Beam offsets

[Anonymous]

Hi,

When defining a beam cast integrally with a slab I had initially thought the best way to do it would be to offset the beam down to correctly represent the true stiffness of the system.  However upon seeing the results, I was puzzled as to the "saw tooth" shape of the bending moment diagram in the beams, and alot of membrane force in the slab.  

After reading the following post  http://forums.autodesk.com/t5/Autodesk-Robot-Structural/T-slab/m-p/3185418#M915 I thought I would try to follow the solution offered, ie no beam offset.  The bending moment in the beam now looks like I expect.  I created a trial model, a cantilever beam and slab with 2 back spans, all equal length. The only load case is self weight.  See pictures for comparison;

Left is no offset, right is offset to match slab level.  Note saw tooth bending diagram on right.

Membrane force in local x, and panel cut of bending in x direction, overlaid on bending map.

So in the "no offset model" (left), I get peak beam hogging over the first support of 2320kNm, versus only 1485kNm in the centre beam on the right model with offsets.

My question is, which method of modelling produces results which are closer to "reality".  I'm running the same system as a monolithic 3D volumatric element in the background as a comparison.  I'll post stress maps when it finishes running.  

Tony

[Artur.Kosakowski]

Tony,

After reading the topic you refer to you already know what I would try to do

[Anonymous]

Artur, yes I knew you would say that too ............

Well, I waited 1/2 an hour for my model to run  and now I have some results from my 3d solid version;

I added 3 solid cuts, one along the edge beam centrline, one across the slab parallel to the beam, and one perpendicular to the beams.

First is x-direction.  You can see that the slab midspan is in tension on the bottom and compression top 

Then y-direction.  

The entire slab is in tension all the way back past the first internal support.  This disagrees with my previous post where the membrane force in the panel was zero for no bar offset.  

So back to my original point.  I understand that for design of the beams, it's far easier to make the simplification that they do all the work and the slab does none (in the beam span direction), then reinforce the beam accordingly.  However if i was trying to really optimise the system and not reinforce over conservatively, can I assume that the slab takes some of the load in tension / compression.  Is the real kNm value of beam hogging somewhere in between the saw tooth and the idealised "no offset" method, or should I be doing 3d models of everything that take 30 mins to run, and converting stresses into mm2 of reinforcement?

Thanks for your comments!

oh OK another sexy pic for you Artur

[Artur.Kosakowski]

Tony, I'm sure the slab will take some tension /compression (due to bending) but you should display stresses for the top or bottom layer rather than in plane forces The in-plane forces for such model with vertical loads and linear static cannot occur in the model (mind that in the solid you have real heights of a slab (and beams)  so that the top and bottom layers 'move' with respect to each other under vertical load whereas surface elements and bars are dimensionless in this 'direction'.

If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.

[Anonymous]

another edit hmmmm, 

If I use the peak stresses above the 1st support on the edge beam (just picking rough numbers for this example);

4MPa tension, 12MPa compression.

I assume linear and triangular distribution of the stress in the edge beam (750 wide * 1200 deep) from top to bottom.

From the map it looks as if the zero stress point is somewhere above mid height so I guess 500 down from the top of the slab, (just guessing).....Then I calculate the following;

4MPa x 500mm x 750mm x 0.5 = 750kN

12MPa x 700mm x 750mm x 0.5 = 3150kN

(2/3 x 500mm) x 750kN + (2/3 x 700mm) x 3150kN = 1720kNm.  

In my beam and slab model my edge beam had 1780kNm.

Now I'm really confused 

[Artur.Kosakowski · Accepted solution]

Tony, please mind that the method with the use of  arbitrary increase of beam moment of inertia (the decision what coefficient should be used is opened for discussion) is the approximate method I adopted for myself rather than the exact solution (a solid model ).

The solid model includes effects that are not the part of the shell one (real shapes of beams and slab rather than lines and flat surfaces that influence model deformation). The difference of 3-4 % seems to me the perfect result.

[Artur.Kosakowski]

One more idea that I just came to my mind: modeling the slab you 'overlapped' part of the slab with beam ('double cross section') making this part more rigid than it is the the solid model. More rigidity -> larger bending

[gustavo_c_vasconcellos]

Dear Artur, 

how can I get the moment of inertia option? See attached.

And how do you choose or calculate the factor (in your example 1.7, it is the total height / slab height?

Thanks

Gustavo

[Artur.Kosakowski]

You should modify the section of  a beam in the model. See the attached picture.

