Beam / slab interaction

[mathias_peron]

Hi everyone, I'm running an experiment to understand what's the best way to model the beam-slab interaction.

I've read very interesting topics on the forum that partly answered my questions. But I still need enlightening.

A - RC SLAB / RC BEAM

As adviced in the Autodesk university HAndout, a good method to model a beam supporting a slab is to increase its moment of inertia to make it match the corresponding T-beam inertia (see bellow).

However, I'm not totaly conviced because:

1- It is geometrically incorrect. The position of the axis of the beam doesn't match the slab

 -> leads to incorrect stiffness

2- There is overlapping of concrete

 -> overestimation of stiffness.

My question is: Wouldn't it be more accurate to increase the moment of inertiaof the beam to match a corresponding rectangular beam bellow the slab (new inertia = (bh^3/12)+(bh)d²) ? In doing so, we can still choose to design the beam as a rectangular or a T, and with a correct geometry (see bellow).

B - RC SLAB / STEEL BEAM

I tried to use the rigid links to model the interaction between a concrete slab supported on the flange of steel I beams. I couldn't understand why the moment in the beams is so low. Can someone explain me?

Have a nice day,

Mathias.

[mathias_peron]

Anyone?

It is very important someone help me understand this as I need to run a seismic analysis of a composite bridge.

Thanks in advance,

Mathias.

[Artur.Kosakowski]

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mathias.peron wrote:

Hi everyone, I'm running an experiment to understand what's the best way to model the beam-slab interaction.

I've read very interesting topics on the forum that partly answered my questions. But I still need enlightening.

A - RC SLAB / RC BEAM

As adviced in the Autodesk university HAndout, a good method to model a beam supporting a slab is to increase its moment of inertia to make it match the corresponding T-beam inertia (see bellow).

However, I'm not totaly conviced because:

1- It is geometrically incorrect. The position of the axis of the beam doesn't match the slab

 -> leads to incorrect stiffness

2- There is overlapping of concrete

 -> overestimation of stiffness.

My question is: Wouldn't it be more accurate to increase the moment of inertiaof the beam to match a corresponding rectangular beam bellow the slab (new inertia = (bh^3/12)+(bh)d²) ? In doing so, we can still choose to design the beam as a rectangular or a T, and with a correct geometry (see bellow).

The handout as far as I remember just suggest to use the rectangular beam with increases IY rather than the offset and the value of the increase should be such as the difference between the T beams you intend to design and the rectangular beam you actually used. If you want to be exact on the picture above the beam defined under the slab should have its height reduced by the height of the slab comparing with the beam on the left side.

B - RC SLAB / STEEL BEAM

I tried to use the rigid links to model the interaction between a concrete slab supported on the flange of steel I beams. I couldn't understand why the moment in the beams is so low. Can someone explain me?

Very often because the slab is rigid enough to 'carry' the steel beams rather than being supported by them. You may also generate denser mesh for 'better' bending diagram along the beam.

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.

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[mathias_peron]

Thanks Artur for your answer,

A /

I'm sorry if I didn't express myself correctly. But what I mean is, instead of increase the moment of inertia of the beam by the ratio Iy(T-beam)/Iy(rectangular beam), wouldn't it be more correct to increase it by the ratio Iy(part of the beam actually bellow the slab)/Iy(rectangular beam).

In doing so, we make sure to not count too much concrete. And it works as well as for T-beam as for rectangular beam bellow the slab (I'm not talking only about T-beams). see bellow.

B / 

Ok I understand. So do you confirm that the use of rigid links is the correct way to model a composite deck?

By the way, the moment is then the average value between the positive and negative value? (example (-35+50)=15)

Side question since I'm here: What are offsets for and when do we use then usualy?

Have a nice day and thanks again!

[Artur.Kosakowski · Accepted solution]

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A /

I'm sorry if I didn't express myself correctly. But what I mean is, instead of increase the moment of inertia of the beam by the ratio Iy(T-beam)/Iy(rectangular beam), wouldn't it be more correct to increase it by the ratio Iy(part of the beam actually bellow the slab)/Iy(rectangular beam).

In doing so, we make sure to not count too much concrete. And it works as well as for T-beam as for rectangular beam bellow the slab (I'm not talking only about T-beams). see bellow.

The idea is to have 'correct' values on the bending moment diagram when you transfer the beam from the model to the RC Beam module and I think you can decide what works best for you 

B / 

Ok I understand. So confirm that the use of rigid links is the correct way to model a composite deck?

I'd say it depends what you need. If you focus on the slab then you may use offsets. For rigid links there is a question where to place supports and bending moment diagram is not 'nice'. You may also decide on the same approach as above and define steel profiles by user defined values of properties with 'increases' IY. 

By the way, the moment is then the average value between the positive and negative value? (example (-35+50)=15)

This seems to be the best approximation. 

Side question since I'm here: What are offsets for and when do we use then usualy?

When you want to have correct stiffness of the deck but you don't focus on design of the beams for bending.

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.

[mathias_peron]

Very good thank you.

One more thing, in seismic analysis / foot fall analysis of a bridge. What is the best way to model the deck? 

