Thick Walled Cylinder Question

[PipesAndStuff]

Hello,

I'm determining the change in length of an 8-inch (DIPS) SDR11 HDPE pipe after pressurizing due the Poisson effect. I'm treating the pipe as a thick walled cylinder since the pipes diameter/thickness < 20.
I'm using the attached equations to compute axial, tangential, and radial stresses. Then computing the axial strain and multiplying by the pipe's length.

Here are the parameters:
Poison Ratio = 0.45
Elastic Modulus = 150,000 psi
Inside Radius = 3.7 inches
Outside Radius = 4.5 Inches
Inside Pressure = 180 psi
Pipe Length = 1000 ft

When I compute the stress for the inside wall of the pipe, I get a change in length of 29.1 Inches.
When I compute the stress for the outside wall of the pipe, I get a change in length of 2.9 inches.

I'm not sure which result to use or if I am approaching this problem correctly. I appreciate any insight people have for this problem.

Thanks,
Tony

 

[goutam_freelance]

The exact elongation calculation is complicated. The inside and outside surfaces will try to elongate differently, so shear stresses may develop, which may try to make the elongation uniform.

Using your formulae (with sign correction in sirgma_r & sigma_theta) in Matlab I get the following stresses:


And the strains are as below:

The longitudinal strain is almost constant at 0.9461e-3 in/in

So the elongation is 1000ftx12x0.9461e-3=11.35 in

 

[XR250]

I don't understand. For just the length change, isn't is just PL/AE? With P being the pressure acting on the end area?

 

[LittleInch]

Never heard of the poisson effect?

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj-mMirluSMAxUpWkEAHaX1B5oQFnoECBUQAQ&url=https%3A%2F%2Fwww.cpchem.com%2Fsites%2Fdefault%2Ffiles%2F2020-04%2FPP813-TN%2520Poisson%2520Effects.pdf&usg=AOvVaw0aBuF4vrG7eFj1x2iqTML7&opi=89978449

 

[XR250]

Never heard of the poisson effect?

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj-mMirluSMAxUpWkEAHaX1B5oQFnoECBUQAQ&url=https%3A%2F%2Fwww.cpchem.com%2Fsites%2Fdefault%2Ffiles%2F2020-04%2FPP813-TN%2520Poisson%2520Effects.pdf&usg=AOvVaw0aBuF4vrG7eFj1x2iqTML7&opi=89978449

Now I have So if you just take a pipe, seal off one end and pressurize the other end, PL/AE doe not apply?

 

[prex]

sigma_theta+sigma_r is not almost constant, it is exactly constant.
To me the elongation due to end pressure only is 30 in, the contraction due to Poisson effect id 27 in, for a total elongation of 3 in

 

[goutam_freelance]

is just PL/AE? With P being the pressure acting on the end area

This is for uniaxial stress P is applied at outside surface.For internal pressure there is triaxial stress.

 

[LittleInch]

sigma_theta+sigma_r is not almost constant, it is exactly constant.
To me the elongation due to end pressure only is 30 in, the contraction due to Poisson effect id 27 in, for a total elongation of 3 in

It's not as simple as that.

Yes, seal off a pipe and you have end cap force. How that translates to expansion though needs to be assessed. A 10m length of pipe will have very little,friction from any supports so it expands as you say. This is 330m of pipe and the friction from the supports will tend to reduce expansion.

But all this for PE is dwarfed by what happens for one degree C change in temperature. It's expands 10 times that of steel.

 

[XR250]

Fair enough. I saw,"I'm determining the change in length of an 8-inch (DIPS) SDR11 HDPE pipe" and went with what I know.
Learn something new every day.