Floating Stairs

[Trenno]

Reviewing some existing RC stair design and have stumbled upon something very similar as shown below.

What is the design philosophy behind this? Does it work as a triple cantilever (from each face of adjoining wall)? Pinned or Moment connection to the wall?

Very curious - these seem to be the flavour of the month for architects...

 

[racookpe1978]

It is a messy analysis, so let's go to extremes, then see what approximations are probably 'good enough" In other words, in the real world, is the result "right enough" to be safe for people?
Assume that central "wall" were strong enough so it does not deflect significantly.
Assume the two end walls (at left and right in the elevation above) don't deflect either.
Call the three platforms A, B (middle) and C.
The stair sections then become A-B and B-C.


1. Assume each step were simply fastened only against shear loads on both ends to the walls on both sides. So, when people walk down, their weight is held up against bending by the step's resistance (net S and I right?) by the four shear pins at each end. The load on one step can't get transmitted to any other step. Your max load would be the maximum number of people who could fit on each step x maximum weight per person: base that on length of step x nbr people/foot (wide) of each step. Max bending load is at the center based on that maximum distributed load.

IF that above assumption were true, then the maximum load on the platform would = area of platform B x assumed weight per person x assumed nbr of person/area. There would be no extra loading on the platform, because the shear pins in each of three walls around platform B would carry all of the platform B weight + total of the people weight on top of platform B.

No other loads could hit platform B.

IF (big "IF" there!) the sides of platform B were fastened securely to the 3 walls around platform B, then platform B would have some of its weight and moment carried by those connections into the walls around platform B, and then you could assume some of the cantilevered load on platform B would be carried out into the walls around platform B, and the final shear load on platform B would be less. Moment loads on the walls around B would increase of course, and those walls would have to resist bending, and not just shear.

2. IF the individual steps on A-B and B-C were NOT fastened entirely into the walls around those steps, then the stair weight and stair people weight would be added to the platform at B. Worse case: Assume the two stairs were a welded assembly so the stair stringers carried the entire stair dead weight + stair live weight. Then the platform A would carry 1/2 the total weight, and the platform B would carry 1/2 of A-B weight + 1/2 of B-C total weight.
That weight could be either pivot point loaded to platform B, or firmly loaded into platform B.
If pivot loaded, the downward load of A-B might push only "down" at the two stringers at each side of stair A-B, and the two stringers of stair B-C where they attached to platform B.

If firmly connected to platform B, the load from above might push sideways (to the left) at platform B resisting the rotation force of the stair by pushing the wall at the right of platform B to the right.

Most likely, NONE of the connections are perfect moment nor perfect shear connections. Each will fail (yield or bend) until it can move no more, then the remainder of its load will be transmitted to the next joint. Until it yields or bends.

 

[Trenno]

Just a clarification - there is only one single central wall supporting both flights of the stair.

 

[Trenno]

I was thinking that the two stair flights can possibly cantilever out to pick up the mid height landing.

Thus in the region of wall where both landing and flights meet, the reo/ferrules would need to be designed to take the weight of the flight plus the weight of the it's share of landing.

Summary: two propped cantilevering flights and a single span landing.

 

[asixth]

can't argue if its standing up. you can cantilever a slab off a wall, i've done that before. you need to ensure than there is a way to transfer the moment, the slab bars should be cog inwards because the slab wall junction becomes more efficient, like at the bottom of a cantilevered retaining wall. And i wouldn't have a lot of faith in the architect either, particularly aussie architect's, some of them are completely oblivious to the concept of load bearing elements and the limits of how far a floor can cantilever.

 

[Ingenuity]

It is a messy analysis...

Indeed it is - I am not sure what all your words say, I am not following your logic.

Trenno,
Keeping it simple, I say it is a single blade/spine RC wall (adequately connected to the building floor slabs) and the stair treads cantilever off the spine wall, and the mid-landing cantilevers off the adjacent treads, pretty much as you state.

