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Stair stringer with multiple flights and landings

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?

 

RE: Stair stringer with multiple flights and landings

how worried are you that vibration of the stair is going to be a problem?

RE: Stair stringer with multiple flights and landings

(OP)
Not concerned about vibration so much. The steps and landings are concrete filled pans, which should dampen vibration. Static deflection is ok, about L/400.

RE: Stair stringer with multiple flights and landings

For strength, it really is that straightforward.

BA

RE: Stair stringer with multiple flights and landings

Yep, straightforward.  And you are right about the stiffener.  Put it in.

RE: Stair stringer with multiple flights and landings

The long stairs will suffer from impact vibrations (of people bouncing down them) and a static stiffness may not be appropriate.

Dik

RE: Stair stringer with multiple flights and landings

I agree with the others.  I would provide X-bracing on the bottom of the stringers as sidesway will be a bit of an issue.  I have found X- or W-bracing to be necessary on anything over about 10 treads.

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

Quote:

Not concerned about vibration so much. The steps and landings are concrete filled pans, which should dampen vibration. Static deflection is ok, about L/400.

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

Hi there,

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

JacksPanic...you should start a new thread rather than hijack this one!

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

My apologies! didn't mean to highjack.  i thought it was relevnt to the topic.

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

Is it possible to provide a 'lip' on the stringer so it bears on the existing concrete and reduces/eliminates the shear connection.  Anchorage only holds it in place.

Dik

RE: Stair stringer with multiple flights and landings

dik...exactly

RE: Stair stringer with multiple flights and landings

JacksPanic,

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

Of course there will be horizontal reactions on all supports. The bending of the stringer pull on the support (like an arch).

Note : If your support are pin, the stair is more flexible and more suceptible to vibration !

RE: Stair stringer with multiple flights and landings

PicoStruc,

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

You are correct. I agree, roller at top, i.e. no Rh reaction.

RE: Stair stringer with multiple flights and landings

TedEP

What is the span? Foot fall induced vibration could be limiting criteria.

RE: Stair stringer with multiple flights and landings

If you have it bolted at both the top and the bottom I don't see how that will react as a roller on top. In order for the end connection to act as a roller the stringer needs to be able to deflect on that end when subjected to a force. If its restrained by bolts on both ends I would think it would have a thrust force. Maybe I am missing something.   

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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...

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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.   

RE: Stair stringer with multiple flights and landings

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 !

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

Quote (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.

....exactly

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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.

RE: Stair stringer with multiple flights and landings

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.

  

RE: Stair stringer with multiple flights and landings

(OP)
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.    

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