JPE - Sept09 - cover2-4.pmd - Pipes & Pipelines International ...

154
Stress (MPa)
Global collapse, fixed-grip tension (IV.1.6.3-1 with k = 0):
As above (Equns 13 and 14) but with k = 0 (the limit load
does not depend on the crack position in the cross section).
Local collapse, pin-loaded (IV.1.6.3.2), solution (a):
d= t+ c, t1= t and W > d
This solution is approached when yielding takes place
across the whole loading-bearing area 2(t + c) t.
n
L
600
500
400
300
200
100
Stress (MPa)
0
0 1 2 3 4 5 6 7 8 9 10
400
300
200
100
=
⎛ αγ ⎞
2 ⎜
⎟ ⎟+ ⎜⎝1+ γ
⎟ ⎟⎠ c1
2
⎛ αγ ⎞
4 ⎜
⎟ + c
⎜
1
⎝1+ γ⎠
⎟
(IV.1.6.2-1 with l = 0) (15)
2
Strain %
8αγ
k ⎛ αγ⎞
c1
= 1− −⎜
⎜ ⎟
1 γ ⎜1 γ
⎟ (IV.1.6.2-3) (16)
+ ⎜⎝
+ ⎠ ⎟
Valid for:
1
1
g
> k ³ 0 and a£ - k and b<
2
2 1+
g
True stress R-O n=15
Eng stress R-O n=15
0.2% offset
0
0 0.2 0.4 0.6 0.8
Strain %
The Journal of Pipeline Engineering
True stress R-O n=15
Eng stress R-O n=15
0.2% offset Fig.5. Stress-strain curve used:
Local collapse, pin-loaded (IV.1.6.3.2), solution (b):
d= t+ c, t1= t and W > d
Sample issue
This is approached when yielding spreads through the
smallest ligament along the plate thickness. Solution (b) is
always less than or equal to Solution (a).
⎛ 2α
⎞
d= t ⎜
⎜1 ⎟
⎜⎝
− ⎟+
c, t1= t( 1− 2k)
and W > d
1−2k⎠⎟ n
L
⎛ 2α
⎞
⎜
⎜1 ⎟
⎜⎝
− ⎟(
1+
γ)
1−2k⎠⎟ =
⎛ 2α
⎞⎟
⎜
⎜⎜⎝ 1− ⎟+
γ
1−2k⎟⎠ Local collapse, fixed-grip tension:
1+ g( 1-2a) nL =
1+
g
(a - top) curve up to 10% strain;
(b - bottom) curve up to 0.8% strain.
(17)
(18)
(19)