Membrane Stress- What is it? 1

[iv2jm]

Hey folks,

I'm curious what a membrane stress is, and if it's pertinent to tubular beam sections analyzed by shells.

It's not something I remember from and classes and seems like its more relevant to pressure vessels.

May case involves a swing arm constructed from bent and welded sheet metal- basically box sections. I was considering bending stresses, but now that I've read about membrane stresses (and am a little unclear on them) I'm not sure if my analysis is accurate. Its one of those 'I didn't know I didn't know it' cases...

I looked around here but didn't think I found what I needed. I didn't even find a wiki article to be skeptical about! I apologize if I am duplicating any efforts.

Thanks for you help
Jimmy

 

[jte]

Membrane stress is simply a tensile or compressive stress which is uniform through thickness: Load/Area.

Now in your situation, if you have modeled the box section as a beam (either FEA or hand calc’s) and apply a moment, you’d evaluate the results vs allowable bending stresses. If you’ve built a shell or solid element FEA model, then the tensile “flange” would be experiencing tensile membrane stress while the compressive “flange” would be experiencing compressive membrane stress. The thing to look for here is whether a particular element is in a bending situation.

Acceptance criteria will vary depending on what code you are designing to.

jt

 

[Crompto29]

Outside of Pressure Vessel Design I haven't come across membrane stress.

An example of membrane stress is the uniform stress across the thickness of a pressurised shell.

I would imagine its closest equivalent in structural design would be the uniform axial stress in a beam under tensile or compressive load.

Membrane stresses and bending stresses are for Pressure Vessel Design.

Axial Stresses and bending Stresses are for Structural Design.

Check out PD 5500 Appendix A or ASME VIII:2009 Div 2 Section 5.2.2.2 for good definitions of all pressure vessel Stress Categories.

 

[BigTank]

see, while i generally agree with the interpretations given here, i think that the word 'membrane' when applied to a stress is something as conceptual as it is technical in terms of engineering importance, and thus applies to much more than pressure vessels.

first and foremost, stress is stress. force/area.

a membrane stress implies a stress equal over a surface resulting from some loading. often the loading that can impose a stress in this manner is a uniformly distributed load like internal or external pressure. thus it's presence in pressure vessels.

i'm not sure that a membrane stress will be uniform across a thickness...i don't think that is a valid assumption all of the time. nearly all pressure vessel calculations assume a thin walled vessel right from the get-go, thus inherently eliminating a stress gradiant across the thickness by nature of the calc. the equations for anything otherwise are very different from those used in section VIII. this thin-wall assumption might be where this idea comes from.

remember that calculated stresses often should be viewed as 'average' in some way. i.e. there might be differential elements that extend a bit further from a neutral axis, say, as a flange thickness along a length of beam might differ.

think of a round table top loaded around the outside edge of the table by a ring of steel. bending stress is imposed on the top across the diameter, obviously. differential elements adjacent to the diameter will help support said diameter by providing a 'membrane' through which to transfer stress to the next adjacent element...and so on as you move away from the diameter and around to 90°. the stress in each element away from the center of the table, and the diameter as you move in an annular fashion will be different from the element before.

very difficult to quantify without using some finite element method.

in your case, your best bet might be the bending analysis you've done with some testing and/or research on similar designs. analyze some realistic loadings coming from different directions to get a sense of stiffness in different planes. don't forget about column buckling...can be just as useful as beam equations if you know how to use it.

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Fitter, happier, more productive

 

[BigTank]

that was a crappy job of trying to explain myself. sorry. i hope it doesn't confuse you more.

and strike this sentence: 'a membrane stress implies a stress equal over a surface resulting from some loading.' that just plain didn't come out right, and my head is mush right now...

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Fitter, happier, more productive

 

[ColonelSanders83]

According to ASME Section VIII app 3

"Membrane Stress - the component of normal stress which is uniformly distributed and equal to the average value of stress accross the thickness of the section under consideration."

Similar wording can be found in other guides which I unfortunatly no longer have access to.

Membrane stress is applicable to almost any section under load.

Membrane stresses are primary stresses and must be compared to primary stress allowables. Many FEA packages have the capability to slice geometry along a plane and calculate the membrane stess at that location. Somtimes determining between membrane and bending stresses can become very murky for complex geometries. The good news is it should be very simple for your geometry.

Please see here for details on calculating membrane stress

http://www.eng-tips.com/faqs.cfm?fid=982

This FAQ was written (not by me) for pressure vessels, but the approch is valid regardles of your component.



Always remember, free advice is worth exactly what you pay for it!

 

[iv2jm]

Thanks for you input, it's been quite helpful.

That FAQ on how to calculate membrane stress got me thinking it might only be applicable for pressure vessels, and prompted the question.

Perhaps I should have done this earlier, but some simple hand calcs compared to FEA with simple geometry helped clarify the definitions!

I appreciate the help!

Jimmy