Lateral Stability of Structures 7

[damo74]

Folks,

I have a lateral stability problem that keeps appearing in front of me.

When looking at simple 2 storey housing of typical construction I would normally assume that any wind load on the front/rear walls is transmitted to the gables via diaphragm action of the timber floor. Also, any wind load on the gables will be transferrred to the front and rear walls by the same mechanism.

However, when steps are introduced in the floor panel (say from gable to gable along the centre of the dwelling parallel to the front wall), my logic of transferring all of the wind load down to foundation breaks down. The floor is then split up into 2 seperate diaphragms. When behaving as horizontal deep beams, the front diaphragm spans from the front shear wall to the step in the floor. The rear diaphragm spans from the rear shear wall to the same step in the floor.

By my reckoning, I require some form of lateral stability at the step in the floor. This could be provided by an additional wall or possibly a steel/concrete frame. The wall option doesn't always suit the layout and the frame option appears to be an overkill for simple 2 storey house construction.

Could anybody confirm that my logic is correct and, if so, provide me with any other solutions that they have used for this case of the stepped floor as I'm sure it's quite common.

Thanks

 

[MikeE55]

I think your logic is correct. You have to detail in such a way as to transfer the diaphragm load across the step in the floor.

 

[damo74]

I agree. Any suggestions as to how I might do this?

 

[DaveAtkins]

I disagree. I recommend considering each diaphragm as a rigid, three sided, open on one side, diaphragm. Lateral load is transferred to the shear walls, in typical fashion, but the torsion in each diaphragm is resisted by a couple in the perpendicular walls.

DaveAtkins

 

[damo74]

Thanks DaveAtkins,

I had thought of this possible solution also, but thought of the timber floor as not being rigid enough. According to a few books, a timber floor is very flexible and weak. Would you ignore this and design the floor as a horizontal cantilever with a couple taking the torsion anyway?

damo74

 

[kxa]

If I understand this correctly, you want to have the two-level or stepped floor to act as one. In this case, figure out the chord loads for as if it were a one level floor and at the steps point transfer the loads to the adjacent (parallel) walls. You need to design the walls so that the point loads from the chords along the rim joists (tension & compression) are safely transferred to rest of the structure.

 

[damo74]

kxa,

"at the steps point transfer the loads to the adjacent (parallel) walls. You need to design the walls so that the point loads from the chords along the rim joists (tension & compression)".

I'm not sure I understand fully. Could you spell it out a little further for me?

 

[kxa]

I do a lot better on paper But will try. If you are analyzing the floor as a deep beam, you will have, let's say, compression in the front and tension in the back. the side walls take the shear. Now that the floor is split in two levels by the steps (how many?), the tension and compression forces in the front and rear chords (rim joists) need to still be resisted by something. Since the chords are no longer continuous along the front and rear, you might be able to resist the chord loads by placing solid blocking in the walls together with metal straps since the loads can be either tension or compression. The wall will also need to resist the resulting shear.

Hope this helps. It's a thought anyway. Depending on the loads and the number of steps (offset) it may be possibility.

 

[AggieYank]

kxa, I have to disagree with your creative solution. I agree that it will work for the bending resulting from the diaphragm action, but how will it resist the shear? Imagine a 30 foot long steel beam. At the very center, a 1 foot section of the web is cut out. Now, the flanges could still handle the compression / tension, but there is no way to resist the shear, meaning it will fail.

As opposed to a lateral brace or frame at the drop, if you could detail the drop in such a way as to make the diaphragm continuous, that would obviously be much preferred.

Assuming you have 2x framing and around 6 inches:
If the drop is something like 6 inches, it seems to me like adding a 2x12 or something simliar at the drop point would work. On the high side, the plywood is nailed to the 2x12. On the low side, the plywood is nailed to the lower 2x8 framing. The key point is that the 2x8 nailed directly to the 2x12, so that the shear is transferred. You'd have to design the nailing pattern and 2x8/2x12 for the diaphragm transfer shear. If the drop is larger than 8 or so inches, it may be easiest to use a deeper glulam at the edge of the drop, nailing your 2x framing on the low side directly to the glulam.

If it is TJI joist framing, it will be similar to above.

NOTE: I've never done this before, as I've never had a floor drop in a wood building. This is just brainstorming of how I would do it.

 

[kxa]

AggieYank, This is a two-storey house and appears to be of wood frame construction. The steps are located in mid span and should not see much shear loads (along the steps). Anyway, the idea is to follow the load path and provide enough structural support that would safely withstand the design loads.

 

[DaveAtkins]

Yes, I know that authors have said that a wood diaphragm cannot be rigid. For this situation, I would definitely be OK with assuming the half diaphragms are rigid, and analyzing them as I stated earlier.

