Mono Stringer with thin HSS tube 1

[fp23]

Just looking for a reality check/opinions on this. I'm designing a mono stair stringer for a client (pdf attached showing the layout and section). The stair has 2 short runs with landings and one longer run. The client would like to keep the monostringer as thin as possible. I'm suggesting an HSS8x2x1/2. I've modeled this in Risa 3D with 40psf off center, or a 300 lb point load at the edge of the tread. I'm keeping the deflection limited to 1/4" at the end of the tread. The reactions are fairly reasonable since the short stringer runs at the top and bottom can spread out the torsion into a T/C couple.

I've checked vibration per the AISC design guide and making the vertical and horizontal periods work is not a problem. The stair has handrails the start horizontally coming out from the wall and go under the treads and turn up, so it is pinned to the wall for horizontal stability at 4'oc. I am at about 1.98%g for the eq 4-8 in the design guide. I think with the added stiffness of the welded angles, handrails, etc I should be able to get this under the recommended 1.7%.

I have 2 questions:

1) Intuitively an 8x2 makes me a little worried that it's going to feel bouncy when someone stands off-center however with the analysis that I have done I am getting more comfortable with it. Does this seem like a crazy idea to anyone else?

2) I've seen some people posting about checking vibration using dynamic analysis in Risa 3D. What loads do you use for the dynamic analysis? is it the 168# point load in the AISC design guide? or just the stair weight? When I run the dynamic analysis using the point load I don't get any mode shapes with participation over 25 but it does seem like it's giving me some possibly useful information on the frequency. The model won't run with just the dead load.

 

[phuduhudu]

The mono string size doesn't seem unreasonable if it is working for deflection and strength. As you say it is the torsion component that could be the concern but if your deflection is less than 1/4" at the tread end with a point load then that should be OK. Are you using a pattern distributed load with all the load on one half of the stair (e.g. a crowd of people all standing on one side) as that would give you the worst torsion and deflection. I would check the mode shapes and frequencies under both a point load and full distributed load and distributed load on one side of the stair only. For stairs a natural frequency over 10Hz is good (

https://core.ac.uk/download/pdf/237022538.pdf)

 

[fp23]

@Phuduhudu Thanks for your response! I do have seperate load cases set up where each tread is only loaded on one side. The 300# pt load is producing the worst deflection because I modeled it right at the end of the tread. Thanks for the article too, I like the idea of using a smartphone to measure acceleration once it's installed.

 

[KootK]

The 8x2 HSS nags at my intuition as well. But, then, I got burned pretty badly on a stair like this once upon a time. It underwent three fixes over the course of two years and never actually got fixed.

My primary caution to you on this is to makes sure that your modelling isn't overly optimistic:

1) Does your software account for HSS warping torsion in addition to St Venant torsion? Many FEM programs don't.

2) Are your high and low supports truly rigid laterally (and perhaps torsionally) or ought they be modelled with springs or slide bearings? Concrete floor will be very rigid. Wood floors will be pretty flexible. Steel floors will land in between. The support rigidity will massively affect the overall vibration performance.

With respect to the loads to consider for vibration, that very much depends on the occupancy and owner expectations. If it's a residence, it may be enough to consider one or two people inducing the vibratory load. If it's a musing, you might want to consider a small army of girl guides walking down the stair in lockstep. Your stair might pass muster for the former. It wouldn't stand a chance for the latter.

 

[fp23]

@KootK thanks for your insights.

I'm using Risa 3d which does have a setting that you can turn on to account for torsional warping so I think I'm set there. I also have some extra stiffness left unaccounted for from the L4x4 angles that are welded to the top which makes me feel better.

As far as the supports go, I'm connecting into a little bit of everything, a steel beam, wood walls, a concrete wall, and an LVL beam. My client is the steel fabricator and I have warned them that it is difficult to predict the vibration performance. I think I am going to let them know that we can try this out based on my analysis but there could be some field stiffening that has to be done at the connections or potentially to the HSS tube.

This is going to be in a house so I'm not worried about large groups. It also has 2 turns with landings but there is a run of 11 steps between the landings where a walker could get things oscillating.

 

[KootK]

Any change the handrail thing is cantilevering off of the concrete wall? I would find that quite desirable. If it's coming off of a wood wall, I would worry that the vibration restraint would wind up pulling out the rail to wall fasteners.

 

[KootK]

I don't see the L4x4's doing much to alleviate vibration.

The condition that I feel is the most risky is having the top or bottom of the stair tied into a wood diaphragm when that diaphragm has been assumed to provide lateral restraint in the modelling.

