Are minimum reinforcements additive? 6

[darkjmf1]

Hello,
I am designing a RC beam with a section which, due to architectonical reasons, is much larger than required, resulting in minimum reinforcement both for bending and torsion.
Do I have to calculate both As,min for bending and longitudinal Asl,min for torsion separately and eventually adding them up in the section?
Or could I just calculate both As and Asl required by analysis and just check if the sum of them complies with As,min and Asl,min?
I am using ACI, but I guess this discussion could be applicable for any concrete code.
Thank you all in advance.

 

[JAE]

I've always treated flexural reinforcement and torsional reinforcement derivations separately and added them to the beam.
Al (for torsion) is intended to be sprinkled around the beam section - flexural minimums only apply in the tension side of the beam - which could occur in multiple sides - but is always focused on the side.

 

[MR_E30]

I agree with JAE and design the same way, as flexure and torsion do two different things to the concrete beam and should be addressed appropriately.

 

[darkjmf1]

Of course I intend to add both reinforcements to the beam, but I am concerned about the minimum.

Let's try to explain it with numbers:
- Flexural: As,req=5. As,min=10 (at the tension side).
- Torsional: Asl,req=7. Asl,min=11 (let's say that the total reinforcement is equally distributed at each side, being these figures those corresponding to the flexural tension side).

So the two scenarios I ask about are:
(1) Respect both minimum values, so the total reinforcement at that side would be 10+11=21.
(2) Just attend to the required values, resulting in 5+7=12. In this case, 12 is bigger than both minimum values (10 & 11).

The difference of deployed reinforcement is quite big at each scenario (21 against 12). That's my concern!
Providing that, at the end of the day, the final result of (2) complies with both minimum, would it be a proper interpretation?
Which way would you choose?

 

[BAretired]

I would use 12 bars in that case, but I'm not certain it would be the correct interpretation of the code. I don't recall any such example arising in practice.

BA

 

[JAE]

The minimums are additive in my book. They are dealing with forces/stresses which are additive to a section.

 

[darkjmf1]

For sure forces/stresses are additive, but ACI explains that the purpose of minimum reinforcement is to avoid sudden failure after initial crack.
In the (worst) case that both cracks due to flexure and to torsion appears simultaneously, can't we assume that, as long as the final amount of reinforcement covers both minimum, this sudden failure is avoided?

More on this (following with my previous numerical example):
First I design for flexure obtaining As,req=5 & As,min=10. The second 5 bars are required only after cracking, so they are not supposed to be specifically stressed.(???)
Afterwards I design for torsion, obtaining Asl,req=7 & Asl,min=11. Let's say that, for the 7 required bars, I could take advantage of those previous 5 bars which were "unused", so I only need to add 2 more bars.
Eventually it will result in 5+7=12 bars, complying with both minima.

Sorry for all the brainstorming, but I am really haunted by this question.
Thank you all. I really appreciate your contributions.

 

[Tomfh]

Nothing wrong with adding minimum steel, but I agree with darkjmf1 that you could argue they needn’t be added since any additive tensile stresses in steel would presumably be additive on the concrete too, meaning it will crack earlier.

Eg if it’s on the verge of flexure cracking, it will immediately crack when torsion applied. It’s not like we have to build up the entire torsional cracking force from scratch.

 

[KootK]

1) The intent of the minimum flexural reinforcement is to ensure enough post-cracking capacity that ultimate bending failure is ductile-ish. To the extent that any longitudinal steel is being utilized in torsion at a particular section, that steel is not available for this purpose. So, in general, I believe that the minimums are additive, envisioning a possible hierarchy of events as follows:

a) You load up and get enough torsion to cause torsional cracking and engage the longitudinal rebar in the torsion resisting mechanism. Given that minimum torsion is intended to occur at low levels of load, there is every possibility that this happens well before Mu kicks in.

b) You continue to load up until flexural cracking at which point you engage those bars and do not have the bars from step [a] available because they're already in use.

c) If the bars from [a] and are not additive, you won't have enough rebar at step to get you over Mcr and flexural failure will be sudden and brittle.

2) Tensile demand on the longitudinal torsion bars will generally be at a maximum at the supports and at a minimum at mid-span, similar to a regular shear diagram. Because of this, one could argue that there is little torsion demand at the beam mid-spans where flexural demand is at a maximum and, therefor, the requirements are not additive at that location. I don't do this, however, as the tracking is too onerous for my liking. You'd almost have to superpose a flexural bar tension graph onto a torsional bar tension graph and make sure that you didn't exceed Mn anywhere along the span.