DaveAtkins

 

[HouseBoy]

I have a few questions:
Is the stepped floor at the first floor level only? If so would there be much wind load on this floor?
Even so, could you look at the front half and back half as two seperate diaphrams, each of half the depth?
The term rigid has specific meaning (I thought) when talking about diaphrams. Wood diaphrams are known as flexible diaphrams aren't they? That distinction has to do with how the loads are distributed to the shear panels (based on relative stiffness of the shear walls I thought). It doesn't mean that becasue they are not rigid they don't work as diaphrams.
If you're looking at a "simple" 2 story house, perhaps the 2 shallower diaphrams will be sufficient( compared to one deeper diaphram)

 

[AggieYank]

kxa, I respectfully disagree again. In a typical beam under uniform loading, the shear at the middle is ~zero. Let's say again that you have a long beam in which you cut out a 1 foot section of the web in the middle of the span. Each half of the beam is essentially unsupported on it's interior end. Even if the flanges could theoretically handle the shear, I'd be hesitant to go route.

Again, in the case of this diaphragm, I'd add a deep beam next to a shallower beam to transfer the shear, as I explained in the previous post.

 

[AggieYank]

houseguy. Whether a diaphragm is rigid or flexible depends on the diaphragm itself, and not the shear walls (or other lateral resistance). Generally, a concrete floor is a rigid diaphragm, while a wood (plywood) diaphragm and metal deck (without concrete) is flexible. It depends on the stiffness of the diaphragm material.

Here is a good refernce on diaphragms.

http://urban.arch.virginia.edu/~km6e/arch721/content/lectures/lec-03/home.html

In my opinion, you could treat the two diapragms as separate. They would have to be either supported at the center, or designed for the extra torsion resulting from only being laterally supported on three sides. However, this doesn't pass my common sense test. do I really want a wood framed structure with two separate lateral resistance systems in it? What happens to the partitions or cieling at the point where the two diaphragms joint?

 

[bjb]

The IBC defines rigid and flexible diaphragms. A diaphragm is rigid when the lateral deformation of the diaphragm is less than or equal to 2 times the average story drift. So wheather or not a diaphragm behaves rigidly does depend on what the vertical lateral load system is. If the diaphragm is stiffer than the shear walls (or bracing moment frames, etc.) then the diaphragm could behave rgidly. As an example, wood shear walls are more flexible than masonry shear walls, so it is possible for a wood diaphragm to behave rigidly with wood shear walls but behave "flexible" with masonry shear walls. In chapter 16 of "Design of Wood Structures-ASD 5th edition" by Breyer, an example is given where the diaphragm deflection is compared to wood shear wall deflection, with the result being that the wood diaphragm can be considered rigid.

I agree with the approach that DaveAtkins takes in his first post.

 

[pba]

I pretty much agree with DaveAtkins. If the floor is rigid enough for you to assume a diaphragm with it all at one level it does not suddenly get weaker just because there is a change in level.

Assuming as per the example, a change in level running across the building such that the gable walls intercept two levels of floor:

Horizontal (wind) force is transferred to the two parts of the floor where it forms a shear force in the diaphragm. Consider the diaphragm as a cantilever spanning from the front or back wall with the free end at the change in level. The bending moment is wl^2/2. Assuming that the step occurs near the centre of the building, this is actually the same bending moment as assuming simple supports at front and back walls with a continuous floor level as wl^2/8 (in this instance) has a value of l twice that of the cantilever.

Now in order to ensure rigidity of the cantilevers the gable walls provide a restoring moment by horizontal forces acting as a couple.

If the change in floor level is substantially away from the centre of the building, a shear force will be present at the change in level which should be resisted by a vertical truss formed at the change in level.

 

[damo74]

Thanks guys. I can see it is a hotly debated subject and has given me enough food for thought.

 

[AggieYank]

pba, I'm not seeing how the two diaphragms are supposed to be cantilevers spanning from the outside wall to the floor drop. There is no rotational rigidity at the outside wall. The only reason the two diaphragms would work with the break in the middle, in my opinion, is because of the shear walls running perpendicular to the "cantilever span" which would carry the torsion resulting from the diaphragm being free at one end.

The best way to find a solution to a problem is the simplest way. To me, the simplest way is to add a deeper member (on the high side) at the floor drop attached to a shallower member (at the low side) with a connection that could develop the entire diaphragm capacity.

 

[kxa]

pba, Can you please explain how the gable wall (end wall) can resist the moment caused by the cantilever diaphragm?

 

[damo74]

By my understanding of pba's idea, the twisting moment on the diaphragm is resisted by an equal and opposite couple (couple being the 2 gable walls) and the shear is resisted by the front or rear wall.

Sketch a square shape on plan. This is the floor. Draw north, south, east and west. Assume the front wall is due south (this is the cantilever support). The north side is the tip of the cantilever. The floor is fixed to walls on 3 sides, namely south, east and west.

If the force is applied to, say, the west gable, the floor will attempt to rotate about the south eastern corner.

Assuming the floor is fixed to the east and west walls, these will provide a moment resisting couple, as the east wall reaction is acting due north and the west wall reaction is acting due south. The southern wall can be designed to resist the total shear force applied to the west wall, as in a typical cantilever. We do not need to worry about any moment resistance at the support of the cantilever (i.e the southern wall) because the resisting moment is applied by the couple as stated earlier.

That's how I applied my logic. Does everyone agree?