Terciary beams, Is this even possible? 2

[IngDod]

I got myself into a bit of a mess, I was approached to design a system with beams of very long spans (40 feet) supporting a second level(not a roof). I pointed out that it was most likely not possible to do the 40 feet span.. and the arch suggested the following system: Simply support the 40feet beam at the middle on another beam that spans in the perpendicular direction from column to column... It seemed a good idea on paper and I have seen this things before... Now the 40feet span beam (secondary) is resting on a 26feet span beam (primary).... to support the steel deck I need of course more beams... so lets call this ones tertiary beams... they span 13 feet and are supported by the secondary beam... I calculated everything and everything checked out for ultimate and serviceability conditions. However for the tertiary beams I only checked for deflection of that beam and I did not account for deflection of the secondary beams... Basically I got a beam with differential settlement on both ends... My question.. how should I calculate the deflection of this thing?.. I want to avoid any damage to non structural elements on top of the deck. This is still in the design stage, so there's no danger involved.

I attached a sketch to make everything easier to understand. The sketch only shows the section where the primary beam supports the secondary.

 

[CELinOttawa]

You must account for all deflection which will affect a given system or surface, which is the total deflection of all three of your "layers" of beams in this case.

And I agree that this is a silly layout and dumb way of addressing the problem.

 

[IngDod]

Sorry for reposting.. but I want to clarify some things, For total load (as shown on sketch) the absolute deflection at midspan of the tertiary beam is 3.5cm, this is too much If a traditional beam simply supported on both ends was considered (using the L/240 for dead plus live load). The visible deflection of the beam will not be a concern since everything is covered by drywall, however serviceability of course is... the live load deflection of this is 1.62cm.. the L/360 limit assuming simply supported is 1.11cm. However if I could account for "settlement" of both ends of the tertiary beam I would probably be within margins... My real worry is how would this affect serviceability of the tiles or any other non structural surface on top of the steel deck. I am not assuming the beams and steel deck to act compositely, since they are not usually built as such here.

 

[CELinOttawa]

You need to respect the deflection requirements, but the use of several layers of beams doesn't preclude pre-cambering them.

I would suggest you pre-camber and ensure that you also check the vibration characteristics of the floor. If this is beyond your ken, you can have a look at ATC 93 or Design Guide 11. If this is still too much, contact Dr. David Allen (one of the authors of those documents) who has consulted for us before. Fantastic, a dream to work with, and very reasonable rates.

 

[IngDod]

CELinOttawa: Thanks, I had misgivings since the beginning.. but I got convinced into trying it out.

 

[Ron]

To put it bluntly, your system is "ass backwards".

Your architect's concept is commonly known as a "sky hook"....doesn't work. If you have enough vertical room to do that kind of crap, you have enough room to put a logical purlin/beam/girder system in place to take the loads.

 

[Triangled]

Wood panelized roofs in the west u.s. used to be designed like this, girders, secondary carrier beams, 8' oc purlins spanning 24' +\- (where expansive column free floor space desired) until longer engineered wood members became economically available.
Don't think I've seen it on a floor. But camber, as stated above, may help, though not with vibration. Offhand, I'd expect your tertiary members to realize almost full live load at some point, your secondaries not so much, and your primaries rarely if ever.

 

[IngDod]

@Triangled: Thanks, the main limitation here is that a truss capable of spanning this distance without actually costing more than the actual structure was about 1.5m tall. And there's no commercially available girder of enough depth for this. The owner is adamant about having a column in the middle of the span... Hence having to deal with this thing.

 

[IngDod]

This made me ponder on something.... Common practice is to analyze secondary beams as simply supported and size them based on the deflection obtained from this condition... so lets say you size it for the usual L/360 of live load and select a section close to this limit... lets say you select a section with a deflection of 0.8cm and the L/360 is 1.1cm.... then you size the main beam for a deflection of L/360.... say 1.5cm.... if the secondary beam frames into the main at center or near the center... would this not lead you to a situation where your secondary beam actual deflection would be 0.8 + 1.5 = 2.3 > 1.1 ?... actually L/180 Worse than the L/200 at which AISC tells you that doors wont close?

How is this situation different from what is happening to me right now?.... Provided I can get deflections below the L/360 for live load (which I just managed to do by decreasing the spacing of the tertiary beams) why would this be such a bad idea. I am trying to play devil´s advocate... I would still use a different system if possible.

 

[Enhineyero]

Hi ingod here is my take on this:

1. effect on tiles and finishes - I believe that your should be concerned with differential settlement between the ends of your tertiary beam, since the maximum differential settlement is 2.3cm (3.5-1.2) then your finishes would likely be damage because difference between the levels is beyond 2.0cm, which is the maximum allowable deflection for some codes to prevent damage for finishes.

