Page 210 - Marks Calculation for Machine Design

P1: Shibu/Sanjay
January 4, 2005
Brown˙C05
Brown.cls
192
U.S. Customary 14:35 STRENGTH OF MACHINES SI/Metric
solution solution
Step 1. Calculate the axial stress (σ axial ) due Step 1. Calculate the axial stress (σ axial ) due
to the internal pressure (p i ) using Eq. (5.4). to the internal pressure (p i ) using Eq. (5.4).
2
2
p i r m (100 lb/in )(24 in) p i r m (700,000 N/m )(0.7m)
σ axial = = σ axial = =
2t 2 (0.25 in) 2t 2 (0.0065 m)
2,400 lb/in 490,000 N/m
= =
0.5in 0.013 m
2
2
= 4,800 lb/in = 4.8 kpsi = 37,700,000 N/m = 37.7MPa
Step 2. Calculate the hoop stress (σ hoop ) due Step 2. Calculate the hoop stress (σ hoop ) due
to the internal pressure (p i ) using Eq. (5.5), or to the internal pressure (p i ) using Eq. (5.5), or
use the fact that the hoop stress is twice the axial use the fact that the hoop stress is twice the axial
stress. stress.
σ hoop = 2 σ axial σ hoop = 2 σ axial
= 2 (4.8 kpsi) = 2 (37.7MPa)
= 9.6 kpsi = 75.4MPa
Step 3. Display the answers for the axial stress Step 3. Display the answers for the axial stress
(σ axial ) found in step 1 and the hoop stress (σ axial ) found in step 1 and the hoop stress
(σ hoop ) found in step 2, in kpsi, on the element (σ hoop ) found in step 2, in kpsi, on the element
of Fig. 5.4. of Fig. 5.4.

9.6 75.4

0 0
4.8 4.8 37.7 37.7

0 0
9.6 75.4

Step 4. Using Eq. (5.1), calculate the rotated Step 4. Using Eq. (5.1), calculate the rotated
stress (σ x x ) where from step 3 the unrotated stress (σ x x ) where from step 3 the unrotated
stresses are stresses are
σ xx = σ axial = 4.8 kpsi σ xx = σ axial = 37.7MPa
σ yy = σ hoop = 9.6 kpsi σ yy = σ hoop = 75.4MPa
τ xy = 0 τ xy = 0