Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
➢ Collapse strength is defined as the external pressure required to
collapse the specimen of casing.
➢ Primary collapse loads are generated by the hydrostatic head of the
fluid column outside the casing string.
➢ With any external pressure, Pe and internal pressure, Pi , the classical
elasticity theory for this 2-D problem can be applied at any r, between
ri and ro.
➢ Assuming the pipe is subjected to only an external pressure, Pe (i.e.
Pi=0) yields:
 d



  n t − 1 

Pcr = Pe = 2( yield )eff  
2
  dn  
  t  
Pcr is called “yield-strength collapse”
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
➢ Strength of the casing under external pressure depends on:
▪ Length,
▪ Diameter,
▪ Wall thickness of the casing,
▪ Physical properties of the casing material (yield point, elastic limit,
Poisson's ratio, etc.).
➢ Casing, having a low dn/t ratio and
low strength, reaches the critical
collapse value as soon as the material
begins to yield under the action of
external pressure. This is so-called
'yield range'.
➢ In contrast, casing with high dn/t ratio and high strength, collapses
below the yield strength of the material (collapse can occur at lower
pressures than predicted by the previous equation).
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
➢ In this case, failure is caused by purely elastic deformation. The
collapse behavior is known as failure in the elastic range.
➢ The transition between the failure modes is governed by the tube
geometry and material properties.
➢ The transition from yield-strength collapse to elastic collapse is not
sharp but covers a significant range of dn/t values.
➢ Based on the results of many experimental tests, API has adopted two
additional collapse-pressure equations to cover the transition region:
▪ A plastic collapse rating for dn/t values just above the yieldstrength collapse region.
▪ A transition collapse region between the plastic collapse and
elastic collapse regions.
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
1
Copyright: Dr. Ahmed Kamel
2
3
PENG 3305
COLLAPSE PRESSURE
Yield-strength Collapse
 dn


  t − 1 

Pcr = Pe = 2( yield )eff  
2
  dn  
  t  
Upper Limit for the yield strength collapse:

F3 
 + (F1 − 2)
(F1 − 2) + 8 F2 +
( yield )eff 

d
1 n =
t

F3 

2 F2 +
( yield )eff 

2
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Plastic Collapse


 F1

Pcr = ( yield )eff 
− F2  − F3
  d n 

  t 

Upper limit of the plastic collapse range is calculated by:
2
dn
( ) (F − F )
=
t
) (F − F )
F + (
yield eff
3
Copyright: Dr. Ahmed Kamel
yield eff
1
4
2
5
PENG 3305
COLLAPSE PRESSURE
Transition (between elastic and plastic) Collapse


 F4

Pcr = ( yield )eff 
− F5 
  d n 

  t 

Upper limit of the transition or lower limit of elastic collapse range is
calculated by:
F2
2+
F1
dn
=
3
t
F2
3
F1
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Elastic Collapse
Pcr =
Copyright: Dr. Ahmed Kamel
46.95 106
 d n  d n 
  − 1
 t  t

2
PENG 3305
COLLAPSE PRESSURE
F1 = 2.8762 + 0.10679  10 −5 Y + 0.21301  10 −10Y 2
− 0.53132  10 −16Y 3
F2 = 0.026233 + 0.50609 10 −6 Y
F3 = −465.93 + 0.030867Y − 0.10483  10 −7 Y 2
+ 0.36989  10 −13Y 3
 3(F2 / F1 ) 
46.95 10 
2 + (F2 / F1 )

F4 =
2
 3(F2 / F1 ) F2  
3(F2 / F1 ) 
Y
−  1 −
(
)
2
+
F
/
F
F1   2 + (F2 / F1 )
2
1

3
6
F5 = F4  F2 
 F1 
Y is the effective yield strength
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
EXAMPLE #1
Compute the collapse pressure rating for 5 1/2 in., N-80 casing with a
nominal wt./ft of 20 lbm/ft.
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Biaxial and Tri-axial Loading
➢ Performance properties are only for zero axial tension & no pipe
bending.
➢ Many casing properties are altered significantly by axial tension or
compression & bending stresses.
➢ The table values for the performance properties often must be
corrected before they are used in a casing design application.
➢ The effect of axial stresses on internal or external pressure is
explained by Ellipse of Plasticity equation:
 + P 
 + P 
 t
i  =  1− 3  z
i




4
 yield 



 yield 
2


1   z + Pi 
+ 

2 

 yield 
➢ (σt+ pi) / σy is positive if the pipe is subjected to an internal pressure
(burst) and negative if it is subjected to an external pressure
(collapse).
Copyright:
Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Biaxial and Tri-axial Loading
➢ Axial tension has a detrimental
effect on collapse pressure rating
and a beneficial effect on burstpressure rating.
➢ Axial
compression
has
a
detrimental effect on burstpressure rating and a beneficial
effect on collapse- pressure.
➢ In casing design practice, it is
customary to apply the EOP only
when a detrimental effect would
be observed.
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Biaxial and Triaxial Loading
➢ API recommended procedure for determining the collapse pressure in
the presence of a significant axial stress, z .
▪ Effective yield stress, (σyield)e, is first computed by:

 
2
 
 
 



yield
e 
3
1  z 


z
= 1− 
 − 2 

 

4 



yield 

 yield 
 yield 


▪ This equation is the EOP with Pi=0 (worst case)
▪ The effective yield strength is used in collapse (dn/t) equations to
determine the mode of failure.
▪ Collapse equations are then used for determining effective collapse
pressure.
▪ For an elastic mode of failure, collapse pressure is independent of
effective yield strength, and a corrected collapse pressure does not
have to be computed. The nominal collapse pressure shown in tables
can be used.
Copyright: Dr. Ahmed Kamel
PENG 3305
COLLAPSE PRESSURE
Biaxial and Triaxial Loading
EXAMPLE #2
Compute the corrected collapse-pressure rating for 20-in., K-55 csg with
a nominal wall thickness of 0.635-in. and a nominal wt/ft of 133 lbf/ft for
in service conditions where the axial tension will be 1,000,000 lbf. Also,
compute the minimum external pressure required for failure if the
internal pressure will be 1,000 psig.
Copyright: Dr. Ahmed Kamel
PENG 3305