Page 169 - Marks Calculation for Machine Design
P. 169
P1: Rakesh
14:16
January 4, 2005
Brown.cls
Brown˙C03
U.S. Customary ADVANCED LOADINGS SI/Metric 151
Step 4. Calculate the maximum radial stress Step 4. Calculate the maximum radial stress
(σ r ) and the tangential stress (σ t ) at the radius (σ r ) and the tangential stress (σ t ) at the radius
√ √
( r i r o ), using Eqs. (3.45) and (3.46). ( r i r o ), using Eqs. (3.45) and (3.46).
2 2
3 + ν r i 3 + ν r i
σ r max = σ o 1 + σ r max = σ o 1 +
8 r o 8 r o
2 2
3 + 0.3 1in 3 + 0.3 0.025 m
= (10 kpsi) 1 + = (86.5MPa) 1 +
8 36 in 8 1m
3.3 3.3
= (10 kpsi) (1 + 0.0278) 2 = (86.5MPa) (1 + 0.025) 2
8 8
= (10 kpsi)(0.4125)(1.0278) 2 = (86.5MPa)(0.4125)(1.025) 2
= 4.36 kpsi = 37.5MPa
2
√ 3 + ν r 2 √ 3 + ν 1 − ν r i r
r i r o 1 − ν r i i r i r o 1 + 2 i
σ t = σ o 1 + 2 + 2 σ t = σ o 8 + r 2
8 3 + ν r o r o 3 + ν r o o
3 + 0.3 3 + 0.3
= (10 kpsi) = (86.5MPa)
8 8
2 1− 0.3 0.025 m (0.025 m) 2
1 − 0.3 1in (1in)
× 1 + 2 + × 1+ 2 + 2
3 + 0.3 36 in (36 in) 2 3+ 0.3 1m (1m)
3.3 3.3
= (10 kpsi) = (86.5MPa)
8 8
0.7 1 1
0.7 0.025 0.000625
× 1 + 2 + × 1 + 2 +
3.3 36 1296 3.3 1 1
= (10 kpsi)(0.4125) = (86.5MPa)(0.4125)
× (1 + 0.012 + 0.00077) × (1 + 0.0106 + 0.000625)
= 4.18 kpsi = 36.1MPa
Step 5. Using Eq. (3.47), calculate the factor- Step 5. Using Eq. (3.47), calculate the factor-
of-safety (n) at the inside radius (r i ) where the of-safety (n) at the inside radius (r i ) where the
principal stress (σ 1 ) is the maximum tangential principal stress (σ 1 ) is the maximum tangential
stress found in Step 3 and the principal stress stress found in Step 3 and the principal stress
(σ 2 ) is zero. (σ 2 ) is zero.
1/2 1/2
2 2 2 2
σ + σ − σ 1 σ 2 1 σ + σ − σ 1 σ 2 1
1 2 1 2
= =
S y n S y n
2
2
2
2
((8.25) + (0) − (8.25)(0)) 1/2 1 ((71.4) + (0) − (71.4)(0)) 1/2 1
= =
50 n 50 n
2 1/2
2 1/2
((8.25) ) 8.25 1 ((71.4) ) 71.4 1
= = = =
50 50 n 50 350 n
50 350
n = = 6.1 n = = 4.9
8.25 71.4
Clearly the design is safe. Clearly the design is safe.