2. Serviceablity in terms of visual perception - I think that for your tertiary beam you should take into consideration the Span as 26ft. My reason for this is people would look at the system as a whole, like those of a flat slab, since the middle support is also deflecting. However one other concern for you would be vibration since the deflection is relatively significant.

 

[CELinOttawa]

This still feels like a stupid system; I know you think so as well, and please know I am not meaning to be insulting.

What about honeycombed beams? What about WWF? There has to be something commercially available to you which will do this span; 40' is just not that crazy! By my "back of the envelope" you need a heavy W27 beam, which are not at all uncommon, and possibly a tension cover plate or built composite with a concrete floor.

What loading are you designing for that you can't get this to work clear-span?

 

[IngDod]

@CELinOttawa: I understand, I also dislike this idea very much.. but I am limited in the sections that are available... and the problem is that picking anything other than sections that are commercially available is not a possibility here.. honeycombed is not possible and I am limited to rectangular hss.. not even W shapes. the loads are Dead = 62lbf/ft2 and Live = 62lbf/ft2. The "tallest" hss beam is only 14", which is what I am using for the primary... the secondary is 12.6 inches.. which is the next smallest section. So I feel that I am basically forced into this, and while it feels pretty stupid I cant see a structural (failure, instability)reason no to use it if nothing better is available.

@Enhineyero: Thanks, those values were for dead load.. for live load the absolute deflection at midspan of the tertiary is 1.6cm.. the differential would be around 1cm. I am concerned on the visibility part.. and also I would not want anyone walking on the floor to feel any unevenness. The dead load deflections are rather large... around 1.5 cm, but I am assuming that any deflection due to the weight of the concrete on the steel deck (wich is most of the dead load)will not count towards this perception since the floor will deflect as the concrete is being poured and the final surface will still be level. Deflection due to steel deck is about 1cm, deflection due to surface finish is about 0.5cm.

Could you please explain more on the 26ft for visibility... this is the one area were I am mostly worried.. the tertiary spans only 13feet.. resting on the secondary which spans 40feet and then the tertiary which spans 26feet. Both the 40feet and the 26feet deflect within L/360 in their respective directions (for the 40feet I checked for both 40/360 at mid-span and 20/360 at quarter span).

 

[Triangled]

I might be getting mixed up with the words tertiary and primary and secondary, but ...
What if you added another "secondary" assuming that is your 40' span, so that you had two secondaries supported at third points on your "primary", the 26' span. Now your tertiaries are spanning 26/3' instead of 26/2', your secondaries are supporting less load and your primaries, though supporting more load are supporting it at (perhaps) better points for deflection.

 

[paddingtongreen]

Frankly, I don't understand why, if you can get a forty footer to carry a heavy load, why can't you get four or five to take less load and a completely conventional structure, beams long way supported on girders going the short way.

With your arrangement, the maximum deflection is at the center of the secondary beam with a very slight chance that it is a short distance from there along the central tertiary member.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[IngDod]

@Triangled: Yes "secondaries" are 40feet... The problem with this is that as it is right now the 40feet are attached to columns at both ends.. in order to have them at third points of the 26 feet "primary" I would have to reduce the spacing of the columns.. And guess who is not going to like that idea..

@Paddingtongreen: Thanks for your reply, the problem is the that the columns that support this beams (40feet)at their end points are spaced 13 feet... to have more beams spanning 40 feet I would have to reduce the column spacing to half at least... which is very narrow.

The system looks like this... Its a rectangular building, with three lines of columns... the first and last have columns spaced every 13 feet... half of this columns carry 40feet beams and half 20 feet beams. The middle line has columns spaced at 26 feet.. this is the line that carries the 26feet beams that support the 40feet beams.

 

[Triangled]

I'm confused... a plan view might help

 

[IngDod]

Thanks, I am adding the plan view... Hope its more clear now.

 

[AELLC]

That looks like a "mat" analysis- the primary will attract more moment since it is shorter. You could solve iteratively until you get equal deflections at the intersection of the 2 beams.

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.

 

[IngDod]

@AELLC: Thanks for taking a look. This was my "control" check to make sure my results were realistic, both beams have equal deflection at mid span. I decided to add cross braces at the end frames to avoid any dependance on the long span beams for lateral stability of the structure... This beams will be simply supported... welded in the contact areas to keep them in place.. but I don't see how a "connection" of this kind can be relied upon to transfer lateral load from end to end of the beam.

This thing is ugly, dumb and stupid.. but apparently it can support itself.

 

[AELLC]

Oh don't be so downtrodden. I have been forced to design beam systems with up to 5 levels of transfer in a few wood custom homes I have done.

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.