sm8 100

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PROBLEM (8.100) A pressure vessel of inner radius r and wall thickness t is fabricated from a
welded pipe with helix angle
φ
and equipped with two end plates, as shown in Fig. P8.100. If pressure
inside the vessel is p, determine:
(a) The normal stress w
σ
perpendicular to the weld.
(b) The shear stress w
τ
parallel to the weld.
Given: r = 4 ft, t = ½ in.,
φ
= 38o , p = 200 psi
SOLUTION
90 38 52
2o
ta
pr pr
tt
σσ θ ===−+=−
Principal stresses
(200)(4 12) 19.2
12
ty
pr ksi
t
σσ
×
== = =
9.6
2t
ax ksi
σ
σσ ===
τ (ksi)
18027
o
αθ =−=
x’
6
1( ) 14.4
2
avg t a ksi
σσσ =+=
1()4.8
2ta
R
ksi σσ =−=
(a) 'cos
wx avg
R
σ
σσ == + α
=
=+ 14.4 4.8cos76 15.56 ksi
(b) sin 4.8(sin76 ) 4.66
o
w
R
ksi τα =− =− =−
19.2 ksi
4.66 ksi
x
’
76o
9.6 ksi
Weld
x
15.56 ksi
y’
α
104o
R
C
O
σ
σavg
σ
(ksi)
σ
t
R
a
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