Ribbed slab bending and lateral loads

[IngDod]

Greetings,

Short Version: Is it logical that Im getting high torsion in a beam receiving the ribs of two ribbed decks during earthquake load action?

Long version:
I'm designing a two story concrete house, a rather simple structure.But my area is seismic so i must consider lateral loads. The floor system consists of two spans of one way ribbed slabs, my design approach was first design for gravity loads and then check for lateral loads. For the ribbed slabs i used ACI coefficients to determine their moments and the moment they would transfer to the exterior beams as torsion.. The torsion was much greater than the exterior beam sections given to me by the architect could take; so I assumed redistribution of torsion (This is a compatibility torsion case as I understand) and it was ok; I would detail minimum torsion steel and be done with it. I set up a SAP2000 model to verify my results, I modeled the ribs as independent T-Beams and my approach to model the torsion redistribution was to pin the ribs of the slab at the connection to the exterior beams, leaving it fixed for the beam in the middle. (This is a two bay structure in the direction of the ribs, so three beams, one in the middle of the ribs and two at the ends). As expected the moment coming from both ribs canceled at the middle beam.

My problem started when i applied the response spectrum for the earthquake, I don't know of any approximate hand method to calculate this problem (I know portal and cantilever method, but I honestly don't know how to distribute the horizontal forces from the earthquake to each frame, I know how to distribute base shear vertically to each floor; but not horizontally within each floor). So I decided to use the software for this, but I'm getting a great deal of torsion in the middle beam; basically the ribs of the deck are bending as if they were normal beams from the moment frame and transferring this moment to the beams. Again my question is, is this behavior realistic? or it stems from my way of modelling the slabs... I think Im not getting slab action for horizontal load, only a set of independent beams.

My first impression was that I'm facing an error coming from my flawed technique of modelling the slabs, I have seen many structural book examples about lateral load, and usually they analyze the structure as separate 2D frames.. so a torsion induced by bending of the slabs would be lost I believe.

 

[asixth]

I would think that the flat slab between the ribs behaves as a diaphragm to distribute any lateral forces to the shear walls or columns and would not rely on the torsion in the ribs.

 

[briancpotter]

It's difficult to know whether torsion is reasonable without knowing more about the lateral-resisting system and how it's laid out. I suspect a problem may be improper fixity/stiffness values somewhere. Can you provide a diagram?

If you'd like to do a hand analysis, it's relatively simple with the aid of SAP2000. Create a shell model for each lateral resisting element, and place a 1k lateral load on each one. Then find the horizontal deflection of each element, and use it to calculate the relative rigidity of the lateral elements. It's then relatively simple to calculate the lateral force distribution.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[IngDod]

Greetings, I’m uploading a picture of the model with some notes for better understanding: It’s a two level concrete house; the lateral resisting system is moment frames in both directions. My doubts arise because I modeled the system as a whole, the entire structure with the slab and its ribs; this resulted in earthquake load torsion being generated at the beam that receives slab ribs from two sides. After much reading I have found that the “common” method of modeling seems to be separating lateral force resisting system from the gravity load system; in my case where I have moment frames it would mean ignoring the slab stiffness completely when subjected to lateral loads. Basically modeling the system with only the slab weight and loads being distributed to the supporting beams mainly for the purpose of mass for earthquake loading and dead and live load for earthquake combos which include such loads. Is this approach correct? I understand the logic behind it; ignoring any contribution from the slab would lead to more conservative results for the beams and columns; but this completely ignores any torsional effect the slab may cause on the beams.

briancpotter: Thanks for your answer; I had thought of this before but i was uncertain of it validity and how to proceed about it. My understanding of stiffness is that its basically the amount of force required to displace a structural element or system by a certain amount (say a centimeter or an inch). In the case of lateral forces my first "trial" will be a single column with the load applied on top, i should get a result easily verifiable with stiffness equations for single members. I could do the same for a one story frame, I have a dynamic book where they derive a very simple expression for one level, one bay moment frames using condensation. Up to this point I can envision the kind of results i would get. But what happens as i have more stories and more degrees of freedom? Would applying a 1kip force to each level give me a fair representation of the stiffness? Earthquake lateral forces are first distributed vertically to each level, and afterwards a distribution to each moment frame or shear wall would ensue; this means I would need stiffness or relative stiffness for each independent element or moment frame per level, correct? How would i go about determining this?. If i apply a 1kip load to each level I could use the difference in displacement between two level to determine the "net" displacement for a particular level and use the force/displacement relationship as that level stiffness?. So basically for moment frame, this is what im more likely to deal with in my location, I could model each frame individually as a 2D model, apply a load, find the displacements and compute that frame stiffness per level?; then i could find the earthquake loads per level and distribute it to each frame according to its stiffness?.

Also I have seen that assigning rigid diaphragms to each levels completely eliminates axial load on the beams, and even worse it inhibits truss behavior in trussed frames. I wanted to be able to distribute the load manually so i could apply it to each frame in my model and recover the axial loads from beams and truss-chords.