I think I am going to let them know that we can try this out based on my analysis but there could be some field stiffening that has to be done at the connections or potentially to the HSS tube.

Just as a data point, this his how it went with me:

1) Stiffened the HSS. No meaningful improvement.

2) Cross braced the landings to make them stiff in plan. No meaningful improvement.

3) Fill the HSS with concrete to add mass. No meaningful improvement.

4) Owner gave up and decided the vibration would make a nice conversation piece for his well to do friends.

I've seen some monumental stairs where the engineer detailed a mechanism under the landings that allowed for weight to both be added to the landing and shifted around on the landing. This, in anticipation that there might be problems and that trial and error may well be required to solve them. Pretty clever. Obviously, this would tend to look ridiculous on a stair in a house with a contractor client.

 

[fp23]

Unfortunately the handrails will be attached to a wood wall primarily.

I agree that the welded angles won't help much for torsional strength but they do almost double my Ix (transformed section) which makes a notable difference in the AISC vibration calcs, about 20% increase in Hz.

Thanks for sharing your experience, data point 4 made me laugh. I've designed one before where I used an 8X6 (or 4 I can't remember) tube. It felt a little bouncy to me but no one ever complained.

After your comments I'm probably going to push them to use a slightly wider tube and then give them a caveat that parts of this analysis are subjective and this could feel bouncy and require field fixes.

 

[KootK]

I agree that the welded angles won't help much for torsional strength but they do almost double my Ix (transformed section) which makes a notable difference in the AISC vibration calcs, about 20% increase in Hz.

I believe you. However, I also do not believe that strong axis flexure is the mode of vibration that would bite you here. Adding margin to that which is non governing isn't really adding margin with respect to outcome.

Tube-schmoob. Watch those diaphragm connections. If it's wood, get something behind the stringer that looks like a plausible drag strut.

 

[Greenalleycat]

We've designed some similar stairs here, though not identical - a couple of snips below
Typical construction here is an RHS stringer then welded SHS stubs welded to a flat plate that solid timber treads are attached to
It creates a pretty hidden detail, it's nice
Typical RHS is 200x100 (8x4 in Americanese) - we don't have a 200x50 like you seem to (8x2)

One of the big concerns we've found is that a point load + balustrade moment load combination really fucks these things up
You get quite noticeable deflections and generate large tensions in your end fixings
In our case that's a cluster of 3 - but in your case that would only be 1 fixing as the angle wouldn't be wide enough for 2 or 3?

 

[fp23]

Good points and thanks again for your thoughts on this, they've been very helpful.

At the 2 points where I'm connecting into wood floors I will definitely have them add blocking and coil strap to drag some horizontal load into the diaphragm.

 

[JAE]

I did a stair that cantilevered off a large steel tube buried in a wall - the treads looked like they were floating out of the wall.

We kept the deflection at the end of each tread to 3/16" under a 200 lb. load.
I believe the buried tube was a heavy 8x6.

After construction it felt bouncy at the ends of the treads. Not so much near the wall.

8x2 seems, feels, looks, feeble.

 

[KootK]

Good points and thanks again for your thoughts on this, they've been very helpful.

You're welcome. It's kind of our role here to be negative ninnies so keep that in mind. You pitch your great idea, we hammer away at it mercilessly, you run off and do what make sense to you. 'Tis the circle of life. Based on my reputation here, you'd probably be astonished at the risks that I'm willing to take when I feel that the situation justifies it.

I'm using Risa 3d which does have a setting that you can turn on to account for torsional warping so I think I'm set there.

Make sure that RISA is accounting for torsional warping in HSS. Not just in WF and Channels where it's an obvious problem. Frankly, I don't yet know how to do that for HSS by hand. I just know that, at your proportions, it's a thing. Just like how you can twist a 2x8 with your hand even though it's a torsionally excellent, closed section.

 

[KootK]

...data point 4 made me laugh.

It was something a bit special. Straight scissor. If a single person got anywhere near the mid-landing, that landing would dance around in plan like a Ouija board trying to spell your name in cursive. Quite visible lateral movement with no discernable vertical movement to speak of.

 

[fp23]

@Greenalleycat - Thanks for your example. Fortunately I have a pretty solid tread configuration with a flat plate that extends almost to the edge of the tread and a vertical fin on the front that stiffens it up. I have done treads in a similar way to your example before and had the same difficulty of getting the wood fasteners and flat plate bending to work.

@JAE - Thanks for your example and opinion as well!