sm8 94

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PROBLEM (8.94) A closed cylindrical pressure vessel of inner diameter d and wall thickness t is
constructed with a helical welding that make an angle
φ
with the longitudinal axis as depicted in Fig.
P8.94. The vessel is subjected to an internal pressure of p. Determine:
(a) Tangential and axial stresses.
(b) The maximum in-plane shearing stress.
(c) The absolute maximum shear stress.
(d) The normal stress w
σ
and shear stress w
τ
acting on planes perpendicular and parallel to the weld.
Sketch the results on a properly oriented element.
Given: d = 2r = 4 ft, t = ½ in.,
φ
= 55o , p = 500 psi
SOLUTION
(a) Principal stresses
(500)(2 12) 24
12
tpr ksi
t
σ
×
== =
12
2t
aksi
σ
σ ==
(b) In-plane maximum shear stress
max 1()6
2ta ksi
τσσ =−=
(c) Absolute maximum shear stress
max 1
() ( 0)12
2
at ksi
τσ =−=
(d) 12 24 0
xa yt xy
ksi ksi
σ
σσσ == == = τ
+ =−
For
θ =−
90 55 35 :
o
'11
( ) ( )cos2 18 4.10 13.9
22
x
xy xy ksi w
σ
σσ σσ θ σ =++− =−= =
'' 1()sin25.2
2
x
yxy ksi w
τ
σσ θ τ =− − =− =
y
’
12 ksi 5.2 ksi
x
’
35o
Weld 13.9 ksi
24 ksi
x
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