Page 170 - Marks Calculation for Machine Design
P. 170
P1: Rakesh
January 4, 2005
Brown˙C03
Brown.cls
152
U.S. Customary 14:16 STRENGTH OF MACHINES SI/Metric
Step 6. Using Eq. (3.47), calculate the factor- Step 6. Using Eq. (3.47), calculate the factor-
√ √
of-safety (n) at the radial distance ( r i r o ) of-safety (n) at the radial distance ( r i r o )
where the principal stress (σ 1 ) is the maximum where the principal stress (σ 1 ) is the maximum
radial stress found in Step 4 and the princi- radial stress found in Step 4 and the princi-
pal stress (σ 2 ) is tangential stress also found pal stress (σ 2 ) is tangential stress also found
in Step 4. in Step 4.
1/2 1/2
2 2 2 2
σ + σ − σ 1 σ 2 σ + σ − σ 1 σ 2
1 2 1 1 2 1
= =
S y n S y n
2
2
2
2
((4.36) + (4.18) − (4.36)(4.18)) 1/2 1 ((37.5) + (36.1) − (37.5)(36.1)) 1/2 1
= =
50 n 350 n
(18.26) 1/2 4.27 1 (1356) 1/2 36.8 1
= = = =
50 50 n 350 350 n
50 350
n = = 11.7 n = = 9.5
4.27 36.8
Clearly the design is very safe. Clearly the design is very safe.
Notice that the stress element at the inside radius (r i ) has a lower factor-of-safety than
√
the one at the radial distance ( r i r o ). This means it is the most important stress element in
deciding whether the design is safe or not.