Casing Design Triaxial stress analysis
Aguieb Larbi Ben Yagoub Mohammed Prepared by: Tan Nguyen
Casing Design
Combined Stress Effects (Triaxial
stress analysis)
The fundamental basis of casing design is that if stresses in the pipe wall exceed the yield strength of the material, a failure condition exists. Hence the yield strength is a measure of the maximum allowable stress. To evaluate the pipe strength under combined loading conditions, the uniaxial yield strength is compared to the yielding condition.
The most widely accepted yielding criterion is based on the maximum
distortion
energy
theory,
which
is
known
as
the
Huber-Von-Mises Theory. This theory states that if the triaxial stress exceeds the yield strength, a yield failure is indicated. Note that the triaxial stress is not a true stress. It is a theoretical value that allows a generalized three-dimensional stress state to be compared with a uniaxial failure criterion (the yield strength).
Casing Design
s
VME
1 2
s
z
s t
2
s
t
Where s
Y
– minimum yield stress, psi
s
VME
– triaxial stress, psi
VME: Von Mises Equivalent s
z,
t,
s
s
– axial tress, tangential
r
stress, and radial stress, psi
s r
2
s
r
s z
2
s Y
1
Casing Design
Setting the triaxial stress equal to the yield strength and solving equation (1) give the results: s
t
pi
s
Y
3 s z
2
pi 1 s z pi 1 4 s Y 2 s Y
(2)
pi –internal pressure s
t
– tangential stresses
(3)
This equation is for the ellipse of plasticity. Combining this eq. and the equation of tangential stresses together and let r = r i, will give the combinations of internal pressure, external pressure and axial stress that will result in a yield strength mode of failure.
Casing Design
As
axial
increases In
tension and
contrast,
critical
increases, the
the as
critical
burst-pressure
critical collapse-pressure decreases. the
burst-pressure
axial compression increases, the decreases
collapse-pressure increases.
and
the
critical
Casing Design
Example Compute the nominal collapse pressure rating for 5.5 ’’, N-80 casing with a nominal wall thickness of 0.476 ’’ and a nominal weight per foot of 26 lbf/ft. In addition, determine the collapse pressure for in-service conditions in which the pipe is subjected to a 40,000 psi axial tension stress and a 10,000 psi internal pressure. Assume a yield strength mode of failure. Solution
For collapse pressure rating, r = r i then eq. (3) becomes
s
t
pi ro ri 2
2
2 p r
2 e o
ro r i 2
2
pi ro ri
pi
s
t
s
s
t
2
r r i
t p i
s
s
Y
s
Y
2
pi
Y
Y
t
2 e o
s
pi
s
2 p r
2 o
Y
s
2
pi
2r o2 pi pe 2 2 ro r i s Y 25.52 pi pe 2 2 5.5 4.548 80,000
pi
pe
12,649
pe
12,649
Casing Design
z
s
From eq. (2) with
pi
0
we have
s
Y
pi
t
s
1
s
Y
pe
12,649
p e
1
12,649 psi
For in-service conditions of
pi
t
s
s
Y
z
s
pi
s
Y
10,000
z =
s
40,000 psi and p i = 10,000 psi
pe
12,649
40,000
10,000
80,000
0.625
Solving eq. (14) gives s
t
s
Y
p e
pi
10,000
12,649
16,684 psi
pe
0.5284
