Combination of radial and axial+bending loads in piping

[NovaStark]

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)

 

[BigInch]

Calculate combined stress using von Mises and check against an equivalent yield stress (yield stress in simple tension/SF). You might use a SF, safety factor, of = 2 for example.

"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/vonmisesstress.html

 

[BigInch]

If it is a piping code design, check the code. It will tell you which method to use. Von Mises can't be used in many. Tresca is generally favored for even more simplicity.

 

[NovaStark]

I understand the Tresca and Von Mises stresses which would would be more useful had I stresses in one coordinate system (xyz) and not two, (xy and radial).

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.

 

[BigInch]

It's only a 3D world.

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.

 

[NovaStark]

Sorry, I mixed up my terms, by radial I meant hoop. So that xy and hoop are in different coordinate systems with no clear way to combine to check if S(combined) < S(allowable)

 

[BigInch]

In code piping design we ignore direct radial (pressure) stress, finding it easier to set a direct limit to the hoop stress, knowing that pressure stress is always only a small percentage of that. With radial stress out of the way, we can concentrate on hoop and axial stresses by themselves and play with Mohr's circle diagrams to find the maximum shear stress. We set the safety factor low enough to account for the fact that we ignored the radial stress components.

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.