Strength of a partially Submerged Pipe Casing

[csus_student]

Im not sure how to analyze this.

I have a 8ft dia. pipe casing that I am submerging into the mud in 10 ft of water. the top is open. What i need to find is if the .25" wall thickness is sufficent to keep the casing from collapsing. I know i have about 624 psf at the bottom of the casing, but how do I determine if the casing can handle it?

Assume Fy of the steel is 36ksi.

Let me know if i need to provide any more information, or just state the assumption you made if you need to make one.

This is not a HW assignment, but something I am doing at work.

Thanks in advance!

Jared

 

[csus_student]

Here is a simple sketch of the situation.

 

[ank_gl]

Calculate the static pressure at the bottom & see section 13.5 Thin Shells of Revolution under External Pressure, Roark's formula for stress & strain.

 

[stewartcs]

Im not sure how to analyze this.

I have a 8ft dia. pipe casing that I am submerging into the mud in 10 ft of water. the top is open. What i need to find is if the .25" wall thickness is sufficent to keep the casing from collapsing. I know i have about 624 psf at the bottom of the casing, but how do I determine if the casing can handle it?

Assume Fy of the steel is 36ksi.

Let me know if i need to provide any more information, or just state the assumption you made if you need to make one.

This is not a HW assignment, but something I am doing at work.

Thanks in advance!

Jared

API 5C3 gives another method also that you can use to determine the collapse resistance of the casing.

EDIT:
A quick hand calculation using API 5C3 gives me about 1.8 ft before it collapses (with your given data). It appears this is due to the large diameter of the casing (8 ft).

CS

 

[Q_Goest]

Hi stewartcs. Interesting about the API code. Do they take into account the length of pipe exposed to external pressure? Do they also consider the linear pressure distribution?

Are you familiar with ASME BPV code and how they do it? I don't believe ASME code considers the linear pressure distribution, but I could be wrong. Also, the code method is very complex, requiring one to reference various figures for the material in question. It's pretty painful to do it by the code, so I wonder how easy it is in comparison to use the API code.

 

[stewartcs]

Hi stewartcs. Interesting about the API code. Do they take into account the length of pipe exposed to external pressure? Do they also consider the linear pressure distribution?

Are you familiar with ASME BPV code and how they do it? I don't believe ASME code considers the linear pressure distribution, but I could be wrong. Also, the code method is very complex, requiring one to reference various figures for the material in question. It's pretty painful to do it by the code, so I wonder how easy it is in comparison to use the API code.

Hi Q,

Long time no see!

No, API doesn't account for the length of pipe exposed to external pressure. They also do not consider the linear pressure distribution. However, they do account for axial tension in the pipe.

They have 4 formulas based on empirical data and common theories. The 4 formulas are:

[1] Yield Strength Collapse Pressure - (theoretical basis)
[2] Elastic Collapse - (theoretical basis)
[3] Plastic Collapse - (empirically derived)
[4] Transition Collapse (plastic/elastic transition that is) - (arbitrarily derived)

Eqn. [1] is based on the pressure that generates minimum yield stress on the inside wall of the tube calculated by means of the Lame equation.

Eqn. [2] was derived from the theoretical elastic collapse pressure formula by W.O Clinedinst.

Eqn. [3] was derived by statistical regression analysis.

Eqn. [4] was arbitrarily derived to allow extension of the average plastic collapse pressure for higher D/t values.

I am, or was, familiar with ASME BPV code but haven't looked at it in a while. The API formulas can be easily used in a simple spreadsheet without the need for referring to any charts or tables.

Best Regards,

CS

 

[Mech_Engineer]

It's going to be difficult to accurately predict the buckling strength of such a structure, mainly due to the fact that it has such a low wall thickness to diameter ratio. Small discrepancies in the circularity of the wall's cross-section (tank ends up elliptically or oval-shaped) can have drastic effects on it's overall buckling strength. Additionally, it can't really be modeled using the submerged pipe codes because it has a relatively short legnth, the hydrostatic load changes drastically along its legnth, and (I'm assuming) it's bottom is fixed to the floor, meaning it it stiffened against buckling on the bottom. I'm not sure there is a quick and dirty analytical solution to this problem.

