Decagon slab 1

[structuralex]

A slab is supported by blockwork in the shape of a decagon with a "radius" of 5.5 metres. The slab cantilevers out another 1.5 metres on all sides. There is a stud wall running through the middle which can accommodate internal columns. (please see attached)
Instead of designing the slab with radial and circumferential reinforcement, can it be designed orthogonally by simply taking 1 metre strips spanning over the 2 rows of beams and blockwork, and then adding additional top reinforcement local to the cantilevers - which would make the backspans act as a two-way slab in some areas..
Thoughts?

 

[dik]

The limiting load, if I recall is qr^2/6 for a plastic radial 'fan' failure. Check it out

Dik

 

[a7x1984]

No need to make things more complicated than you need to. Directly from ACI 318:
R13.6.2.5 — If a supporting member does not have a
rectangular cross section or if the sides of the rectangle are
not parallel to the spans, it is to be treated as a square support having the same area, as illustrated in Fig. R13.6.2.5.



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[ishvaaag]

Provide rebar enough for the factored tensile principal stresses in flexure in every of two orthogonal directions. The rebar will show equal capacity in every direction, what uses to be practical for near point symmetrical tensile principal stress requirements like those typical with near circular plans.

 

[a7x1984]

ishvaag: how is what you describe different from the ACI 318?

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[BAretired]

I think I would design the interior portion as stated by the OP with main steel bottom west to east and temperature steel bottom north to south.

For the cantilevers, I would add top steel normal to the wall, carrying it an equal distance to the inside. Temperature steel in the cantilevers would be parallel to the wall, i.e. circumferential. Two or three circumferential tie bars could be added to control the flying ends of the cantilever reinforcement.

BA

 

[structuralex]

BAretired: the east-west span is straight forward in terms of strength and deflection. As for the north-south span - would carrying the cantilever steel back an equal distance to the inside be sufficient? And what would control the deflection of those north-south cantilevers?

 

[hokie66]

I would keep all the reinforcement orthogonal, use the same amount in both directions, and add some trimmers around the perimeter.

 

[BAretired]

structuralex, the dead weight of the slab inside the wall balances the dead weight outside. Two or three top tie bars at the ends of the cantilever reinforcement would look after live load on the balcony, but if you want to, you could extend some of the steel a bit further. Deflection should not be a problem in my judgment but you might want to explore it with some numbers.

Hokie's idea appeals too. Perhaps it is the simplest.

BA

 

[ishvaaag]

Well, reading the quote from the ACI code it is quite different. The quote points to an area equivalent (and kind of support).

What I am describing is closer to the classical concept of reinforcing for tensile stress in shells considered as membranes, you deal with the tensile stress, and one trick to do that is to use rebar that shows equal capacity in every direction, as 2 equal orthogonal reinforcements at whatever vector in the shell does (omiting the small difference in capacity due to different cover in the 2 layers). We do the same here, but for flexure, and to start we use a model with the actual geometry, not one equivalent as per the ACI quote.

So, practically you read the tensile principal stress at the point in the face where the tension is tensile, and then there you simply imagine a elastic setup for the stresses that give you a moment per unit length, that needs be covered by the capacity of the mesh in one direction (and as well, and then, the other, since equal).

This results for many situations quite practical, starting from the point from higher stresses, you may find you only need the basic mesh plus another superimposed (or better, parallel) mesh to get a rational reinforcement, sometimes two superimposed (or better, parallel) meshes.

So by using just the scalar value of the biggest tensile stress at the face, the equal capacity mesh allows you to disregard the orientation of the principal stress. It is more applicable than it looks in that you adapt to the equal value contour plan of the principal stresses, so there having more tensile stress in one direction than the other can be reasonably dealt with. It also gives you excellent (at least qualitative) appraisal of where the reinforcement is needed.

I may also add that I have used such reinforcement scheme (as main, but not only device for design) in maybe tens of thousands of square meters of slab without no problem whatsoever. No wonder since it puts reinforcement where needed.

 

[ishvaaag]

... well, my english ...

with no problem whatsoever.

 

[a7x1984]

ishvaag: I do like your use of the scalar contours like you describe, but it "feels" like more work than needed for this application. What is the fallacy of using the ACI method in this instance?

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[BAretired]

To paraphrase what ishvaaag has said...equal reinforcement in two orthogonal directions provides equal reinforcement in all directions. That is an important concept which may not be immediately obvious but can be shown to be true.

BA

 

[a7x1984]

That sounds reasonable to me.

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