[antoine.carimalo]

Very interesting topic, tanks for you help.

It is clear now for the no-cracked behavor but how could it possible to design renforcement and control real deflection, based on this value ?

I mean,

The TT floor is a good example. How to make a safe reinforcement design If the part of bending crossing among beams/slab is calculated with the non craked rigidity. What is the RSA method to take into account the rebar rigidity and cracks.

For this case I prefer to design manually but after, in general case of slabs and beams, how to determine modifiers on beam stiffness to render true calculations ?

I am a beginer on this kind of design so, to be safe when I design a floor where I canot said slabs are supported by beams, I use 2 models, one for the slab design, second for the beam design. Run reinforcement design on each one, adjusting the deflection insite beam modulus and slab modulus to make it compatible.

So complicated to do in reality.

Any solution ?

[Artur.Kosakowski]

You can use the RC beam design module and determine the reduced stiffness of beams and then do the same for panels (map of reduced stiffness in the RC Required reinforcement module). Then you can update the model and calculate it again.

If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.

[gustavo_c_vasconcellos]

Dear Arthur,

can you make a small video showing how you do determine the reduced stiffness?

Thanks

Gustavo

[Artur.Kosakowski]

I would determine the ratio between 'cracked' deflection calculated in the RC Beam Reinforcement module and the one from the static analysis of the model for beams and the values from the attached map for slabs.

[gustavo_c_vasconcellos]

Great!

Thanks

Gustavo

[antoine.carimalo]

Very good idea.

But I am not sure it is runing well for all kind of floor.

Ok for a TT slab

Maybe Yes for any kind of one sway slab, if the span of the beam is the same as the span of the slab

In cases here above we could expect that craking have the same behavior in slab/beams

But

If we expect to reinforce the beam for any reasons, the slab will but unloaded (and vice versa). It means the reduced stiffness must be different

I think weed need to have deflection compatibility to perform a true design, not a rigidity compatibility.

"use the RC beam design module and determine the reduced stiffness of beams"

You mean we calculate the reduced stiffness dividing the deflection in the reinforced concrete  beam modulus by the elastic deflection given in the structural model.

Maybe I don't understand well you're solution

Cdy

Antoine

[Artur.Kosakowski]

In short my proposal is to find out what cracked stiffness (with generated reinforcement) is and then update this information back to the model to calculate it again. For bi-directional slabs you can check the maps of reduced stiffness for either of the directions and then use the orthotropic E1/E2 slab thickness definition.

Of course this is just mine proposal and any better solutions are welcomed.

[antoine.carimalo]

Thanks Artur

We can debate on many proposal to choose the rigidity factor to apply.

I need to know if there is a problem in the RSA reinforced design method ?

Note I am a begineer in this kind of slab and I do not have other soft to do that.

[antoine.carimalo]

Don't you know it is necessary to mach cracked deflection beetwen structural members designed separatly?

[Artur.Kosakowski]

According to my knowledge the method used in Robot is typical for this kind of programs and is sort of similar to what you do calculating reinforcement by hand (where you even assume beam as fully rigid support for beam which is of course not true in Robot). I can try to suggests some solutions based on my knowledge of the program yet I'm not in the position to decide how you should design your structure. My understanding is that what  you are ultimately looking for is non linear behavior of material in a solid model which is the domain of much different programs than Robot.

[antoine.carimalo]

Dear Artur,

I understand your position.

In general case I use RSA to design floors with simply supported slabs by 2 ways :

1 - design slabs as claddings

2 - design slabs as shells with analytical transfer of loads and with a big rigidity multiplier on beams (around x5 x10)

Applying first method I need to models : one for design beams, second for design slab.

Second method is more appropriate at work because I use only one model. I have no problem if beams are designed fully rigid (with big rigidity multipliers). Be careful that deflection are matching well. I need to limit beam deflection in the external modulus sometimes.

But I am very confuse when I want to solve other kind of floors like TT slabs. Is this case I can't compare manually to be in peace with my mind.

In this case adjustment of deflection of beams in external modulus imply that the beam takes more loads that the exported loading cases. And vice-versa with slabs, depend on deflection limitations.

This rational requirement means I need 2 shell models to converge.

Anyway if we don't correct rigidity modifiers if we use analytical transfer on MEF slabs, it means deflection of beam must be corrected at reinforcement design.

I think it is for this consideration that beams are very soft in reinforcement slab modulus.

Can you confirm if I have well understood the RSA design requirements ?