sm8 99

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PROBLEM (8.99) A cylindrical pressure tank of inner diameter d is fabricated by shaping steel
plates of thickness and welding the plates along helical arcs of angle
c
t
φ
with a transverse plane
(Fig.P8.99). The end caps are spherical and have uniform wall thickness
s
t. The maximum internal
pressure in the tank is p. Calculate:
(a) The normal and absolute maximum shear stresses in the caps.
(b) The normal and absolute maximum shear stresses in the cylinder.
(c) 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 = 2.4 m, = 15 mm,
c
t
s
t = 10 mm,
φ
= 30o , p = 1.4 MPa
SOLUTION
(a) Stress in the sphere
1.4(1.2) 84
22(0.01)
pr
M
Pa
t
σ == =
max 1
() (0) 48
22
a
M
Pa
σ
τσ =−==
(b) Principal Stresses
1.4(1.2) 112
0.015
tpr
M
Pa
t
σ == =
56
2t
a
M
Pa
σ
σ ==
Absolute maximum shear stress
max 1
() ( 0)56
2
at
M
Pa τσ =−=
(c) 56 112 0
xa yt xy
MPa MPa
σ
σσσ == == = τ
For 30
θ =:
o
'11
( ) ( )cos2 84 14 70
22
wx xy xy
M
Pa σσ σσ σσ θ == + + − =−=
'' 1( )sin2 24.2
2
wxy x y
M
Pa ττ σσ θ == − =
70 MPa
x
’
30o
Weld
x
24.2 MPa
y’
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