Concrete Slab Idealization using beam elements

[asixth]

Hi guys,

I have a reinforced slab of irregular plan dimensions, beam penetrations, transfer beams etc. It was my original intent to design the slabs using emperical formulas for slabs supported on four sides, and design the beams using a triagular load allocation. For justification purposes, I decided to perform an analysis using beam elements and reducing the torsional stiffness so the elements work mainly in strong-axis bending (eliminating the Mxy component and distributing to moment to Mxx and Myy).

My question is this:

Is this an acceptable method to design a reinforced concrete structure? I am only looking at ultimate design and will use code provisions to design for deflections. It also allows me to consider many patterned live loading combinations.

 

[DaveAtkins]

I think you will be OK, as long as you design the beams for minimum torsion per the Code. Your situation is what is known as "compatibility torsion," because if the beams can twist in a ductile manner, the beam torsion will redistribute into the slab as bending.

DaveAtkins

 

[JAE]

One thought - if you look at four joints forming a "box" in your slab - in reality, with a concrete slab, these four joints would not move relative to one another in the plane of the slab due to the slab diaphragm rigidity. This isn't really included in the model as you now have it. Your model would allow the whole slab to deflect horizontally such that the "boxes" would form into parallelagrams.

Since good modeling attempts to mimic the behavior of the structure, you've then left out an essential constraint in your model.

What you could do is add fictional diagonal elements - with zero weight - and perhaps pinned ends forming X's in each box to mimic the slab in-plane stiffness without interfering with the natural vertical bending of your beam-slab elements.

This may or may not be a big deal if the loading results in minimal parallelagramming (is that a word?) but with lateral or unbalanced forces, the lack of a diaphragm stiffness could affect the distribution of vertical moments throughout the model.

 

[haynewp]

I would check the results against the strip method and see if I was close. Park's book on slab design is a good guide for this.

 

[asixth]

JAE,

The software I am using allows nodal freedoms to be constrained to each other, saying that, instead of modelling an x-y translational freedom for each node, I can model one translational freedom for both x and y directions, constraining the model to one displacement. This will model the diaphragm action while eliminating the need for fictional bracing elements. Good pick up,I will include it in the analysis.

haynewp,

I have used emperical moment distribution factors from the code to design the slab, and I did distribute load to the beams based on a triagular load allocation. Because of the irregular nature of the structure, I wanted to perform a simple analysis to justify my design. For example, there is a load bearing wall running parallel to the slab edge at the extremity of the right hand side cantilever, which under certain patterned loading, will hog the transverse beam running left-right. I didn't allow for this in my original design.

 

[haynewp]

Just a thought; Is neglecting the torsional stiffness of the members reducing your column design moments? I think I have seen this before so it may not be an uncommon assumption. I guess you are assuming the compatibility torsion will be released prior to the columns failing.

 

[Robbiee]

I think this thread relates to your question,

http://eng-tips.com/viewthread.cfm?qid=176537&page=18

 

[asixth]

Thanks Ailmar,

Going by what was posted on the FE thread, modelling the slab using beam elements will give me illogical results. My opinion differs, the displacements of the slab may be incorrect modelling the slab as a grillage but I think the distribution of forces are very represent of the actual conditions.

 

[JAE]

asixth - one thing to always remember is that deflections are simply represntations of forces in the structure.

Where there is deformation of structural elements, there must be moments, forces, etc. within those elements.

Your statement that the displacements in your model might be incorrect - but the forces would be correct - is somewhat counter-intuitive to Hooke's Law.

Remember that most all software analysis programs first solve the matrix of equations for displacement - then simply back calculate the resulting forces from those displacements.

Just thought I'd point that all out - although you may be quite aware of it.

 

[asixth]

JAE,

I was thinking more of the cracking, creep and shrinkage of reinforced concrete affecting the calcuation for deflections.

I agree with your comment though.

 

[haynewp]

I would expect the final distribution of forces at ultimate to be different than what you have from your elastic model. I am still not sure if it is safe to always ignore the torsion affect on the columns. (haynewp waits for big argument he knows is coming....)