Longitudinal stress in a pipe
Longitudinal stress in a pipe
(OP)
Internal pressure in a pipe leads to longitudinal stress, how is that?
Thomas
Thomas
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RE: Longitudinal stress in a pipe
At any capped end or valve, you'll develop longitudinal stresses unless the cap or valve is independently supported.
When you put hoop stresses in a cylinder, the cylinder gets shorter from Poisson's effect. If the pipe is restrained, this will give longitudinal stresses about 1/3 of the hoop stress.
At an unblocked ell or tee, you'll develop longitudinal stress in a pipe due fluid flowing.
RE: Longitudinal stress in a pipe
for circumeferncial stress, a free body diagram of a cylinder of length L, diameter D, wall thickness t and internal pressure P has the following stress relationship:
P*D*L=2*S,c*t*L, or S,c= PD/(2t)
For the same cylinder, the longitudinal stress is found by a similar free body diagram:
P*pi*D^2/4= pi*D*t*S,l, or S,l=P*D/(4t)
so the circumferntial stress is twice the longitudinal stress
RE: Longitudinal stress in a pipe
For pipeline computations, I have often simply dropped the longitudinal stress stated in Thick Walled Pressure Vessels, then applied Von MisesHencky. Of course this is in the absence of themal fluxuations which may cause stresses due to restraining. Also, JStephen correctly points out the implication of Poisson's Ratio.
Wow, "Law of the Hot Dog"! I never quite thought of the phenonema as such, probably won't forget about it now! "Law of the Hot Dog", sounds more like Mr SmartyPants in hockey getting his just beets.
Kenneth J Hueston, PEng
Principal
SturniHueston Engineering Inc
Edmonton, Alberta Canada
RE: Longitudinal stress in a pipe
RE: Longitudinal stress in a pipe
From a Stress Intensity (Tresca) perspective, the longitudinal stress exists, but is irrelevant. Stress intensity is defined as "the difference between the algebraically largest principal stress and the algebraicaly smallest principal stress at a given point." [VIII2 4112(a)] So if you take your principal stresses from highest to lowest as P1, P2, and P3 then stress intensity is P1P3.
If you agree that the circ stress (P1) is the highest tensile stress, and longitudinal is half that (P2) (and tensile), and that the radial stress is close to zero (except for thick wall cylinders) then the stress intensity = circ stress  radial stress. The longitudinal stress plays no role, though it does exist.
The von Mises criteria offers a similar approach to Tresca, and if you play with some numbers, you'll find that the longitudinal stress has little impact on the von Mises stress also.
jt
RE: Longitudinal stress in a pipe
RE: Longitudinal stress in a pipe
RE: Longitudinal stress in a pipe