Page 205 - Marks Calculation for Machine Design
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P1: Shibu
January 4, 2005
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Brown.cls
Brown˙C04
COMBINED LOADINGS
p
i
i m
s xx = p r + M 187
2t p r t
2
m
p r
s hoop Outside of tank s hoop = i m
t
FIGURE 4.32 Edge view of bottom stress element.
The normal stress (σ xx ) is shown as just a dot in Fig. 4.32 as it is directed outward and
perpendicular to the edge of the stress element. Also, as the internal pressure (p i ) acts on
the inside surface of the element this is not a plane stress element.
U.S. Customary SI/Metric
Example 11. Determine the stresses on the Example 11. Determine the stresses on the
bottom element shown in Fig. 4.31 for the pres- bottom element shown in Fig. 4.31 for the pres-
surized tank in Fig. 4.28, modeled by the surized tank in Fig. 4.28, modeled by the
simply-supported beam in Fig. 4.29, where simply-supported beam in Fig. 4.29, where
2
2
p i = 200 lb/in = 0.2 kpsi p i = 1,400,000 N/m = 1.4MPa
D = 6ft = 72 in = 2 r m D = 2m = 2 r m
t = 0.5 in t = 1.3 cm = 0.013 m
w = 1,800 lb/ft w = 24,300 N/m
L = 24 ft L = 8m
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. (4.30). to the internal pressure (p i ) using Eq. (4.30).
2
2
p i r m (200 lb/in )(36 in) p i r m (1,400,000 N/m )(1m)
σ axial = = σ axial = =
2 t 2 (0.5in) 2 t 2 (0.013 m)
7,200 lb/in 1,400,000 N/m
= =
1in 0.026 m
2
2
= 7,200 lb/in = 7.2 kpsi = 53,846,000 N/m = 53.8MPa
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. (4.31), to the internal pressure (p i ) using Eq. (4.31),
or use the fact that the hoop stress is twice the or use the fact that the hoop stress is twice the
axial stress axial stress.
σ hoop = 2 σ axial σ hoop = 2 σ axial
= 2 (7.2 kpsi) = 2 (53.8MPa)
= 14.4 kpsi = 107.6MPa
Step 3. Calculate the maximum bending mo- Step 3. Calculate the maximum bending mo-
ment from Eq. (4.35). ment from Eq. (4.35).
1 2 1 2
M max = wL M max = wL
8 8
1 1
= (1,800 lb/ft)(24 ft) 2 = (24,300 N/m)(8m) 2
8 8
= 129,000 lb · ft = 194,400 N · m