Two Layers of Tension Rebar

[ottles]

How often do you use two layers of tension rebars distance 1 inch apart (the 2 layers). The outer side would yield first before the inner ones. Usually how many percentage yielding of the outside side before the inner ones yield? and why is this allowed in structural books. I only want single layer in my design but I saw others doing 2 layers. What is your experience and say on this? Thank you.

 

[KootK]

Depends what you're designing. For beams and deep raft foundations, I use multiple layers quite often. For deep, relatively narrow beams, it can be tough to get an efficient amount of rebar into the section without resorting to multiple layers or bundling. Usually, both layers yield completely at ultimate strength. Whether all the bars yield or not, reliability principles can be used to ensure a uniform margin of safety.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[ottles]

In column design.. the contribution of inner rebars are only a lower fraction compared to the outermost rebars (since the separation in column rebars are at least 4 inches). In beam, don't you compute for the contributions of each layers of rebars maybe because the separation is only very close 1 inch? If you had computed it.. what results did you get? Since the distance is only 1 inch, could some be approximate principle that is involved or used?

 

[KootK]

In column design.. the contribution of inner rebars are only a lower fraction compared to the outermost rebars (since the separation in column rebars are at least 4 inches).

Are you designing a column here? If so, that's important for us to know. I've only used muli-layer cages for lower level columns in pretty tall buildings. And, in those cases, there wasn't really any rebar tension to speak of. All axial.

since the separation in column rebars are at least 4 inches). In beam, don't you compute for the contributions of each layers of rebars maybe because the separation is only very close 1 inch?

I don't understand these limits. I've seen column bars closer together than four inches and beam bars typically are spaced as a) 1.4 db or b) Some spacer bar dimension that makes the space greater than 1.4 db. Other spacing minimums associated with aggregates size etc apply too.

what results did you get?

As I mentioned previously, all of the bars generally yield for beam designs where I use multiple layers.

Since the distance is only 1 inch, could some be approximate principle that is involved or used?

The traditional procedure has been this:

1) Assume that all of the rebar yields and treat it as one giant lump of reinforcing located at the centroid of the tension steel including all tension layers.

2) Verify that all layers of reinforcing steel do in fact yield.


I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[ottles]

The traditional procedure has been this:

1) Assume that all of the rebar yields and treat it as one giant lump of reinforcing located at the centroid of the tension steel including all tension layers.

2) Verify that all layers of reinforcing steel do in fact yield.

I'm only referring to beams. For mere 1 inch (or 1.4 db) distance between layers. This centroid thing may work. But if the distance between layers becomes larger like 3" or 5" or 3 db.. the outermost rebars of the beam would surely yield before the inner ones.

For those who have actually computed for the strain of the outermost bars and inner bars layers. What percentage do you usually get? How many percentage of strain of the outermost bars before the inner bars begin to strain (again all for beams only). Thanks.

 

[jayrod12]

That still has significant bearing on the depths of beams you're contemplating.

When it's say a 18" deep beam, then a large spacing like that would have a significant effect on the strains in each layer. A 48" deep beam, I feel the centroid method still applies.

Even with a small spacing between bars, the outside layer will always yield first. Why do you feel that is a concern? Are you worried about reaching rupture strain on the outer layer before you get yield of the inside layer?

 

[ottles]

That still has significant bearing on the depths of beams you're contemplating.

When it's say a 18" deep beam, then a large spacing like that would have a significant effect on the strains in each layer. A 48" deep beam, I feel the centroid method still applies.

Even with a small spacing between bars, the outside layer will always yield first. Why do you feel that is a concern? Are you worried about reaching rupture strain on the outer layer before you get yield of the inside layer?

Yes. For let's say a 18" deep beam and 1" between 2 rebars layers.. will it reach rupture strain on the outer layer before you get yield of the inside layer? Or will they still be both elastic. Reviewing 5 structural books. They all use the centroid method. For a 18" deep beam, what spacing of rebars layers before you reach the threshold where centroid no longer applies approximately?

 

[rapt]

Ottles,

I would always calculate the strain at each layer, so an inner layer may not reach yield. You cannot base it on a guess. Normally beams with multiple layers are very heavily reinforced so the neutral axis is fairly deep. There is no general rule about what percentage of yield strain you are going to get in each layer. It depends on steel depths and neutral axis depth.

There is nothing to worry about if you calculate it properly, other than the fact that you are no fully utilizing the steels capacity. So you only do it if you have to.

The other option, if there are a lot of beams is higher strength steel (e.g. PT).

 

[jayrod12]

Technically the centroid method would apply for a first run in all cases. It would allow you to get a rough determination of the neutral axis depth. You would then have to actually go through the calculations to determine the actual strain at each layer of steel.

Generally people have a spreadsheet that completes this for them for multiple layers of steel.

 

[KootK]

You can make an upper bound estimate of your lower bar strain pretty easily. Draw a straight line from -0.0035 on your stran diagram at the compression edge to +0.002 at the inner layer of reinforcing. Then just read the outer layer strain from that same line. You'll find it much less than the rupture strain for most practical situations.

Algebraically, upper bound strain = d_max x (0.002 + 0.0035) / d_min - 0.0035

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Kootk,

Definitely an Upper bound as it is the balanced point for the inner layer, bit what use would it be? Except also that .002 does not apply for higher strength steel does it!

