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