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nt external pressure,
po = external pressure,
pi = internal pressure,
and
?p = po pi.
To provide a more intuitive understanding of the sense of this
relationship, Eq.6 can be rewritten as
Vol2 page 0294 eq 001.png....................(7)
where
D = nominal outside diameter,
and
d = nominal inside diameter.
In Eq. 7, we can see the internal pressure applied to the
internal diameter andthe external pressure applied to the external
diameter. The "equivalent" pressure applied to the external
diameter is the difference of these two terms.
Axial strength
The axial strength of the pipe body is determined by the pipe
body yield strength formula found in API Bull. 5C3, Formulas and
Calculations for Casing, Tubing,Drillpipe, and Line Pipe
Properties.[1]
Vol2 page 0294 eq 002.png....................(8)
where
Fy = pipe body axial strength (units of force),
Yp = minimum yield strength,
D = nominal outer diameter,
and
d = nominal inner diameter.
Axial strength is the product of the cross-sectional area (based
on nominal dimensions) and the yield strength.
Combined stress effects
All the pipe-strength equations previously given are based on a
uniaxial stressstate (i.e., a state in which only one of the three
principal stresses is nonzero). This idealized situation never
occurs in oilfield applications because pipein a wellbore is always
subjected to combined loading conditions. 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
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combined loading conditions, the uniaxial yield strength is
compared to the yielding condition. Perhaps the most widely
accepted yielding criterion is based onthe maximum distortion
energy theory, which is known as the Huber-Hencky-Misesyield
condition or simply the von Mises stress, triaxal stress, or
equivalent stress.[3] Triaxial stress (equivalent stress) is not a
true stress. It is a theoretical value that allows a generalized
three-dimensional (3D) stress state to becompared with a uniaxial
failure criterion (the yield strength). In other words, if the
triaxial stress exceeds the yield strength, a yield failure is
indicated. The triaxial safety factor is the ratio of the materials
yield strength to thetriaxial stress.
The yielding criterion is stated as
Vol2 page 0295 eq 001.png....................(9)
where
Yp = minimum yield stress, psi,
sVME = triaxial stress, psi,
sz = axial stress, psi,
s? = tangential or hoop stress, psi,
and
sr = radial stress, psi.
The calculated axial stress, sz, at any point along the
cross-sectional area should include the effects of:
Self-weightBuoyancyPressure loadsBendingShock loads
Frictional dragPoint loadsTemperature loadsBuckling loadsExcept
for bending/buckling loads, axial loads are normally considered to
be constant over the entire cross-sectional area.
The tangential and radial stresses are calculated with the Lam
equations for thick-wall cylinders.
Vol2 page 0295 eq 002.png....................(10)
and
Vol2 page 0295 eq 003.png....................(11)
where
pi = internal pressure,
po = external pressure,
ri = inner wall radius,
