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Analysis of Cantilever Corner Balcony

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csways_

csways_

Structural
May 3, 2019
16
I've been tasked with analyzing a conventionally-reinforced concrete cantilevered balcony at the corner of a high-rise condominium. The balcony, and others in the stack, had been supplemented with an HSS column at the outboard corner to remediate purported excessive deflection. The Owner now wishes to remove the HSS columns because of corrosion and deterioration of adjacent concrete.

What is the design methodology for a cantilevered corner balcony like this? And, what are reasonable options for strengthening should the balcony slab be determined to be under-reinforced, etc.?

A simple sketch of the general balcony layout is attached.
 
 https://files.engineering.com/getfile.aspx?folder=f6c97aa2-44aa-458c-bc63-7d580aa5329f&file=IMG_20200111_202619191.jpg
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A fea plate analysis would be my choice. As for choice of upgrade I don't think there are that many obvious options, with the limited info. Creating a support beam that cantilevers off the walls would be one that comes to mind, but what are the walls? does this has column continue above this level so extra load and hevier deflection criteria. To many questions.

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."
 
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3D software is the easiest. It naturally accommodates the two way action.

If it has already been propped because it sags too much then isn’t it a moot point as to whether it works without the props?

As for rectifying. I see a lot of corner balconies with retrofitted corner columns. Sometimes retrofitted perimeter beams too.
 
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If you get lucky and it's a long term defection problem and not a strength problem, you may be able to re-level the surface. That's a big if, but not ruled out from what you've posted.
 
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The Owner wishes to remove the columns at the outboard corner. Perimeter beams are an option as there are building columns at the corners. See the revised sketch with column locations, attached.

FEA analysis of the balcony slab is an option, but I would prefer to dig into the methodology for design. Can anyone recommend a reference for analysis? All I have been able to find in a quick search is this excerpt from an unknown text, which really isn't applicable, also attached.
 
 https://files.engineering.com/getfile.aspx?folder=a0431312-ebaf-4508-b5e4-ba3aab55023c&file=415421705-Cantilever-Corner-Slab.pdf
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Can you run a tension rod from the slab corner back to the wall? If acceptable, it should be simpler to handle.
 
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If the slab was originally designed as a two way cantilever, it may have no bottom steel. If that is the case, adding a corner column was the wrong solution as it creates a demand for bottom steel. Hopefully, the slab had nominal bottom steel, but that should be confirmed.

One solution to reduce deflection is to add a beam under the slab as illustrated below:

CornerCantilever_jwblzu.png




BA
 
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Equivalent frame or strip methods would be options for hand analysis.

Since deflection has already been noted to be an issue you may be looking at a demo and replace situation or carbon fiber reinforcement. In the carbon fiber option you'd need to jack up the slabs to "unload" the slab and back out the existing deflection.

Rapt, SpSlab, or Adapt would be good choices for software using the strip method as well.

Open Source Structural Applications:
 
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csways,

If you would like to analysis by hand, try "consistent displacement method" - set equations of cantilever beam deflection for both spans (Δ1, Δ2, in directions with beam length L1, and L2), and use the relationship, Δ1 = Δ2, and wtot = w1 + w2, to solve the portion of load taken by beam in direction 1, and direction 2. I believe you have learnt this in school, just a reminder here.
 
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An upstand beam along one edge could help, provided you can carry a backspan into the building.

It sounds like this building has experience severe serviceability problems in the past. You don't want to do something to make it worse.
 
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