Page 316 - Marks Calculation for Machine Design

P1: Shashi
January 4, 2005
15:4
Brown.cls
Brown˙C07
STRENGTH OF MACHINES
298
Step 16. To answer question (c), calculate the factor-of-safety (n a ) using Eq. (7.29), which
represents the distance (d a ) in Fig. 7.14.

σ a 80.6MPa
S ut 1 − (595 MPa) 1 −
σ m | σ a S e 229.1MPa (595 MPa)(0.648)
n a = = = =
σ m σ m 202.3MPa 202.3MPa
385.6MPa
= = 1.91
202.3MPa
) was substituted from Eq. (7.30).
where the alternating stress (σ m | σ a
Step 17. To answer question (d), calculate the factor-of-safety (n c ) using Eq. (7.31), which
represents the distance (d c ) in Fig. 7.15.
S e
S e σ a
+
σ m | c S ut σ m S e
n c = = =
σ m σ m S e σ a
σ m +
S ut σ m
229.1MPa 229.1MPa
= =
229.1MPa 80.6MPa (202.3MPa)(0.385 + 0.398)
(202.3MPa) +
595 MPa 202.3MPa
229.1MPa 229.1MPa
= = = 1.45
(202.3MPa)(0.783) 158.4MPa
where the alternating stress (σ m | c ) was substituted from Eq. (7.32).
Notice that the factors-of-safety for parts (a) and (d) are the same, and the factors-of-
safety for parts (b) and (c) are very close. This is not unexpected. Also, the factors-of-safety
for all four parts could have been found graphically by scaling the appropriate distances in
Fig. 7.19.
Consider another example where a fluctuating axial load is acting together with a constant
axial load.
U.S. Customary
Example 2. For the stepped rod shown in Fig. 7.20, which is acted upon by both a fluc-
tuating axial force (F 1 ) of between − 200 lb and 800 lb and a constant axial force (F 2 ) of
500 lb, determine
a. The factor-of-safety (n) using the Goodman theory
b. The maximum range of values for the fluctuating axial force (F 1 ) if the mean force (F m )
is held constant
3 "
d = 16 d = 1 "
1
2
8
F 1 F 2
FIGURE 7.20 Stepped rod for Example 2 (U.S. Customary).
The stepped rod is made of high-strength steel, ground to the dimensions shown. The

stepped rod operates at room temperature. Also, the test specimen endurance limit (S ) is
e