Reading thru section 13 of AS3600, when a standard cog is used at a slab edge the development length is reduced by 50%, the development of reinforcement for less than yield strength is linear but must be greater than 12*db. So for a typical slab edge, which is generally using N12's or 16's subject to typical loading conditions, add the side face cover, this gives a zone of approximately 230mm before reinforcement can be utilized in the cross-section for strength. Within this 230mm zone of the slab edge, is the general procedure to be checking this cross-section for strength using the plain concrete provisions of Section 20?
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AS3600 Sect 13 - Flexural design of concrete at slab edges 3
- Thread starter rscassar
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Settingsun
Structural
I take the development length of hooks/cogs the same way as Rscassar described, ie 0 to 100% over the reduced development length, rather than 50% to 100% per Rapt's comment, to be safe conformance-wise. Is this stated more clearly somewhere? It would also help with strut & tie design where the requirement to develop almost instantly is ever present.
On the question at hand, the 230mm length is the same order of magnitude as a slab depth, so loads applied to the slab surface near the edge could be carried non-flexurally to the developed cross-section. Railing moments applied to slab edge would need another strategy.
On the question at hand, the 230mm length is the same order of magnitude as a slab depth, so loads applied to the slab surface near the edge could be carried non-flexurally to the developed cross-section. Railing moments applied to slab edge would need another strategy.
li0ngalahad
Structural
As far as I understand (please rapt correct me if I am wrong), a cog alone does not provide 50% of development, it simply halves the development length. So if you need, say, 1000mm to develop a bar, if you have a cog at the end you just need 500mm.
We can reduce development lenght if lower stresses are required to be developed, however code has an absolute minimum development length required no matter what stress you need to develop, which is 12*db. My understanding is if you have less than that, you have 0% development. The cog still allows to half that minimum value, so the cog alone gives 0% development until you get to 6*db.
So for exmaple a 12mm bar at a slab edge, develops 0 MPa until you get to 72mm (6*db) from the cog, and at that point (with 20mm cover and 40 MPa concrete) your developed stress is 200 MPa and increases gradually, you get to 50% development (250 MPa) at 89mm from the cog, until it's full developed (500 MPa) at 178mm from the cog.
We can reduce development lenght if lower stresses are required to be developed, however code has an absolute minimum development length required no matter what stress you need to develop, which is 12*db. My understanding is if you have less than that, you have 0% development. The cog still allows to half that minimum value, so the cog alone gives 0% development until you get to 6*db.
So for exmaple a 12mm bar at a slab edge, develops 0 MPa until you get to 72mm (6*db) from the cog, and at that point (with 20mm cover and 40 MPa concrete) your developed stress is 200 MPa and increases gradually, you get to 50% development (250 MPa) at 89mm from the cog, until it's full developed (500 MPa) at 178mm from the cog.
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My feeling is that there would be a substantial degree of anchorage from the cog or hook alone, and I would think that the development goes from 50-100% over one half of the straight development length (rather than from 0-100%). Of course, for this to work as assumed, you would want to avoid splitting in the plane of the cog or hook and I imagine there needs to be a suitable amount of transverse reinforcement through that location.
The parallel concept is for shear reinforcement. The implicit assumption in the formula for Vus is that the stirrup is fully anchored beyond the hook (provided that there is a bar of at least equal diameter anchoring the stirrup in its corner). I am aware that ACI and AASHTO go a step further for #6 bars (19 mm) or greater, which require some additional development length past the hook and anchor bar before they are considered effective.
As a side note, there is an interesting paper (attached), which basically concludes that for small diameter fitments, even where an anchoring bar is NOT provided in the corner of the bend, the bend alone provides complete development. (Not that I would advocate designing in this way).
The parallel concept is for shear reinforcement. The implicit assumption in the formula for Vus is that the stirrup is fully anchored beyond the hook (provided that there is a bar of at least equal diameter anchoring the stirrup in its corner). I am aware that ACI and AASHTO go a step further for #6 bars (19 mm) or greater, which require some additional development length past the hook and anchor bar before they are considered effective.
As a side note, there is an interesting paper (attached), which basically concludes that for small diameter fitments, even where an anchoring bar is NOT provided in the corner of the bend, the bend alone provides complete development. (Not that I would advocate designing in this way).
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- #10
Thanks Rapt, that was my approach for a long time but it was raised to me recently that it is 0 to 100% development over half the development length. Before I posted last night I thought to have a read through ACI318-19 for a bit more commentary and kinda lead to the same approach.
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