sm8 96

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PROBLEM (8.96) A steel boiler of inner diameter d and thickness t is welded using a spiral seam
that makes an angle of
φ
with respect to axial axis (see Fig. P8.94). The boiler is subjected to an intrnal
pressure of p. Determine:
(a) The normal stress w
σ
perpendicular to the weld and shear stress w
τ
parallel to the weld.
Sketch the results on a properly oriented element.
(b) The absolute maximum shear stress in the boiler.
Given: d = 2r = 1.5 m, t = 15 mm,
φ
= 60o , p = 800 kPa
SOLUTION
09060
o
xa yt xy
σσ σσ τ θ ====−+= 30−
Principal stresses:
3
(800 10 )(750) 40
15
tpr
M
Pa
t
σ
×
== =
20
2t
a
M
Pa
σ
σ ==
(a) 11
()()cos
22
wxy xy
2
σ
σσ σσ θ =++−
11
(20 40) (20 40)cos( 60) 25
22
M
Pa=+ +− −=
1()sin
2
wxy
2
τ
σσ θ =− −
1(20 40)sin( 60) 8.66
2
M
Pa=− − − =−
(b) max 140
() ( 0) 20
22
at
M
Pa τσ =−==
20 MPa
8.66 MPa
x
’
30o
y’
40 MPa
Weld
x
25 MPa
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