Analyzing a slab as crossed beams

[MALKOBANI]

Hi all

I am wondering if it is OK to model a flat slab as a number of beams in two directions. How the forces differ in both cased.

The reasons for the question are:
1-I don't have a FE program to analyze flat slabs and,
2-Both the direct method and the equivalent frame method for analyzing slabs use the bending theory.

 

[GBor]

Flat slabs of what? And why wouldn't you use plate theory? I'm assuming you are referring to concrete slabs in which case you may want to post this in the structural forum for the civil engineers.

As for calculating a flat slab using beams...not advisable. Yes, they use bending theory, but the bending stiffness of plates and beams are calculated differently. Plates use D=(E*h^3)/(2(1+v^2)) or something like that...trying to recall from memory. For the beam method, you would use EI.

You can derive the plate bending from beams, but you have to do some pretty high-end partial derivatives and superposition.

Is there a reason why Roark's formulas won't work?

 

[cooperDBM]

What you're suggesting is called a grillage analysis. It was fairly common in concrete bridge deck analysis when engineers only had frame analysis programs available to them. It can give reasonable results if set up properly. The main trick is that the torsional stiffness of the beams needs to be properly modeled. Do a web search for "grillage analysis" for more info.

What kind of slab do you have?

 

[GBor]

A "grillage analysis" in the marine world is different from what I understood the OP was asking. We used grillage analyses for beam-stiffened plates where we had an "effective width of plate" that would basically be added to the flange of the attached beam for added stiffness...

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

 

[corus]

GBor is almost correct in the stiffness formulae. Looking in Efunda, the flexural rigidity of plates is Et^3/12(1-v^2) whereas for a beam it is Et^3/12. Equivalently it is EI/(1-v^2) and EI for unit width plates and beams respectively. The difference is due to plane strain effects in the plate.
I've seen people do this before where they assess complex shapes as a series of beams and think it gives the right answer. It's difficult to convince them otherwise, but any answers you get would be rubbish in my opinion.

corus

 

[crisb]

As cooperDBM states this is very common in bridge analysis and is still widely used. The following reference is often quoted:
E C Hambly, ‘Bridge deck behaviour’, E & F N Spon, Second Edition, 1991.

 

[GBor]

Thanks, corus...memory isn't what it used to be and I wasn't smart enough to do an eFunda search . I did actually mean "12" instead of "2", but clearly missed the "+"/"-".

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

 

[MALKOBANI]

Thanks all for the inputs.

This is a two-way concrete slab with geometry irregulrity.

 

[RPstress]

Long and long ago (seventies) we used a grid (grillage) analysis for a metal-skinned sandwich floor panel with a tyre load on it. We found under test that the actual panel was as strong as the grid analysis suggested it would be when the material was accounted for twice: the beams along the panel had the total skin area in their properties and the beams across the panel likewise.

The panel was fastened down all around its edges.

The beams were at a fixed pitch with about a dozen of them across the smallest panel dimension.

Panels designed in this way (with appropriate load factors) saw decades of successful service.