AS3600 Standard Cog Development

[Legoman92]

Hi guys,

Just had a bit of a discussion at work regarding how developed (in terms of strength) a cogged bar is at 0.5Lst past the back of the cog.
My understanding has always been that if you have a standard cog to AS3600 and provide a straight length in the other direction of 0.5 x Lst then you have a fully developed bar at that location. (as long as you have a transverse bar enclosed at the bend if the stress is above 400MPa).

For example lets say you have a N20 Vertical bar (for a pedestal) cogged into a slab. The development length of a N20 Vertical bar (50 cover, f'c = 32 MPa, fy = 500 MPa) Lst = 830 mm

For argument's sake, 0.5 Lst = 0.5 x 830 = 415 mm. Therefore say allowance of 50 (cover) + 20 (bar direction 1) + 20 (bar direction 2) = minimum slab thickness of 505mm to develop the full strength of the bar (as long as a transverse bar runs through the bend).

I've attached the commentary to this post which from my understanding (correct me if I'm wrong) says the cog itself provides 50% of the capacity and then the straight section provides the other 50%.

Therefore, my understanding is if I provide say only 300mm of a straight section (in lieu of 415), it is conservative to say the the capacity of the bar = 300/415 x 500 MPa = 72% ?

Thanks

 

[rapt]

You cannot consider a standard cog to contribute if you are relying on extra length past the cog .

You would have to increase the bend radius of the cog to reduce the bearing stresses in the bend and just consider the total bar length as the length. You cannot include the extra benefit from the tight cog bend.

 

[Legoman92]

The way the code is written it says in the commentary the cog itself contributes 50% and the straight extension provides the other 50%. At least in my understanding

 

[rapt]

You asked for others opinions. I have given mine.

To develop more than 50%, you have to develop more force through the curve, and 13.1.2.5 gives a minimum radius for this. Complying with that minimum radius therefore means you do not get the extra benefit for the cog through the curve from 13.1.2.6.

You either use a cog by itself and get 50%, or use make the radius large enough to avoid bearing stress problems and treat it as an equivalent straight length.

 

[Legoman92]

Ok so by your logic, if the cog + straight length of 0.5Lst only develops 50% of the bar capacity, then why wouldn’t you just put the straight length of 0.5Lst by itself? Or am I misinterpreting what you’re saying?

 

[rapt]

Because the straight length of .5Lst is longer than the length of bar in a standard cog.

The commentary explains that you get a length reduction from the cog.

 

[Legoman92]

Yes so the cog gives you 50%, but the additional 0.5Lst in the other direction gives you the full capacity of the bar at that location. So the total bar length is slightly less than the full Lst required for a straight bar

 

[Just Some Nerd]

I don't think we're on the same page here

Legoman, I'm assuming that your question is whether Case 1 or Case 2 in this sketch below applies. Have noticed at my own workplace that conservatively in spreadsheet calcs people will assume Case B, tends to have the largest impact when it comes to development in something like a pile cap where you're aiming for high development at the piles which are relatively close to the edge.

rapt, I'm thinking you've interpreted the question as being about the length of the cog beyond standard increasing the development at the bend. You're definitely correct that it doesn't - I believe the commentary also raises what you've mentioned regarding bend radius.

----------------------------------------------------------------------

Why yes, I do in fact have no idea what I'm talking about

 

[bugbus]

I think there's some confusion here.

Rapt, I don't think Legoman92 is proposing extending the straight part of the cog and relying on that to provide additional anchorage, which of course it wouldn't.

I think Just Some Nerd got the gist of the question, which is whether the cog provides an immediate 50% anchorage or not. I believe that it does (Case 1 above).

Another case to think about is for a stirrup with a 4db bend. There has been at least one study (happy to dig this out and share it) that shows that small diameter bars used as shear reinforcement can be immediately developed beyond the bend even if there is no transverse bar in the corner. That is to say, the bend can provide 100% anchorage (in some situations). Of course with the transverse bar in the corner, you have the added benefit of controlling splitting in the plane of the bend and also spreading the concentrated anchorage force out over a larger bearing area.

For larger diameter bars, I suspect the splitting/crushing issue in the plane of the bend may become more important, especially where your bends are not oriented in a way that they are exposed to a compressive force like a stirrup hook at the top of a beam. But the commentary seems to say that you can rely on 50% immediate anchorage in these cases.

 

[Legoman92]

Yeah basically I'm saying the straight section contributes the 50%, so Case 1 is my understanding how it works. The difference between the two cases is quite amplified when you're looking at large diameter bars

 

[rapt]

Question,

I assume we are talking about tension development, cot compression?

I am talking about tension only, not compression.

Quote from 1st post

"I've attached the commentary to this post which from my understanding (correct me if I'm wrong) says the cog itself provides 50% of the capacity and then the straight section provides the other 50%."

If you want 50% you can do it with a straight .5Lst or with a standard cog.

If you want more than 50%, you cannot use a standard cog with an extension. You have to use a larger bend radius and calculate the equivalent straight length and to get 100% you need Lst equivalent straight length.

Probably with smaller bars, the 50% is very conservative, but not with bigger bars. You will notice changes have been made to the wording for Fsy > 500MPa as the old rules do not really cover the higher strength. Eurocode have rules on radius depending on bar size/stress.

Compression, if that is the topic is another story.

 

[blihpandgeorge]

this is interesting - i have read the above and the code again a few times and with the benefit of Just some nerd's diagram i would have gone with Case 1. I have seen this applied in the design office multiple times and potentially incorrectly (and by people trying to do the right thing not by find a shortcut)

hi Rapt - for avoidance of doubt, are you saying that case 1 above is not the intention of the standard for a bar in tension?

If case 1 is not correct, then if you need full anchorage a standard cog is not all that helpful and you would need to provide a full straight anchorage, some big radii curves or a terminator.

 

[rapt]

Is the .5Lst length past or before the cog?

My reading of JSN's pictures is that the .5Lst is before the cog. That is ok, as the cog gives 50% at the end of the main bar, then .5Lst further along the bar you get the other 50%. Only 50% of the force is required to reach the cog and the radius of curve is ok for 50% load.

But if the .5Lst is after the cog, then the cog radius must be increased and you get no extra benefit from the cog, the total length must be Lst including the length through the cog. If you were to use the smaller diameter radius in this case, you have the full force through the curve radius and that causes crushing problems in the curve.

 

[blihpandgeorge]

Hi Rapt, good question on orientation. I have annotated JSN's image with a blue line to indicate the rest of the bar. This also neatly illustrates the part of the bar I had considered to be fully anchored in Case 1.

From reading your comments, i believe you are saying that Case 1 is correct?

 

[rapt]

Yes, case 1 is correct, it will provide full development at .5Lst as is shown in Fig 13.1.2.6 in AS3600 and 50% development at the start of the cog.

Rereading the first post, is this bar supposed to be developing in tension or compression?

If tension, is it uplift or bending?

If Uplift, the bar would have to develop to the bottom of the slab, so to the cog (you normally have to get the force to the far face!).

If bending, I am not sure. If you looked at it as one of Kootk's strut tie models, probably to the bottom also.

As a pedestal in compression, it is completely different, cog capacity is 0.

 

[blihpandgeorge]

thanks Rapt