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Hello, I am looking for a formula (in International Units) for checking a pipe of 14" under external pressure. For internal pressure I use Barlow's formula. Is there any formula for determining the spacing between buckle arrestors?

Thank you very much in advance.


For pipe collapse checks, look at
* BS 8010, Pt 3, Annex C
* Timoshenko and Gere, Theory of elastic stability (Book)
* Murphy and Langer, Ultimate pipe strength under bending (technical paper, maybe OTC)
* DNV 1996 and DNV 2000
These are not in any particular order other than as I found them within my reference papers.

For spacing of buckle arrestors, it is a matter of cost and risk optimisation. If the spacing is too short, you pay up front for a lot more buckle arrestors. If the spacing is too long, then if a propagating buckle were to occur, you need to recover and replace a lot of pipe. In simplistic terms, the cost equation can be of the form :

Cost(S) = L*C1/S + K*C2*S
L = Pipeline length
C1 = Cost of buckle arrestor
S = Buckle arrestor spacing
K = Probability of propagating buckle
C2 = Cost of recovery and replacement of buckled section

The curve has a U-shape and the optimum point is obviously at its minimum. The optimum spacing has to be derived for each individual situation (C1, K, C2) and is not really dictated by any codes but by economic risks. In my last project, the spacing was selected at 500m.

Hope this is of some use.


Thank you very much Kiranpatel I will try to find the references but it will take me time.

Regarding the buckle arrestors, I suppose they are designed for the laying time and that the external pressure for 900 m is negligible compared with the stresses coming from the laying ?. Am I correct?

I suppose also that the probability of buckling depends in the laying technique S or J and  water currents. Is there any reference value for c1, k & c2 for 14 “ pipe at 900 m.?

Thank you again, in advance.


If your pipe has no stiffening rings, you may use the formula:
p=allowable external pressure (with this formula it equals 1/3 of the elastic buckling pressure)
E=elastic modulus
t=pipe thickness
D=pipe OD (use consistent units)
If the thickness is relatively high, you should also check the following
S=allowable stress of pipe material
Max.ovalisation should be limited to 1%.

Online tools for structural design


I would not under-estimate the external pressure in 900m of water depth. You may find that the governing criteria for the wall thickness is indeed the pipeline collapse. For the buckle arrestors, you will need even thicker pipe depending on the length of the buckle arrestor and the main line wall thickness.

If you have trouble finding the references, let me know your fax number or email address and I can send over some pages.

With regard to the costs and risks, I cannot give you specific numbers but point out the following :
The cost of the buckle arrestor (C1) will depend strongly on its design, such as wall thickness, method of manufacture, operating condition (e.g. sour service ?), etc. The only way to get this is to go for quotes from suppliers.
The cost of repair (C2) is directly related to the construction vessels involved. As the number of players able to lay this line will be limited, the costs can become distorted depending on market conditions, vessel availability, etc. You should have some estimate of this from your overall project cost database.
K is purely a guess factor, there are no historical data that you can base your values on. However, unless the pipeline is extremely long, I would suggest that you allow for the possibility of one buckle. Less than that, you are exposed to some risks. More than that, you could end up with a lot of spare pipe left over at the end requiring an embaressing explanation to the bean counters.



Thank you Kiranpatel and prex. I have checked the wall thickness based in the formula for buckling of high thickness pipes and because the high internal pressure selected for the pipe (roughly 250 bar & the deeper water is 700 m)the external pressure drives to similar thickness.

For my feasibility study it is enough. I have asked for references it will give culture for next occasions.

Thanks again.

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