks Calculation for Machine Design

P1: Shashi
January 4, 2005
15:4
Brown.cls
Brown˙C07
FATIGUE AND DYNAMIC DESIGN
Step 3. Using Eq. (7.10) calculate the size factor (k b ) as
−0.1133 −0.1133 293
d e 0.143 −0.1133
∼
k b = = = (0.477) = 1.09 = 1
0.3 0.3
Step 4. As the beam is bending, the load type factor (k c ) from Eq. (7.14) is
k c = 1
Step 5. As the beam is operating at room temperature, the temperature factor (k d ) from
Eq. (7.15) and Table 7.2 is
k d = 1
Step 6. 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 = = = 0.83
K f 1.2
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)(85 kpsi) = 42.8 kpsi
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 cantilevered
beam using the Marin equation in Eq. (7.7) as

S e = k a k b k c k d k e S = (0.92)(1)(1)(1)(0.83)(42.8 kpsi)
e
= (0.764)(42.8 kpsi) = 32.7 kpsi
Step 9. Calculate the mean force (F m ) and the alternating force (F a ) as
F max + F min (5.6lb) + (2.4lb) 8lb
F m = = = = 4lb
2 2 2
F max − F min (5.6lb) − (2.4lb) 3.2lb
F a = = = = 1.6lb
2 2 2
Step 10. Calculate the mean bending moment (M m ) and the alternating bending moment
(M a ) as

M m = F m L = (4lb)(2.5in) = 10 in · lb
M a = F a L = (1.6lb)(2.5in) = 4in · lb

Step 11. Calculate the area moment of inertia (I) for the rectangular cross section as
1 3 1 3 −5 4
I = bh = (0.5in)(0.0625 in) = 1.02 × 10 in
12 12