calculation of burst yield
TRANSCRIPT
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
Calculation of Burst Yield and Collapse Yield for Round Tubing
Burst Yield We assume no external pressure for the calculation of burst yield. If we denote axial stressas sa, hoop stress sh and radial stress sr, then from thick-walled analytical results:
Where pi is the internal pressure, F is the tension force (weight here), ID is the tubing innerdiameter and OD is the outer diameter. Substituting (1) - (3) into the following Von Misescriterion
we get:
Where B = (OD2 + ID2) / (OD2- ID2), Sy is the yield strength. We should ignore the negativesign in (5) because it is physically insignificant. So, from the positive root, we can get theburst yield equation.
Figure 1 shows the burst yield for a tubing with OD = 2.375", WT = 0.175" (using its mini-mum value of 0.167") and 70,000 psi yield strength.
F(1)
(2)
(3)
(4)
(5)
(6)
(OD2 - ID2)4
πσ a =
(σ a = (B - 1)+1
(OD2 - ID2)
2(B2 + B + 1)
(OD2 + ID2)σ h =
(σa - σh )2 + (σh - σr )2 + (σr - σa )2 = 2Sy 2
σ r = p i
pi burst =
p i
σa2 (B - 1)2 + 4(B2 + B +1)(Sy
2 - σa2))
(σ a = (B - 1)+1
2(B2 + B + 1)pi = σa
2 (B - 1)2 + 4(B2 + B +1)(Sy2 - σa
2))
Coiled Tubes
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January 2007. ©Tenaris. All rights reserved
Burst & Collapse Graph
Figure 1. Burst yield and collapse yield curve.
15000
10000
5000
0
-5000
-10000
-15000
0 5000
Burst Yield
Collapse Yield
Physically insignificant burst
200001500010000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
Substituting (1), (7) and (8) into (4), we get
where C = 2 OD 2/(OD2- ID2). The negative sign is physically insignificant. The positive root isthe collapse yield solution. Because conventionally collapse pressure is negative, we add anegative sign before the positive root. So,
the collapse curve based on (10) is shown in Figure 1.
To make the whole curvelook better, we take thephysically insignificant rootfrom the burst result(equation 5) to add a thirdcurve to figure 1.
Burst and Collapse Curve
-σ a 4Sy2 - 3σa2
2Cpo
collapse =+
-σ a 4Sy2 - 3σa2
2Cpo =
+ (9)
(10)
Calculation of Burst Yield and Collapse Yield for Round Tubing
Collapse Yield We assume no internal pressure. Denote the external pressure as p0. The axial stress is thesame as that given by (1). The radial pressure at the inner surface is zero.
From analytical calculations, we get hoop stress
(7)
(8)
σ r = 0
OD2 - ID2
OD2
σh = -2po
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.087" 0.095"0.080" 0.102" 0.109"
1.000" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 5000 10000 15000 2500020000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.087" 0.095"0.080" 0.102" 0.109" 0.116"
0.134" 0.145"0.125" 0.156" 0.175"
1.25" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 10000 20000 30000 40000 50000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
Pressure capacity curves
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.50" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 10000 20000 30000 40000 700006000050000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.75" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 20000 40000 8000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.116" 0.125"0.109" 0.134" 0.145" 0.156"
0.190" 0.204"0.175"
2.00" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 1000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
2.375" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 1200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175"
2.625" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 1200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.145" 0.156"0.134" 0.175" 0.190" 0.204"
0.224"
2.875" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
0 20000 40000 140000100000 1200008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175" 0.225" 0.250"
3.5" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
0 50000 200000150000100000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.224" 0.250"0.204"
4.5" HS-70™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
10000
5000
0
-5000
-10000
0 50000 250000200000150000100000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.087" 0.095"0.080" 0.102" 0.109"
1.000" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 5000 10000 30000250002000015000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.087" 0.095"0.080" 0.102" 0.109" 0.116"
0.134" 0.145"0.125" 0.156" 0.175"
1.25" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 80,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 10000 20000 30000 40000 50000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.50" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 10000 20000 30000 40000 50000 60000 70000 80000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.75" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 80,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 20000 40000 60000 10000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.116" 0.125"0.109" 0.134" 0.145" 0.156"
0.190" 0.204"0.175"
2.00" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 20000 40000 60000 10000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
2.375" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 80,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 60000 12000010000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175"
2.625" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 60000 14000012000010000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.175" 0.190"0.156" 0.204" 0.224"
2.875" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 80,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 60000 160000100000 120000 14000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175" 0.225" 0.250"
3.5" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 50000 100000 250000150000 200000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.224" 0.250"0.204"
4.5" HS-80™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 80,000 psi yield strength.
