Page 201 - Marks Calculation for Machine Design

P1: Shibu
14:25
January 4, 2005
Brown˙C04
Brown.cls
U.S. Customary COMBINED LOADINGS SI/Metric 183
Step 2. Calculate the maximum tangential Step 2. Calculate the maximum tangential
stress using Eq. (4.26). stress using Eq. (4.26).
2
2
r + R 2 r + R 2
σ max = p o σ max = p o
t
2
2
r − R 2 t r − R 2
o o
2
2
= (9,650 lb/in ) = (48,680,000 N/m )
2 2 2 2
(4in) + (0.75 in) (0.1m) + (0.02 m)
× ×
2
2
(4in) − (0.75 in) 2 (0.1m) − (0.02 m) 2
2
2
= (9,650 lb/in ) = (48,680,000 N/m )
(16 + 0.5625) in (0.01 + 0.0004) m
2 2
× ×
(16 − 0.5625) in 2 (0.01 − 0.0004) m 2
2
2
= (9,650 lb/in ) = (48,680,000 N/m )
(16.5625) in (0.0104) m
2 2
× 2 × 2
(15.4375) in (0.0096) m
2
2
= (9,650 lb/in )[1.073] = (48,680,000 N/m )[1.083]
2
2
= 10,353 lb/in = 10.35 kpsi = 52,737,000 N/m = 52.74 MPa
Step 3. From Eq. (4.27) the maximum radial Step 3. From Eq. (4.27) the maximum radial
stress is stress is
σ r max =−p =−9,650 lb/in 2 σ r max =−p =−48,680,000 N/m 2
=−9.65 kpsi =−48.68 MPa
Step 4. Display the stresses found in steps 1, Step 4. Display the stresses found in steps 1,
2, and 3, in kpsi, on the edge view of the stress 2, and 3, in MPa, on the edge view of the stress
element shown in Fig. 4.27. element shown in Fig. 4.27.
10.35 52.74
9.65 9.65 48.68 48.68
0.13 1.15
10.35 52.74
Edge view Edge view