Page 199 - Marks Calculation for Machine Design

P1: Shibu
14:25
January 4, 2005
Brown.cls
Brown˙C04
U.S. Customary COMBINED LOADINGS SI/Metric 181
solution solution
Step 1. Calculate the maximum shear stress Step 1. Calculate the maximum shear stress
using Eq. (4.22). using Eq. (4.22).
2Tr o 2Tr o
τ max = τ max =
4
4
π r − R 4 π r − R 4
o
o
2 (72,000 lb · in)(4.0in) 2 (9,000 N · m)(0.1m)
= =
4
4
4
4
π((4in) − (0.75 in) ) π((0.1m) − (0.02 m) )
576,000 lb · in 2 1,800 N · m 2
= 4 = 4
803 in 0.000314 m
2
2
= 717 lb/in = 0.72 kpsi = 5,740,000 N/m = 5.74 MPa
Step 2. Calculate the minimum tangential Step 2. Calculate the minimum tangential
stress using Eq. (4.28). stress using Eq. (4.28).
2pR 2 2pR 2
σ min = σ min =
t
2
2
r − R 2 t r − R 2
o o
2
2
2 (9,650 lb/in )(0.75 in) 2 2 (48,680,000 N/m )(0.02 m) 2
= 2 2 = 2 2
(4in) − (0.75 in) (0.1m) − (0.02 m)
10,856 lb 38,944 N
= 2 = 2
15.4375 in 0.0096 m
2
2
= 703 lb/in = 0.7 kpsi = 4,057,000 N/m = 4.06 MPa
Step 3. From Eq. (4.29), the minimum radial Step 3. From Eq. (4.29), the minimum radial
stress is zero. stress is zero.
σ r min = 0 kpsi σ r min = 0MPa
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. 4.26. element shown in Fig. 4.26.
0.70 4.06
0 0 0 0
0.72 5.74
0.70 4.06
Edge view Edge view