10000
5000
0
-5000
-10000
0 50000 100000 300000250000150000 200000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.087" 0.095"0.080" 0.102" 0.109"
1.000" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 5000 10000 3000015000 20000 25000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.087" 0.095"0.080" 0.102" 0.109" 0.116"
0.134" 0.145"0.125" 0.156" 0.175"
1.25" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 90,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 10000 20000 30000 40000 6000050000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.50" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 10000 20000 30000 40000 8000060000 7000050000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.102" 0.109"0.095" 0.116" 0.125" 0.134"
0.156" 0.175"0.145" 0.190" 0.204"
1.75" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 90,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 20000 40000 1000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.116" 0.125"0.109" 0.134" 0.145" 0.156"
0.190" 0.204"0.175"
2.00" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 20000 40000 1200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.116" 0.125"0.109" 0.134" 0.145" 0.156"
0.175"
2.375" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 90,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 20000 40000 1400001200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175"
2.625" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 60000 160000120000 14000010000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.145" 0.156"0.134" 0.175" 0.190" 0.204"
0.224"
2.875" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 90,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 20000 40000 60000 180000160000120000 14000010000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.190" 0.204"0.175" 0.225" 0.250"
3.5" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 50000 100000 250000150000 200000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.224" 0.250"0.204"
4.5" HS-90™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 90,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 50000 100000 350000200000150000 250000 300000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.125" 0.134"0.102" 0.145" 0.156" 0.175"
1.25" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
30000
20000
10000
0
-10000
-20000
-30000
0 10000 20000 30000 40000 700006000050000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
1.50" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 110,000 psi yield strength.
30000
20000
10000
0
-10000
-20000
-30000
0 10000 20000 30000 40000 1000009000080000700006000050000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
1.75" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
30000
20000
10000
0
-10000
-20000
-30000
0 20000 40000 60000 12000010000080000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
2.00" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 110,000 psi yield strength.
20000
10000
0
-10000
-20000
0 20000 40000 140000100000 1200008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.134" 0.145"0.125" 0.156" 0.175" 0.190"
0.204"
2.375" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 20000 40000 1600001400001200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.134" 0.145"0.125"
2.625" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 110,000 psi yield strength.
25000
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0 20000 40000 1800001600001400001200001000008000060000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.145" 0.156"0.134" 0.175" 0.190" 0.204"
2.875" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
20000
15000
10000
5000
0
-5000
-10000
-15000
-20000
0 25000 50000 75000 200000175000125000 150000100000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
0.190" 0.204"0.175" 0.225" 0.250"
3.5" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 110,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 10000050000 150000 400000350000250000 300000200000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)
www.tenaris.com
January 2007. ©Tenaris. All rights reserved
0.204" 0.225"0.175"
4.5" HS-110™
Burst and Collapse yield calculated using the minimum wall thickness for the nominal wall thickness shown and 70,000 psi yield strength.
15000
10000
5000
0
-5000
-10000
-15000
0 10000050000 150000 400000350000250000 300000200000
BURS
TYI
ELD
(psi
)
LOAD (lbs)
COLL
APSE
YIEL
D(p
si)