Combination of radial and axial+bending loads in piping
Combination of radial and axial+bending loads in piping
(OP)
I have a query about combination of radial stresses as well as bending stresses. Basically I'd like to be able to quickly check by hand that the thickness of a pipeline is adequate enough for combined loading.
To make things easier, say for example I have a 10 ft. long pipe that is simply supported and filled with some liquid, say water at some pressure.
In terms of hoop stress, I'd have S(hoop) = PD/2t and S(long) = PD/4t
Structurally I'd essentially have a beam of circular cross-section such that S(bend) = My/I with M being my bending moment taking into account weight of piping + fluid.
How would I be able to combine these stresses so that I can check to see if they are acceptable? Usually I'd combine them using the principle stress equations however that would work if the stresses are in one coordinate system and not two. (My example would have bending about the x-axis, longitudinal stress in the x-direction and a radial stress)
To make things easier, say for example I have a 10 ft. long pipe that is simply supported and filled with some liquid, say water at some pressure.
In terms of hoop stress, I'd have S(hoop) = PD/2t and S(long) = PD/4t
Structurally I'd essentially have a beam of circular cross-section such that S(bend) = My/I with M being my bending moment taking into account weight of piping + fluid.
How would I be able to combine these stresses so that I can check to see if they are acceptable? Usually I'd combine them using the principle stress equations however that would work if the stresses are in one coordinate system and not two. (My example would have bending about the x-axis, longitudinal stress in the x-direction and a radial stress)





RE: Combination of radial and axial+bending loads in piping
"The objective is to develop a yield criterion for ductile metals that works for any complex 3-D loading condition, regardless of the mix of normal and shear stresses. The von Mises stress does this by boiling the complex stress state down into a single scalar number that is compared to a metal's yield strength, also a single scalar numerical value determined from a uniaxial tension test (because that's the easiest) on the material in a lab."
http://www.continuummechanics.org/cm/vonmisesstres...
RE: Combination of radial and axial+bending loads in piping
RE: Combination of radial and axial+bending loads in piping
Unless I am over complicating things to the extent that the hoop stresses can be considered as a stress in a y-direction for example.
RE: Combination of radial and axial+bending loads in piping
And the radial stress is usually pretty small (+/-1000 psi) in relation to the others, which might be typically around 20,000 axial, 10,000 bending, 40,000 hoop stress.
RE: Combination of radial and axial+bending loads in piping
RE: Combination of radial and axial+bending loads in piping
Work with the stresses on the free body element shown. If you want to consider pressure stress in a 3D stress equation, as you would do when designing a mechanical device, and use von Mises, axial stresses are X, hoop stresses are Y and radial is Z. Although Z's angle about the X axis would vary according to where you cut your free body element.