Stair stringer with multiple flights and landings
Stair stringer with multiple flights and landings
(OP)
I have an architecturally driven stair stringer design challenge. The stringer spans 2 flights of stairs and 3 landings, see attached sketch. As such, there are 4 "kinks" in the beam. I know that the beam has to be designed for the global moment WL*L/8, with full strength welds at the kinks to develop the member capacity.
What about the local affects at the kinks? I believe there needs to be a stiffener at the joint, designed for axial load. The axial load, C or T, is derived from breaking the flange forces down into components, see sketch.
Comments? Is it really this straight forward?
What about the local affects at the kinks? I believe there needs to be a stiffener at the joint, designed for axial load. The axial load, C or T, is derived from breaking the flange forces down into components, see sketch.
Comments? Is it really this straight forward?






RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
BA
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: Stair stringer with multiple flights and landings
Dik
RE: Stair stringer with multiple flights and landings
I'm surprised that your deflection is so low...are you sure? It looks like your span is somewhat over 20 feet.
RE: Stair stringer with multiple flights and landings
Concrete filled pans or thick stone for step increase global mass of the stair and then can lower the frequencies of vibration (of the stringer) enough to be really sensitive to vibration. Seriously. More than one mode shape must be accound for too!
The parameter to check for stair vibration is the acceleration response felt by walkers or worst felt by people wating on mid-height landing.
With this kind of stair, you can go up to the fourth walking/running sub-harmonic. Then all stair with vibration frequency lower that 10-12 hz (walking freq. * 4) can be sensitive and further analysis are required by specialized structural engineer.
RE: Stair stringer with multiple flights and landings
I am stuck with a similar stair design problem. Can somebody guide me as to how to design the connection as shown in the attached?
the reason for the bolts being off-centre is: I have to use chemical anchors as it is an existing slab i am fixing to. Many thanks.
RE: Stair stringer with multiple flights and landings
However, for your application, you should provide a "ledge" overrun off the top flange of your stringer channel that will extend over the edge of the concrete. This will reduce some of the shear load on your fasteners and make stair installation much easier. Another way to do this is to create an "L" shaped base plate with a 50 to 75mm overhang onto the concrete. Again, this will significantly reduce the shear load on the anchors.
Pay close attention to the shear reduction values for your anchors as the anchors are quite close together. You will need to reduce the allowables for both spacing and edge distance to the bottom edge of the concrete. Check the anchor manufacturer's tables.
RE: Stair stringer with multiple flights and landings
Thanks for the tip. I agree, an L-shaped plate is a good idea!
(Can the moderators please move the post?)
RE: Stair stringer with multiple flights and landings
Dik
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
I am not sure how you calculated your reactions at the top of the stair.
If the right hand support is regarded as a pin and the left hand support is a vertical roller, the only reaction at the left end is horizontal while the reaction at the right end is both horizontal and vertical. It would be similar to a ladder pinned at the bottom and leaning against a frictionless wall at the top.
Alternatively, if the stair is supported with a pin at one end and a horizontal roller at the other, the only reactions are vertical.
How did you arrive at Rv and Rh?
BA
RE: Stair stringer with multiple flights and landings
Note : If your support are pin, the stair is more flexible and more suceptible to vibration !
RE: Stair stringer with multiple flights and landings
Not sure whose post you are responding to, but if it is mine, you are way off base. The bending of the stringer does not "pull on the support (like an arch)" as you stated. Kindly defend your comment so that I can respond to something semi-sensible.
BA
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
What is the span? Foot fall induced vibration could be limiting criteria.
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
If the structure either side of the stair beam is not able to resist thrust, then the pin/roller assumption is valid. Otherwise, some horizontal force may be present. Its magnitude cannot be determined without knowing the stiffness of the adjacent structures.
A horizontal force is not necessary to satisfy statics so why not consider a vertical reaction at each end and a horizontal reaction of zero?
BA
RE: Stair stringer with multiple flights and landings
Further, if you provide a "lip" or allow the stringer to "hang" on the concrete edge as dik and I suggested, the anchors will carry much less of the vertical load and the horizontal load will be against the concrete, not pulling on the anchors.
RE: Stair stringer with multiple flights and landings
When I have had similar instances of framing I typically create a quick SAP model. I then put the reactions as both pins and then I release one end and compare the results. Look at the forces resulting from the horizontal thrusts, if they are small (which in your case I bet they are manageable) then you can leave as is and design for these forces. If the thrust forces are too large to handle then you have to look at revising the framing to allow the horizontal deflection (so you can realistically model as roller) and to make sure you can live with this deflection. Adjusting the size of your stringer will dictate the amount of horizontal deflection you'll have.
The way you are describing your framing I think you'll have a thrust force unless you modify it to allow it to slip at either the top or bottom horizontally.
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
Dik
RE: Stair stringer with multiple flights and landings
If the beam is straight its a different story.
RE: Stair stringer with multiple flights and landings
Of course, this is not applicable to a stair with allowed tranlation at the top support !
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
Dik
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
If the gravity load is W centered at midspan, span is L and height difference is h,then if Vt, Vb are the vertical reactions at top and bottom and H is the horizontal thrust, from statics:
Vt = W/2 -H*h/L = 11kN
Assume h/L = 0.4
Using the reactions shown on the sketch,
W = (Vt + H*h/L)2 = (11 + 35*0.4)2 = 50kN
Vb = 50/2 + 14 = 39kN
If the reactions shown on the sketch are accurate and my estimated h/L ratio is close, the connection and beam at the bottom of the stair must carry a vertical reaction of 78% of the weight of stair.
To me, that sounds much too high, but I have not done a frame analysis.
BA
RE: Stair stringer with multiple flights and landings
....exactly
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
Specifically for jacks detail, assuming he is attaching to a concrete beam, I don't want to guess that when they post install the anchors that they are going to miss rebar. I have seen to many contractors do too many shady things with post installed anchors when they drill a hole and hit rebar.
RE: Stair stringer with multiple flights and landings
RE: Stair stringer with multiple flights and landings
i have modelled the 1st flight(from ground to 1st fl), so i would think the reactions at the bottom connection is larger as it is "standing" on the ground. i should actually model a flight between 2 slabs. thanks.
does anybody have any tips on dynamics? 4Hz should be ok?
my stair will essentially be a vierendeel frame - 2 stringers with plates welded to them to form treads.
RE: Stair stringer with multiple flights and landings
4Hz is very close to the first and second harmonic walking frequency and is not OK, the structure will resonate and vibration will be perceptible. You should try tuning it more to higher frequency > 8Hz and limit your peak acceleration between 1.5%g-2%g . or you response factor < 8.
RE: Stair stringer with multiple flights and landings
Since there are no dimensions in the OPs sketch there is technically no way to answer this question. In a practical scenario the stair will behave like a beam leaning against the upper support causing compression at the connection. With an exaggerated span the stair will behave like a cable pulling on the upper support.
RE: Stair stringer with multiple flights and landings