That being said, a quick linear buckling run through ANSYS with a fixed base and a simple hydrostaic load on the tank's outer wall shows that it's buckling strength is about 12x that of the simple hydrostatic load. But, keep in mind that is for a perfectly circular tank with a perfectly uniform hydrostatic load on it; any non-linearities in the tank or load will drastically reduce it's strength.

 

[Q_Goest]

Hi Mech_E. You raise lots of good points. Predicting buckling, like anything in the real world, is only as good as the model you use. I think what stewartcs has done though is to simply apply the code with all its inherent conservatism. For example, the API code apparently doesn't account for length of pipe, so it is very conservative on that account for 3 reasons that you mention:

Additionally, it can't really be modeled using the submerged pipe codes because it has a relatively short legnth, the hydrostatic load changes drastically along its legnth, and (I'm assuming) it's bottom is fixed to the floor, meaning it it stiffened against buckling on the bottom.

But making the assumptions used in the code (that the pipe is infinite in length, the pressure load is constant, and there is no stiffening provided by the floor) makes the analysis very conservative.

Interestingly, the ASME BPV code takes into account the length of the cylinder and also any stiffening reinforcement. I'm not aware of anything in the code that takes into account the linear pressure distribution, but I suspect there's some guidance on that. I'm just not familiar enough to know for sure.

Anyway, I'm not surprised the value you got was considerably less conservative (more accurate probably) than an API calculated value. As you elude to, there needs to be some factor of safety applied to a value such as the one you've provided. Personally, I'd start with a value such as provided by the API or ASME code, and then if it wasn't good enough and I knew the value was overly conservative, I might consider trying an FEA model and then applying a safety factor of at least 2 depending on the realities of the situation.

 

[Mech_Engineer]

For anyone curious, here's the first buckling mode for the tank being discussed. I ran the same model with a 1" out of round (elliptical tank) and it had little to no effect on the predicted buckling failure, which is a good sign (I was thinking it might drop the buckling strength by a significant margin).

As far a buckling and FEA go, a linear buckling analysis is not the most conservative estimate but I don't have time to do a non-linear analysis of the tank. I also didn't do any mesh convergence studies, so I wouldn't take this result as gospel.

 

[stewartcs]

It's going to be difficult to accurately predict the buckling strength of such a structure, mainly due to the fact that it has such a low wall thickness to diameter ratio. Small discrepancies in the circularity of the wall's cross-section (tank ends up elliptically or oval-shaped) can have drastic effects on it's overall buckling strength. Additionally, it can't really be modeled using the submerged pipe codes because it has a relatively short legnth, the hydrostatic load changes drastically along its legnth, and (I'm assuming) it's bottom is fixed to the floor, meaning it it stiffened against buckling on the bottom. I'm not sure there is a quick and dirty analytical solution to this problem.

That being said, a quick linear buckling run through ANSYS with a fixed base and a simple hydrostaic load on the tank's outer wall shows that it's buckling strength is about 12x that of the simple hydrostatic load. But, keep in mind that is for a perfectly circular tank with a perfectly uniform hydrostatic load on it; any non-linearities in the tank or load will drastically reduce it's strength.

I agree that it would be difficult to predict a definitive answer for this type of problem analytically. Hence, I used the API codes to get a conservative answer most of the time. If the situation is critical enough that a more exact answer is needed (due to material or cost or whatever) then it may be worth the extra effort to perform a non-linear FEA.

That being said, we use API 5C3 on a regular bases for our casing and riser collapse resistance calcs and have never had a problem. Of course I do have another specialty program that checks the buckling/stability of the column under dynamic loading conditions. But for collapse resistance 5C3 works well for me. Caveat: I deal with long vertical columns (up to 12,000-ft in height).

Also, regarding ovality, API concluded that although theoretical studies on the effect of tubular collapse resistance consistently indicated that an ovality of 1 to 2 percent can effect a reduction in collapse resistance on the order of 25%, experimental/empirical investigations indicate a much smaller effect. Hence, they do not consider it to be a dominant parameter and do not account for it in their collapse resistance formulas.

Now, if you really want to get fancy, you can throw in a soil interaction model with P-Y curves to model the base of the column properly. Unfortunately, soil interaction is very sensitive to parameter changes so I'm not sure how accurate of an answer you would get. Generally speaking it's not worth the extra effort.

CS