API Formules

For Minimum Collapse Failure in the Plastic Range with Minimum Yield Stress Limitations:

Applicable D/t Span

For Minimum Failure in the Plastic Range:

Factors and Applicable D/t Span

For Minimum Failure in Transition Zone Between Plastic and Elastic Range:

Factors and Applicable D/t Ratio Span

For Minimum Failure in the Elastic Range:

Applicable D/t Span

Yp = Minimum Yield Strength

Where:

Minimum collapse pressure in psi
D = Nominal outside diameter in inches
t = Nominal wall thickness in inches
Collapse Pressure Under Axial Tension Stress:

Minimum collapse pressure under axial load can be determined from tables in API Bul 5C2, 20th Edition, 1987.

Internal Pressure

Internal Yield Pressure
(Casing, Tubing and Drill Pipe - Minimum Wall)

Where:
Pl = minimum internal yield pressure in psi
D = nominal outside diameter of pipe in inches
t = nominal wall thickness of pipe in inches
Yp = specified minimum yield strength in psi
Internal Pressure of pipe at 80% of Minimum Yield:
(Also: Maximum Formation Fracturing Pressure)

Internal Pressure of Couplings:

Where:
S = 80% of Yp for mill test pressure and for maximum fracturing pressure
= 100% of Yp for internal yield pressure
W (W1 for special clearance) = outside diameter of coupling
d1 = thread root diameter of coupling at end of pipe in power-tight position
For round thread casing and tubing couplings:

where:
T = included taper on diameter
Other symbols are listed in API Std. 5B.

For buttress thread casing couplings:

Where:
T = included taper on diameter
l = 0.400 in. for 41/2 in. OD
= 0.500 in. for 5 in. through 133/8 in. OD
= 0.375 in. for 16 in. OD and larger
Other symbols are listed in API Std.5B.

Internal Pressure Leak Resistance:

Where: 
P = internal pressure, psi
E = 30 x 106
T = thread taper
N = no. of thread turns make-up
p = thread pitch
W = coupling OD
Es = E1 for round thread
= E7 for buttress thread

Joint Strenght

Round Thread Casing
The following equations apply to both short and long threads and couplings. One is for failure by fracture and the other is for failure by thread jumping or pullout; the lesser of the resulting values is listed as the joint strength.
Fracture Strength:

Pullout Strength:

Where:
Pj = minimum joint strength in pounds
Ajp = cross-sectional area of the pipe wall under the last perfect thread, in square inches
= 0.7854 [ ( D - 0.1425)2 -d2 ]
D = nominal outside diameter of pipe in inches
d = nominal inside diameter of pipe in inches
L = engaged thread length in inches
= L4 - M for nominal make-up, as listed in API Std. 5B
Yp = minimum yield strength of pipe in pounds per square inch
Up = minimum ultimate strength of pipe in pounds per square inch

Buttress Thread Casing
For casing with buttress threads, two formulas are used; one is for the strength of the threaded pipe and the other, for the coupling. The lesser of the values obtained by the two formulas governs.
Pipe Strength:

Coupling Thread Strength:

Where:
Pj = minimum joint strength in pounds
Yp = minimum yield strength of pipe, psi
Up = minimum ultimate strength of pipe, psi
Uc = minimum ultimate strength of coupling, psi
Ap = cross sectional area of pipe, square inches
        .7854 ( D2 - d2 )
Ac = cross sectional area of coupling, square inches
        = .7854 ( W2 - d12 )
D = outside diameter of pipe, inches
d = inside diameter of pipe, inches
W = outside diameter of coupling, inches
d1 = diameter at the root of the coupling thread at the end of the pipe in the power-tight position

Tension Yield Load

Drill Pipe and Round Thread Tubing
Yield strength values for round thread tubing and drill pipe are determined as the product of the specified minimum yield strength for the steel grade and the area of section under the root of the last perfect thread of the pipe or of the area of the body of the pipe, whichever is smaller.
Non-Upset Tubing:

External Upset Tubing and Internal and External Upset Drill Pipe:

Where:
Pj = minimum joint strength in pounds
D = nominal outside diameter of pipe in inches
d = nominal inside diameter of pipe in inches
hs = height of thread in inches
     = 0.05560 in. for 10 threads per inch
     = 0.07125 in. for 8 threads per inch
Yp = specified minimum yield strength of pipe in pounds per square inch. Values are listed elsewhere.