 

[KootK]

Definitely an Upper bound as it is the balanced point for the inner layer, bit what use would it be?

I developed it with a singular, important use in mind: helping OP out with this thread. With that diagram / equation in hand, OP can easily run a few test cases and convince himself that, while the outer layer strain may indeed exceed 0.002, it's not likely to be anywhere near the rupture strain.

Except also that .002 does not apply for higher strength steel does it!

Well yeah, OP would need to apply whatever strain values are appropriate to the materials being used. I do my best to help peers; I'm not a tie-er of shoe laces. Nor is 0.0035 the right number depending on where in the world OP is and what type of concrete is at play.




I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Kootk,

Interestingly most concrete codes do not require that the steel strain does not reach rupture!

Not saying that I agree with the logic!!

 

[KootK]

Interestingly most concrete codes do not require that the steel strain does not reach rupture!

I agree, that is interesting. Good thing rupture is a remote possibility in most cases.

You know those provisions that we have that ask for the reinforced flexural capacity to exceed the unreinforced flexural capacity by some margin? My understanding is that one of the reasons for that is to promote the development of multiple flexural cracks rather than just one which might lead to excess localized strain and possibly rupture. So, indirecctly there may be some consideration of rupture.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Kootk,

That was my assumption, until you look at it and it is completely unrelated to the steel rupture strain!

Also, it is normally based on cracking moment. If you look at a T section,

- for tension on the bottom, the flange is in compression so neutral axis is relatively shallow (as it is very wide) and tension strain is much higher, but Mcr is significantly lower so minimum bottom steel is much lower.

- for tension on the top, the web is in compression so neutral axis is relatively deep and tension strain is lower, but Mcr is significantly higher so minimum top steel is much higher.

So for the face with the higher tension strain we require the lower amount of minimum reinforcement! So the strain in this steel is significantly higher.

I have been complaining about the illogic to the Australian Code Committee for years!

 

[ottles]

You can make an upper bound estimate of your lower bar strain pretty easily. Draw a straight line from -0.0035 on your stran diagram at the compression edge to +0.002 at the inner layer of reinforcing. Then just read the outer layer strain from that same line. You'll find it much less than the rupture strain for most practical situations.

Algebraically, upper bound strain = d_max x (0.002 + 0.0035) / d_min - 0.0035

I'm computing manually as review taking into consideration the strain-stress curve, the strain diagram, elasticity, and the all others including studying the derivation of each formula to ensure each layer has the right strain. But may I know what is d_max and d_min?

Also note that if the loads is beyond fc'/2, stresses and strain is no longer proportional (concrete has no longer linear stress-strain above fc'/2), so the neutral axis would be deeper or higher from middle point close to the ultimate load.

Anyway. In your sample. I'm assuming you take neutral axis in the middle point just for rough estimate. Ok.. but what is d_max and d_min?

 

[KootK]

But may I know what is d_max and d_min?

d_max is the distance from the compression edge to the most outboard reinforcing layer. d_min is the distance from the compression edge t the most inboard reinforcing layer.

Also note that if the loads is beyond fc'/2, stresses and strain is no longer proportional (concrete has no longer linear stress-strain above fc'/2), so the neutral axis would be deeper or higher from middle point close to the ultimate load.

The idea is that strain remains proportional to curvature but the stress does not. Thus the strain gradient that I've proposed remains valid. At least that's our conventional flexural theory. No doubt, strain is not perfectly proportional to curvature either. But then this is practical design, not a PhD dissertation, right?

Anyway. In your sample. I'm assuming you take neutral axis in the middle point just for rough estimate.

The neutral axis would not be in the middle. It would be wherever the strain diagram indicates zero strain.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

That was my assumption, until you look at it and it is completely unrelated to the steel rupture strain!

So for the face with the higher tension strain we require the lower amount of minimum reinforcement! So the strain in this steel is significantly higher.

I don't agree. At least not yet. Specifically:

1) Once cracking occurs, I think that rebar strain rearranges itself significantly and the rebar strain condition prior to cracking become largely irrelevant with respect to possible encroachment upon rupture level strains.

2) For the same localized curvature, more cracks = more distributed rebar strain = less potential for bar rupture. As having the reinforced flexural capacity exceed the uncracked flexural capacity promotes distributed cracking, I think that logic in this approach is fundamentally sound even if the methods for ensuring Mn > Mcr may be flawed in some cases.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Kootk,

I meant that the code formulae for minimum reinforcement/capacity based on an area of reinforcement to resist the cracking moment is unrelated to steel rupture strain.

 

[KootK]

I meant that the code formulae for minimum reinforcement/capacity based on an area of reinforcement to resist the cracking moment is unrelated to steel rupture strain.

Hmm... would you consider these statements to be accurate:

1) In general, reinforcing sections so that Mn > Mcr will promote more distributed cracking and thus reduce the amount of peak strain in the rebar at any one crack. In this sense, reinforcing quantity bears some relation to peak rebar strain, albeit indirectly.

2) The code formulae do not explicitly relate the quantity of reinforcing provided to the specific amount of rebar strain that can be expected. Thus, designing Mn > Mcr helps to reduce rebar strain but does not reduce it to any particular value.

Thoughts?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.