Lateral Loading due to seismic acceleration

[Gnique]

thread507-411736

I went through the 2016 thread looking for guidance and still felt the need to consult with the inmates here. If we take a stair / landing assembly where the landing is supported by four supports free to translate (within say 3" each way) in the X-Y plane and the lower run of stairs free to translate in the X-Y supported by a concrete floor slab with the upper flight connected at the stringer ends to the building structure. Further suppose that the assembly is NOT on the ground floor. It is reasonable to assume that the assembly is loaded in one and only one way - displacement of the building at the points of attachment (two places - at the stringer ends on the top run of stairs). I have also assumed that the six points of contact (two at the lower stair and 4 at the landing) that are free to translate in X-Y are friction-less. When the building moves in and out of the paper (the elevation view that would show the stairs as a sideways "V"), a shear load will be generated at the two connections at the top. Now this next part starts to be kinda half assed. It could be assumed that the top stair acts as an almost infinitely stiff diaphragm that causes the whole assembly to follow along with the building story drift. I realize that the assembly will resist translation because of its momentum. I also realize that a load could be determined by deflection BUT the determination of Iy of the stair run seems to me to verge on the impossible. Also - would Fp even figger into the analysis? I have thought about this a great deal and have even studied the Higgins OSU test and taped together a cardboard model.

https://www.researchgate.net/public...ance_under_Combined_Seismic_and_Gravity_Loads

It concerns me that I am unable to determine the tension chord forces that statics tells me must be generated. In short, I am completely confounded as to how to build a structural model in my mind. Any help in clarifying this little conundrum would be much appreciated. Thank you.

 

[Agent666]

Hi Gnique

Perhaps if you posted a sketch of the arrangement, I'm having trouble visualising the exact arrangement you are describing in relation to some of the questions you have and the arbitrary coordinate system/orientation of the stair with relation to your in and out of the page reference. There seems to be a lot of questions thrown in there!

 

[dold]

I'm pretty sure i'm following you OP.

To simplify for everyone, maybe:

Take a plan view of a stair. Stringers are horizontal in plan and there is a floor beam running vertically that receives the stringers. Halfway between floor x and x+1 is a (heavy) landing. Building shakes plan north-south. The landing is accelerated/responds to the displacement of the floor above (translation north-south). OP wants to know the tens/compression in the stringers, supposedly for designing connections (OP?)? Assume all horizontal boundary conditions released except pinpins at top of both upper stringers. All nodes supported vertically for simplicity.

You have a mass at the end of a cantilever. If this were mounted at ground level i'd just use Fp (conservatively) for the horiz load occuring at the landing along with mass of stairs at C.G. of stairs/flights. (Not trying to be cavalier about egress, but say it's just a storage mezzanine stair, for example). But, if you're up 50 stories in a highrise, the acceleration of the landing is going to depend on the acceleration of floor x+1, and i suppose the stiffness of your stringers (and contribution of the 'sub diaphragms of the treads' for goodness sake). Now that we're thoroughly into the weeds...this depends on the construction of the rest of the building.

Seems like you can resolve this in at least two ways:
1) rod (plan) bracing below the treads, from the landing to floor x+1 (and from floor x to landing - moment to upper flight xbracing via landing pan/slab if it works).
2) If you want to find load via deflection, i assume you already know the drift of the floor in question (x+1) and...everything else that one would use to find this.....? Figure Iy of the stair using parallel axis theorem I=Ic + Ad^2 where d=tread width. You'd have to ensure your stringers act compositely, i.e. your treads must develop the required shear flow between the stringers. Then find P. Then find M. Then find Tens/comp. (probably not the best way to do this)

I trust that you can find tension/compression in the stringers once you nail down what load to use? What exactly are you trying to design here? Connections? Have I interpreted your question correctly?


Ignore the columns and all other framing in pic below. Just pay attention to the landing and the stringers. And floor x+1 beam.

 

[dold]

Following up. I just read the 2016 thread. If you're using the stairs as part of the lateral system of the building, you're doing it wrong. The mass of the stair should absolutely be considered in the main building design. It also must be considered for the stair itself, of course. The only time i would mayyyyybe consider applying the response coefficients of the building to the design of the stair would be in the case where you are deep/high enough in the building to have the ground acceleration 'fully modified' by the building by the time it gets to the stair, if you will... This would reduce your loads anyway, so unless you're really hurting to get a connection to work or whatever, just use nonstructural components.

By the way, is this stair totally isolated from all framing/shafts on all sides except for the connection to the floor above and below? I.e. floating stair?

Couldnt help myself. Is this what you're talking about, OP? 1kip load in red. Rxns in green.