Masonry Stair Towers?

[SteelPE]

I am currently designing a small 3 story building that has 2 egress stairs at either end. Each stair is wrapped in masonry on all 4 sides. The stair dimensions are 8’-2” x 17’-0” (inside of CMU to inside of CMU). These stair towers are each 43’ tall +/-. Code is 2015 IBC.

The owner is wanting to use these stairs to resist lateral loads in the long direction (17’-0”). We have an ultimate shear of approximately 314 kips due to wind (mostly because of large parapets on the roof of the building).

I have never quite designed a stair tower like this before. Is there any design literature that goes through the process of designing a similar stair tower to act as a single unit? That is, to design this masonry stair tower almost as a tube sticking out of the ground with the short walls acting as flanges of a beam and the long wall acting as the web of a beam?

I have see plenty of building constructed this way, I am just not quite sure how they going about doing it, and if there is a simple hand calculation process (or if this is something that need FEM).

 

[XR250]

Quick back-of the envelope here...

157k / tower x 43' x say 2/3 (resultant height) = 4,500 ft-k / 17 ft = 265 k couple at base of tower - seems like a lot! (not including resisting DL)

 

[hokie66]

You would analyze it the same way as for a concrete stair core. Reinforced and fully grouted, that should be no problem. I have used reinforced masonry stair towers for buildings up to 8 storeys. One thing to look out for...cores at two ends will restrain the slab, so you need to pay attention to shrinkage in the slab, and resulting distress in both the slab and core.

 

[SteelPE]

This building is steel framed, so the stair towers are unloaded. I haven't really designed a stair core out of concrete either. I remember seeing a design example somewhere but I can't seem to put my hands on it. It might just make sense to do this out of steel..... Going to have to think about this one a bit.

 

[EulersBucklers]

One thing to look out for is your diaphragm connection to this stair core. You probably only have one wall in each direction that engages the diaphragm providing not much length to transfer all of the shear forces.

 

[r13]

I think you need to be more specific on what bothers you, seems everybody is guessing here. IMO, your challenge lies in how to utilize/design the horizontal diaphragm to carry the story shear to the end stair towers, which are essentially two hollow core cantilever columns, or two out sized shear walls. I don't think you have much freedom in determining location of the towers, but you can decide that either a flexible, or a rigid diaphragm system is the best choice to meet the owner's wish. Once the decision is made, I don't see any difference from the typical building design. Again, IMO, either CMU, or concrete, will perform better than steel tower.

 

[phamENG]

SteelPE - I've designed a couple of these, and FEM/3D modeling software makes it easier. I generally used RISA's CMU shear wall design tool. ETABS has also proven useful. That said, I did some hand calcs to verify and got sufficient agreement to feel comfortable with the model results (sorry, don't recall how close the results were).

My approach was to look at the shaft as a thin walled, cantilevered member. In a stair tower with your dimensions, the doors are typically close to a corner. For this reason, I assumed an open cross section - essentially a weird C shape with the 3'4" opening assumed to be full height. Then it's first principals, which can get tedious if you're ultimately relying on this without a backup - I had RISA/ETABS, and a limited project budget, so I approximated some of this. You can work out your flexural tension and compression forces and direct and torsional stresses that can be translated to your CMU strength checks.

Keep in mind that, if your diaphragm is stiff enough, it will help to restrain warping in your open shape. Combine that with the fact that at the point of load application you really do have a closed shape, your analysis will have a bit of a conservative boost there.

 

[JLNJ]

I think the proportions will let you consider it closed (depending on the size and location of the openings).

I would start with the design as a relatively simple cantilevered rectangular element and see where it goes from there.

 

[SteelPE]

I guess the point is, I have never attempted a design like this before. How do you prove the loads wrap about the corner of the stair?

The initial design calls for a solid grouted cmu wall with bond beams every 4'-0" o.c. There is a door located in the corner of the tower at the basement at at the top level (not in the middle level).

As of now I am trying to abandon the idea in lieu of something I can prove (a steel brace frame) and the client is not happy with the proposed abandonment.

This is something I would like to learn how to do as I run into similar problems every once in a while. Is it just a simple as calculating the properties of the section (Ix, Iy Sx, Sy etc) or is there more to it than that?

 

[r13]

If you can connect the diaphragm and the towers as an integral unit - a horizontal deep beam with end columns, and get the shear to the towers, then, yes, it should be as simple as you were asking. And, I think JLNJ got the point - think simple and make it simple. How you design floor slab with a small opening? The idea can be applied to the walls with door openings too.

 

[phamENG]

I agree - if just stairs and only two openings near a rigid diaphragm there's no reason to consider the cross section open. Elevators with big gurney openings at each floor are another story.

To get the load into the towers, you'll need collectors that tie into the walls. Could be angles between joists and bolted to the wall. Could be a concrete element if you have the depth. Most contractors don't want to stop the masonry to pour a slab onto the block, though.

You're right, though - it is mostly that easy if you're lucky enough to have shafts that line up with (and are centered on) the axis of the building. You just need to pay attention to corner detailing at the bond beams to make sure you have good continuity. It's a tough spot for the mason to get right with the bars crowding as they sometimes do. It's usually not much of a concern, but if you expect the whole shaft to behave as a unit it's a bit more important.

 

[jayrod12]

You only talked about lateral resistance in the long direction of the stair, I would likely be using the two stair cores for all of the lateral. I would bet that it is more than adequate in both directions.

 

[JLNJ]

I think it is as simple as calculating the rectangular tube's section properties, except you will need some special treatment at the doors. The door at the bottom will cause the most headaches - maybe you can get the Architect to push the door a little bit away from the corner.

If you are worried about deflection, this kind of a squatty wall might have some shear deflection considerations, but I doubt for three stories it's a concern.

I imagine the worst case will be the transverse direction where all the shear is taken by the short walls and the force is concentrated near that door. Some jiffy calcs show 11 psi gross shear if the walls are solid grouted and the load is equally distributed. Not too bad.

 

[SteelPE]

So I went back this afternoon to look at my hand calculations and I discovered an issue with my calculation of equation 8-28 of ACI 530. Here I was using my full M/Vd where, for the purposes of this calculation, M/Vd need not exceed 1.0. My wall has a high moments pushing this equation to yield negative answers if you do not cap the value as allowed in ACI.

So, I am thinking I can get a plain straight wall to work. I haven't checked deflection though.

 

[masonrygeek]

TMS' Masonry Designers Guide has some examples in it for shear walls which is where you might have seen some examples. And as PhamEng has said, using computer software would make this easier. There is no reason that a masonry solution won't work here for such a small element.

If you are in the right area, you might be able to contact a local structural masonry coalition who can provide some assistance.