sm8 93

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PROBLEM (8.93) A cylindrical vessel of internal diameter 200 mm and wall thickness 2 mm has a
welded helical seam angle of
φ
= 60o (see: Fig. P8.92). The allowable tensile stress in the weld is 100
MPa. Determine, the maximum value of internal pressure p and the corresponding shear stress in the
weld, using:
(a) Equations (8.4).
(b) An approach based on the equilibrium equations applied to a wedge shaped stress element.
(c) Mohr’s circle.
SOLUTION
(a)
θ
2100 25
22(2)
pr P P
t
σ == =
x’
y’
60o
x
150
P
σ
=
150o θ =
'100 (25 50) (25 50)cos300
22 o
xpp
σ == ++ − , MPap 2.3
=
'' 3.2 (25 50)sin300
2o
xy
τ =− − 34.6 w MPa
τ
=
−=
(b)
:0
'=
∑x
F
pAA 2
)866.0(25100 Δ−Δ
0
0
)5.0(50 2=Δ− pA 25P
x
’
y
’
100 MPa
τ
50P
60o
A
Δ
or
MPap 2.3=
:0
'=
∑y
F
)]866.05.0(50)866.05.0(25[2.3
=
×
Δ
−
×
Δ
−
ΔAAA
τ
or
34.6 w
MPa
τ
τ ==
Continued on next slide
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(c)
1
12
(100) 50 25
22
pr p
p
p
t
σ
σσ == = ==
o
xpp 60cos5.125.37100
'−==
σ , 3.2
p
MPa
=
'' 12.5 sin60 34.6
o
x
yw
pMPa
τ
τ =− =− =
25p 50p
O
τ
σ (MPa)
C
x
’
120o
R
25p
R
=12.5p
60o
50p
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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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