In playing with moment of inertia I believe we change the outcomes, right?

[Artur.Kosakowski]

I consider the increase of Iy as the way of modelling offsets when you 'can't' use them. IMHO again the answer depends on what type of results you need. For footfall offsets may be just right as you don't check forces in beams but I'm afraid that I have limited knowledge in this area to tell you should do this or that.

I hope others will have more experience than me. 

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.

[mathias_peron]

Thank you Artur, Have a nice day!

[Anonymous]

Hello Mr Artur,

I have been following your posts about the beam-slab connection, but, I am not yet satisfied.

Due to this I did three different models and I wanted to share them with you so that you can guide.

Model 1: beam-slab without increasing beam moment of inertia-Iy 

Model 2: Beam-slab with increased(doubled) moment of inertia-Iy

Model 3: Beam-cladding without increasing beam moment of inertia-Iy

The real results (with respect to analytical analysis) was obtained for model 3.

The question is:

Why not at model 2?

Here I copied the model

Model 1: Grid 1 to 3

Model 2: Grid 4-6

Model 3: Grid 7-9

[simjack]

Hello Arthur,

I have a related query. I am trying to check vibrations in a composite floor (downstand steel beams and composite floor slab).  I am mostly interested in vibration response of the steelwork and the slab. I intend to keep changing the beam sizes until I get an adequate response factor (if that makes sense). 

I am trying to find out how to best model the elements and their interaction in robot to allow me to obtain the correct data. Reading through this discussion, I figured there are three ways of doing this:

(1) "transferred" section - Is this primarily intended to be used for concrete slab and beam design? My understanding is that one manually changes the I-value of the beam (not necessarily the dimensions) while the slab properties remain unchanged. And the interaction between the slab and the beams is as non-composite only that the load from the slab is transferred to the underlying beams. In essence this method will provide "correct" results (bending/deflection, vibration response etc.) for both beams and the slab? Would this be possible with steel beams as well?  This may however get very tiring if one has a large number of different beams. 

(2) rigid links - this method is more appropriate for steel beams and concrete. This will also "result in correct" bending/deflection/vibration response etc. for both slab and beams

(3) offset of beams - this method will ensure that the "slab does not carry beams". It will allow for the design of the slab (vibration response, etc.) but will not "calculate" composite "beam" properties and therefore will not provide representative vibration response. 

Could I please ask you to comment on my notes and advise on what method is most appropriate in determining the vibration response of the composite floor slab and down stand steel beams?

Thank you.

[Artur.Kosakowski]

Hi @simjack

As your objective is to determine the vibrations rather than sizing the sections against the acting internal forces the key factor is the overall floor stiffness and for this task the easiest is to model beams with offsets. In other words vibrations and deflections of the floor will be accurate whereas the internal forces in the beams themselves will be not.

If I managed to answer your question(s) press the Accept as Solution button please. This will help other users to find solution(s) much faster. Thank you.

[Anonymous]

Dear Arthur,
I have sent you my concerns on Beam-slab connection, but, no response was
received.
Can you please assist?

[Artur.Kosakowski]

Hi @Anonymous

Where did you send it?

[Anonymous]

Here is the message with associated model

Hello Mr Artur,

I have been following your posts about the beam-slab connection, but, I am
not yet satisfied.

Due to this I did three different models and I wanted to share them with
you so that you can guide.

Model 1: beam-slab without increasing beam moment of inertia-Iy

Model 2: Beam-slab with increased(doubled) moment of inertia-Iy

Model 3: Beam-cladding without increasing beam moment of inertia-Iy

The real results (with respect to analytical analysis-normal structural
analysis methods) was obtained for model 3.

The question is:

Why not at model 2?

Here I copied the model

Model 1: Grid 1 to 3

Model 2: Grid 4-6

Model 3: Grid 7-9

[Artur.Kosakowski]

Hi @Anonymous

You neither attached the model nor your hand calculations but my assumption is that you assumed that the slab doesn't participate in the load transfer at all and is just the area to apply load for a T shape beam acting alone. If you include the slab stiffness in the equation the bending moments in the beam has to be smaller.

If I managed to answer your question(s) press the Accept as Solution button please. This will help other users to find solution(s) much faster. Thank you.

[Anonymous]

I attached the model and I attached it again now. If you haven't received
it, please share with your email so that I can send it directly to your
email.
The hand calculation was giving 1280kNm for middle beam and 640kNm for the
edge beam

[Artur.Kosakowski]

Hi @Anonymous

Can you see the links or attached files to your posts in this topic and download them?

[Anonymous]

I attached the model. Can't you review it?

[Artur.Kosakowski]

Hi @Anonymous

Why you increased for the and why in the same way for the middle and side beams knowing that they are L and T shapes?  Why do you compare a unidirectional slab with the one working in both directions?

See the attached file.

If I managed to answer your question(s) press the Accept as Solution button please. This will help other users to find solution(s) much faster. Thank you.

[Anonymous]

Dear Artur,
1.I modelled the slab as they are at top of beam. That is the reason I
increased the moment of inertia of the beams in the same way.
2. I cahnge all slabs to one way slabs, but, still having the same results
as the prvious ones