Formulas
COLLAPSE PRESSURE
For Minimum Collapse Failure in the Plastic Range with Minimum Yield Stress Limitations:
Applicable D/t Span
API GRADE | D/T RATIO SPAN |
H-40 casing and tubing | 16.40 and less |
K-55 casing and J-55 tubing | 14.81 and less |
C-75 casing and tubing | 13.60 and less |
L-80 and N-80 casing and tubing | 13.38 and less |
C-90 casing and tubing | 13.01 and less |
C-95 casing, X-95 drill pipe, and T-95 casing and tubing | 12.85 and less |
P-105 tubing | 12.57 and less |
P-110 casing | 12.44 and less |
Q-125 casing | 12.11 and less |
For Minimum Failure in the Plastic Range:
Factors and Applicable D/t Span
API GRADE | A | B | C | D/T RATIO SPAN |
H-40 | 2.950 | .0465 | 754 | 16.40 to 27.01 |
J-55 and K-55 | 2.991 | .0541 | 1206 | 14.81 to 25.01 |
C-75 and E | 3.054 | .0642 | 1806 | 13.60 to 22.91 |
L-80 and N-80 | 3.071 | .0667 | 1955 | 13.38 to 22.47 |
C-90 | 3.106 | .0718 | 2254 | 13.01 to 21.69 |
C-95 | 3.124 | .0743 | 2404 | 12.85 to 21.33 |
P-105 | 3.162 | .0794 | 2702 | 12.57 to 20.70 |
P-110 | 3.181 | .0819 | 2852 | 12.44 to 20.41 |
Q-125 | 3.239 | .0895 | 3301 | 12.11 to 19.63 |
For Minimum Failure in Transition Zone Between Plastic and Elastic Range:
Factors and Applicable D/t Ratio Span
API GRADE | F | G | D/T RATIO SPAN |
H-40 | 2.063 | .0325 | 27.01 to 42.64 |
J-55 and K-55 | 1.989 | .0360 | 25.01 to 37.21 |
C-75 | 1.990 | .0418 | 22.91 to 32.05 |
L-80 and N-80 | 1.998 | .0434 | 22.47 to 31.02 |
C-90 | 2.017 | .0466 | 21.69 to 29.18 |
C-95 | 2.029 | .0482 | 21.33 to 28.36 |
P-105 | 2.053 | .0515 | 20.70 to 26.89 |
P-110 | 2.066 | .0532 | 20.41 to 26.22 |
Q-125 | 2.106 | .0582 | 19.63 to 24.46 |
For Minimum Failure in the Elastic Range:
Applicable D/t Span
GRADE | D/T RATIO SPAN |
H-40 | 42.64 and greater |
J-55 and K-55 | 37.21 and greater |
C-75 | 32.05 and greater |
L-80 and N-80 | 31.02 and greater |
C-90 | 29.18 and greater |
C-95 | 28.36 and greater |
P-105 | 26.89 and greater |
P-110 | 26.22 and greater |
Q-125 | 24.46 and greater |
Yp = Minimum Yield Strength
GRADE | FACTORS IN PSI |
H-40 | 40,000 |
J-55 and K-55 | 55,000 |
C-75 | 75,000 |
L-80 and N-80 | 80,000 |
C-90 | 90,000 |
C-95 | 95,000 |
P-105 | 105,000 |
P-110 | 110,000 |
Q-125 | 125,000 |
S-135 | 135,000 |
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 STRENGTH
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 |
D | *.74 D 0.59 | ||
4 1/2 | .30467 | ||
5 | .28631 | ||
5 1/2 | .27066 | ||
6 5/8 | .24251 | ||
7 | .23476 | ||
7 5/8 | .22321 | ||
8 5/8 | .20756 | ||
9 5/8 | .19455 | ||
10 3/4 | .18226 | ||
11 3/4 | .17295 | ||
13 3/8 | .16022 | ||
16 | .14415 | ||
18 5/8 | .13179 | ||
20 | .12636 |
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. |