Rather than just use the stair 'throat' as a structural thickness, you can use the full riser depth (less cover) for the stair sections off the wall. The midlanding will use its slab thickness.

 

[KootK]

Trenno,

Depending on your level of interest, you may want this: Link. It covers every case imaginable to a level of detail that only a university professor would find appropriate.

For your particular case, the question du jour is whether or not the stair treads are cantilevered from the central wall. You should be able to tell us based on the framing detail at the wall in your existing plans. If your sketch is entirely accurate, I expect that you're spot on with your triple cantilever notion.

Nowadays, I'll usually do this without the wall. Architects love it and it's usually entirely doable with good diaphragm connections and perhaps a torsion beam where the mid-landing meets the flights.

When the wall is present, cantilevering the treads from the wall is mechanically appealing and certainly possible. It's not usually what I see done however. More commonly, I see the wall treated as a point support at the mid landing and ignored elsewhere. This can be done by:

1) Running the wall into the mid landing a bit.
2) Having a corbel project from the wall under the mid landing.
3) Providing a shear friction connection between the end of the wall and the landing slab.

Some reasons for not cantilevering the treads include:

1) Contractors like the simpler detailing that results.
2) With normal stair spans, it's quite doable.
3) You can use a nominal 6" wall.
4) The analysis is simple. The flights span to, and cantilever past, a beam element running perpendicular to the wall where it meets the landing. The beam may or may not be contained within the slab thickness. As you've rightly pointed out above, the shear delivered by the landing needs to be dealt with via connection to the wall end over a relatively short distance. This method makes that demand very explicit.

I pass the building below most days on my way to work. The cantilever stair always catches my eye. The landing even caries a brick wall, successfully, without cracking the brick. Landing slab looks to be about 6".

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Tomfh]

The landing cantilevers off the flights, but the flights don't need to cantilever off the spine wall. They can be pin support on the wall. The flights can't rotate anywhere with the slab and landing restraining them.

Of course, it's probably worth making them rigid connections to the wall anyway, as it's not really any harder, and this appears to be the general engineering judgment from the profession from what I've seen.

 

[Compositepro]

It gets a lot simpler if you think how you would build it from only steel beams and columns.

 

[structSU10]

I have designed a stair just like this for a 5 story building. We used corbels at almost every landing. The detailing was very tricky - we utilized straight form savers through the wall at landings, right at the top/bottom most stair, to help with continuity, and lots of compression steel to try and limit long term deflection of all components.

 

[SteelPE]

Kootk

I have never designed one of these and probably never will but I do have a question for you:

"4) The analysis is simple. The flights span to, and cantilever past, a beam element running perpendicular to the wall where it meets the landing. The beam may or may not be contained within the slab thickness. As you've rightly pointed out above, the shear delivered by the landing needs to be dealt with via connection to the wall end over a relatively short distance. This method makes that demand very explicit."

How do you handle the unbalanced loads in your analysis either due to geometry or due to occupancy? Do these unbalanced loads put a twisting force into your wall or do you end up with axial loads in flight of stairs?

 

[KootK]

Axial. Never turn down a free lunch. It's never perfect due to little mini landings at the tops and bottoms of the flights. That's minor stuff though.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[glass99]

See attached the same stair but in glass. We finished this for a client in Kuwait a few years ago. It has a cantilevered landing also which is not visible.

 

[Trenno]

KootK, I know you love sketches...

What do you think of mine?

 

[KootK]

I really do Trenno. Love 'em.

Speaking of pretty sketches, G99 should post us a detail of those glass treads where they moment connect to the wall. I see darkness near the wall. There's a glass voodoo story to be told there, I know it.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Trenno]

But do my sketches make sense? Analysis wise?

 

[KootK]

The first seem unnecessary but harmless. I see the landing as a one way design element. That one way being parallel to the flight.

The second sketch is spot on.

For the third sketch, I would have shown both halves of the beam and had it pinned at the centre instead of fixed. There's nothing wrong with fixing to the wall so long as you follow the design through consistent with that.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.