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| Author | Comment |
bob
 Jun 6, 06 - 10:17 AM |
Hoop Stress Poisson's Effect
In a pipe with no axial restraint subjected to internal pressure, Hoop stress, S = PD/2/t. A Poisson effect of dimensional shortening in directions normal to the hoop stress in the pipe wall is created. Considering the axial direction only, axial pipe contraction therefore = Poisson Ratio * S * Pipe Length /Young's Modulus. Question: Is the Poisson effect of axial contraction accompanied by a corresponding tensile stress = Poisson Ratio * S, or is this a deformation where strain is not caused by the usual accompanying stress? It appears not, as should the pipe be 100% axially restrained at both ends, restraint loads would = Poisson Ratio * Pipe Area * S. Then cutting a free body of the pipe in the area of the support and examining the resulting stress would indicate that the Restraint Load/Pipe Area tensile stress + a Poisson contractive tensile stress, multiplied by pipe area, would = 2 X the restraint reaction. I hence draw the conclusion that the Poisson effect produces no axial load, if the pipe is freely allowed to contract. Is this conclusion correct? Thanks for your comments. |
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bob
Jun 6th, 2006 - 10:48 AM |
Re: Hoop Stress Poisson's Effect
I think I may be able to answer my own question. The poisson stress is not a tensile stress. It is of opposite sign to the hoop stress; therefore compressive. Am I getting closer? |
Randy Conner
Jun 28th, 2006 - 10:17 PM |
Re: Hoop Stress Poisson's Effect
If the pipe is in essence "floating freely" e.g. within low friction o-ring or stuffing seals sealing on the outside of its extreme ends of the pipe, in my opinion the only axial stress on the pipe would be a (normally relatively low) compressive stress reaction to the contents pressure acting against the radial end face of the pipe. If the pipe is on the other hand bulkheaded (e.g. with caps/plugs/plates etc.), is not externally held or restrained, and thus becomes like a self-contained pressure vessel, by free-body analysis one can find that the axial stress in the pipe is instead tensile and of a generally quite higher magnitude (i.e. about half the hoops stress value). If a solid length of piping is axially/externally fixed/restrained on the ends in some fashion, I think this becomes a more complex matter, where Poisson effects etc. might enter more in to the stress picture. |
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