Membrane or thin shell?

[ETET001]

Hi, I am designing footings for columns in a building. The slabs are 200mm think one way. I am just wondering which one is the correct way to model slabs, one way membrane or thin shell with 0 M22 (90 degree on Local axis 2). I got two very different results from these two and don't know which one is correct. I tried to envelope them the result from membrane method is more than 2 times greater than thin shell one. Can anyone please help? Thanks.

 

[Erik Panos Kostson]

If you are referring to membrane elements (finite element analysis), then standard membrane elements have only in plane translational degrees of freedom and thus account for in plane/membrane loads/stresses only (not bending).

Shell elements in your case plate elements, since the slab is very likely flat (shell refers very often to curved thin structure), have both translational and rotational degrees of freedom and thus account for bending as well. In essence the plate/shell elements are a combination of an in plane membrane element and an element accounting for bending.

Membrane elements are used to model thin structures (membranes, fabrics,..) where there are membrane (in plane stresses) stresses only. In order to build up some bending capacity in a membrane we need to add a tension stress, hence in FEA, a nonlinear geometric analysis needs to be run, which can do that, and where the bending stiffness builts up as we get tension in the membrane element (hence why these elements are used with a geometric nonlinear analysis, since this is a nonlinear effect). Of course if the membrane element is stiff, not like a fabric, one might still be able to run it linearly (no large deflections), but then again only in-plane membrane stresses are captured.

Shell/plate elements have bending stiffness. Plates/shells can be used to model slabs, etc and other thick structures that can resist bending loads (a non-tensed membrane cannot take bending/transverse loads). If the plate structure is also thick thus transverse shear is important there is a thick plate theory known as Mindlin, while if the plate is thin, then simple Kirchhoff theory (no transverse shear) is enough.
Very often FEA software will let one choose which one to use.

So it depends what type of structure (thin/thick) and loads (in plane or transverse) that you have when it comes to deciding which of the two finite elements to use.

 

[klaus.]

Membrane element is a special shell element....
like a cable element is a special beam element

it depends on what you want to model .....

 

[KootK]

I generally wouldn't recommend membrane elements for column footings which are dominated by flexure rather than in plane axial stress.

 

[JoshPlumSE]

Erik Panos Kosto sounds like he knows what he's talking about more than I do. But, I'll throw in my $0.02.

Definitely use shell elements for modeling concrete footings and slabs. I would very much recommend going with a thick plate formulation rather than a thin plate. Some years ago the PCA Mats program got my boss in a tizzy because it used a thin shell formulation for the design of our company's new office in the Philippines. I don't know all the details, but I know the design was re-done at the last minute and it was portrayed as a big deal.

In my personal experience, however, it isn't usually that big of a difference. Don't get me wrong, it is definitely poor form to use a thin plate formulation for mat slab foundations. When I was at RISA, one of our developers wrote a paper on the subject to promote the release of RISAFoundation:
Finite Element Considerations for Computer Modeling of Mat Foundations
Dr. Puri is not with RISA anymore, so don't try to e-mail him. It's a relatively short paper, but I'll save you some time and summarize it.... The conclusion was that it was more accurate to use the thick plate assumption (like RISAFoundation does, shocker!) and that the thin plate assumption ended up being overly conservative for design moments.

I'm sure that if we were to revisit the paper, we could come up with an example where it would be un-conservative to use thin plates. But, for the most common cases (like the example presented in the paper), I believe it will be overly conservative.

 

[JoshPlumSE]

One fun note about that paper.... While I appreciate that he acknowledged me for my input and suggestions, whenever I look at that paper it genuinely annoys me that he spelled my name wrong.

 

[Erik Panos Kostson]

Thanks for the kind words, but I believe that you know much more about the practical side of things and your comments about thick plate are spot on I think (I work with different types of fea analysis, and have a focus in fea itself, so it is not possible to know what different applications use in terms of elements).

It can be a bit disappointing when the name is spelled wrongly I agree with you on that

Erik Panos Kosto sounds like he knows wha

.