Stair stringer with multiple flights and landings

[TedEP]

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?

 

[BAretired]

Bolted at each end, it is really no different than a horizontal simple span beam. For analysis purposes, pin/roller supports are assumed but the connections are usually bolted.

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

 

[Ron]

As much as we would like for our structural modeling to dictate the in-place structural response, it just ain't so. Yes, we can model the whole assembly as a simple beam with the roller as BAretired noted; however, that's not the way the structure responds in the field. As noted for this application, the concrete section to which the upper part of the stringer is attached is quite deep, thus the resisting structure is quite stiff relative to the stair section. This will provide a horizontal reaction, so in effect, you will have a pin-pin condition at the supports. This is necessary to consider for the connection design.

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.

 

[jdgengineer]

Agreed with Ron -- that was essentially the point I was trying to make.

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.

 

[jdgengineer]

and BAretired just so you understand my thought process. The only reason that thrust force is there is because of the landings. The beam is longer than a straight line between the top and bottom points and therefore will want to "straighten out". Similiar, to the thrust force on a sloped gable roof without a ridge beam...

 

[dik]

If you model it in a frame program with a pin and a roller, if there is any horizontal translation, I would suggest you have a horizontal for of sorts <G>

Dik

 

[jdgengineer]

Dik -- That is not true. Once you have a landing the beam is "kinked". Based on the stiffness of the beam it wants to straighten out. In order to straighten out it wants to push out one of the supports. No different than a rafter system without a ridge beam (hence the reason people used collar ties).

If the beam is straight its a different story.

 

[PicoStruc]

In the project I done, all stair stringers were bolted at both end, thus creating force( Vertical + shear) and moment transfert to the concrete slab below !

Of course, this is not applicable to a stair with allowed tranlation at the top support !

 

[jdgengineer]

Well I guess the rafter analogy I had didn't make sense, because it's pinned at the top. But it's the same idea. When it deflects it wants to kick out.

 

[dik]

sorry jdgengineer... I would think that if there was any horizontal translation that was restrained, there would be a horizontal force... should have added that the horiz translation was restrained... <G>

Dik

 

[Ron]

Agree dik...any horizontal restraint will result in horizontal force.

 

[BAretired]

If modeled as pin/roller, I think the roller end would move away from the pin. If modeled as pin/pin, the horizontal force would be a thrust, not a tension, so I don't think we are "pulling on the anchors". If anything, we are pushing on the concrete.

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

 

[Ron]

If modeled as pin/roller, I think the roller end would move away from the pin. If modeled as pin/pin, the horizontal force would be a thrust, not a tension, so I don't think we are "pulling on the anchors". If anything, we are pushing on the concrete.

....exactly

 

[mijowe]

for the connection detail I personally would embed a plate with headed studs in the concrete and come back later and provide a welded connection to the stringer.

 

[Ron]

mijowe...most stair fabricators abhor field welding...thus the designs with mechanical or chemical anchors.

 

[mijowe]

I commonly see field welded connection for steel stairs, too may miscellaneous pieces with blind connections, to be bolting everything as well as limited space to even make bolted connections. Also, tube rails where field welding to the stringers is almost always done.

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.

 

[hokie66]

Agree with mijowe about the post installed anchors. I specify ferrules to be cast in, or else a cast in plate like mijowe suggested.

 

[JacksPanic]

I normally have a plate cast in and stringers welded onto afterwards, but with these architects and timelines it was not possible. luckily the contractor on this site is not shady.

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.

 

[hetgen]

JacksPanic

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.

 

[charliealphabravo]

This post reminds me of a recent discussion in Pats Pub over whether a certain shallow frame spanning two supports would behave more like an arch in compression or if it would transition to a cable configuration in tension.

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.

 

[TedEP]

Thanks to all that responded to the original thread. We decided to add hanger supports at the middle landing to the roof in order to squash any concerns about vibration.