sm8 105

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PROBLEM (8.105) A thick-walled cylinder of inner radius a and outer radius b is subjected to an
internal pressure pi , as shown in Fig. P8.101. Determine:
(a) The maximum tangential and radial stresses in the cylinder.
(b) The minimum tangential and radial stresses in the cylinder.
(c) Tha axial stress and the maximum shear stress in the cylinder.
Given: a = 25 mm, b = 75 mm, pi = 35 MPa
SOLUTION
(a) Through the use of Eq. (8.30a) and Eq. (8.27) at r=a (see Fig. 8.27):
22 2 2
max 22 2 2
75 25
( ) 35 43.75
75 25
ti
ba
p
MPa
ba
σ
++
== =
−−
max
() 35
ri
p
MPa
σ
=− =−
(b) By Eq Eq. (8.30a) and Eq. (8.27) at r=b (see Fig. 8.27):
22
min 22 2 2
22(25)
( ) 35 8.75
75 25
ti
a
p
MPa
ba
σ == =
−−
min
() 0
r
σ
=
(c) From Eqs. (8.32) and 8.31b):
22
22 2 2
(35)(25 ) 4.375
75 25
i
apa
M
Pa
ba
σ == =
−−
22
max 22 2 2
(35)(75 ) 39.375
75 25
i
pb
M
Pa
ba
τ == =
−−
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