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

www.tenaris.com

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)