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# Slab using membrane of shell elements

## Slab using membrane of shell elements

(OP)
Hi,
Could anyone please explain to me which degree of freedom that I should constraint for a rigid floor using shell and membrane elements?. I mean that, for example, I have a rigid diaphragm floor using shell element, and is that similar if I constraint this floor in both horizontal (H1,H2) and rotational (RV - rotation about vertical axis) degree oF freedoms.
And for the ridig diaphragm floor using membrane element, is that similar if I constraint H1, H2, RV, RH1, RH2...?
Thanks
Lisu

### RE: Slab using membrane of shell elements

Plate elements utilize out-of-plane stiffness only. On the other hand, membrane elements consider only in-plane stiffness.

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

http://www.engissol.com/cross-section-analysis-des...

### RE: Slab using membrane of shell elements

The full answer to your question depends upon exactly what you are trying to do, what mixed element types you might have in your model, what your terminology is, and what FE program you are using.

I am assuming that your only loading is vertical.  Take X and Y as your two horizontal axes, with Z being the vertical axis.  As JohnBridge says, if you are modelling ONLY with plate elements in the X-Y plane you usually restrain DX, DY and RZ (because the formulation of the plate element usually ignores these degrees of freedom, which would leave you with a singular global stiffness matrix).  Similarly, if you are modelling ONLY with membrane elements in the X-Y plane you usually restrain RX, RY and RZ (for similar reasons).

Many FE programs provide what they probably call a "shell" element, which (depending upon the program's terminology) combines both plate and membrane behaviours.  If you model ONLY with these, you would restrain only RZ.  Then, unless you are performing a large-displacement analysis, your results will show zero membrane forces in your elements.

However I worry about your terminology when you use the terms "rigid floor" and "membrane element" in the same sentence.  I note from your profile that you are a user of ETABS, and wonder whether this has influenced your terminology.  I have not used ETABS for many decades, but my recollection is that it makes some broad assumptions about the behaviour of a building's floor slabs in order to achieve huge reductions in the size of the global stiffness matrix.  One of these assumptions is that the floor slabs are infinitely rigid in their membrane actions.  In other words, for movements DX, DY and RZ (but not for movements DZ, RX and RY) the floor slab moves as a rigid body.

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