3) At the ends of continuous beams, I think that the flexural and torsion demands are definitely additive. There, you've got bar tension demands from both flexure and torsion peaking at the same location.

4) An interesting collary to this is that As_max for bending should theoretically be lowered in the presence of torsion because the torsion will generate a compression field that would be additive to the flexural compression block. Obviously, we don't do this.

 

[Celt83]

ACI 318-08 11.5.3.8 is pretty clear in stating that the torsion reinforcement requirements are additive with the shear, moment, and axial requirements. Assume there is similar language in the latest versions.

Is your beam oversized to the point that you can take advantage of the the exception for As,min,flexure by having and As at least 1/3 greater than that required by analysis.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[Tomfh]

Kootk,

If the member is cracked torsionally, it is also cracked flexurally, thus there is no "step b)" to speak of.

You're double counting the concretes tensile contribution, once towards torsion, and once towards flexure.

 

[KootK]

If the member is cracked torsionally, it is also cracked flexurally, thus there is no "step b)" to speak of.

I disagree. A flexural crack at mid-span is a vertical thing whereas a torsional crack is a diagonal / spiral thing. They may well interact as flexural shear cracks do near supports but I don't see that taking place at mid-span / peak moment locations.

 

[Tomfh]

A torsionally cracked bit of concrete is also flexurally cracked. Take a stick of chalk and twist it in a spiral fracture and see how much flexural capacity it has left...

 

[TehMightyEngineer]

Celt, ACI 318-14 has 9.5.4.3 which is the same: "Longitudinal and transverse reinforcement required for torsion shall be added to that required for the V u , M u , and P u that act in combination with the torsion."

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL, CO) Structural Engineer (IL, HI)

 

[KootK]

A torsionally cracked bit of concrete is also flexurally cracked.

I don't share your certainty in that as far as the governing flexural crack is concerned.

Take a stick of chalk and twist it in a spiral fracture and see how much flexural capacity it has left...

The difference here, in my mind, is reinforcement. With deliberate torsional reinforcement in play to keep torsional cracks down to distributed hairline cracks, I think that there's potential for separate, governing flexural cracks to also develop as shown below. That, particularly, given that a torsion crack all the way through a member tends to be a fairly lengthy thing. Sure, a full depth torsion crack cannot carry uncracked moment across it. But, then, is that the critical crack for the moment? I'm not so sure.

This is really something of a moot point in a way anyhow. Try it another way, for the sake of argument:

1) Let's imagine, for sporting fun, that there is only one kind of crack in play: the combined, flexural-torsion crack (the CFTC).

2) When the CFTC let's go, there will be both torsion and flexure acting across that crack. And both actions must be resisted.

3) If the CFTC is only reinforced for the worst of the minimum torsional requirement or the minimum flexural requirement, there's no way to guarantee that will be enough to satisfy the demand where some level of both torsion and flexure is present on the section.

4) So we're back to having to design for additive requirements if we want to be able to guarantee ductile failure in bending.

 

[BAretired]

I agree that torsional and flexural reinforcement should be additive. I'm not so sure that minimum values of each should be additive. When added together, the OP found that he needed 5+7 = 12 bars to resist both flexure and torsion. Adding the minimums required 10+11 = 21 bars. That seems totally out of line to me. Perhaps it would be more reasonable to provide 12(1 + 1/3) or 16 bars on the face in question.

BA

 

[Agent666]

I was thinking BAretired that while it might cover the loads at 12 bars, covering the loads isn't the intent of the minimum allowances, it's ensuring a minimum level of robustness and semi-ductile failure mechanism as others have said when both tension and torsional mechanisms are occurring. Therefore they'd be additive.

 

[KootK]

Adding the minimums required 10+11 = 21 bars. That seems totally out of line to me.

It seemed out of line to me as well but for different reasons. Frankly, I question whether or not that's been calculated correctly. I've designed my share of concrete beams and don't recall every having such an extreme situation arise. This means what... 50 bars around the perimeter? That's at least 40 bars more than I'd consider to be typical.

 

[darkjmf1]

I am really enjoying this post!
Although it seems that there is not a simple answer to my initial question, I thank you all for the vivid discussion. I am learning a lot from it.

I am far from being an expert as many of you are, but my understanding was in line with the last message from BAretired.
Isn't there a kind of maximum value for the sum of the minimum reinforcements?

By the way, I have noticed that ACI does not give a minimum torsional reinforcemnt for columns.
I assume it is because these elements are not so prone to being torsioned, but the fact is that I also have in my project columns in such situation.
How should I design their torsional reinforcement? Just deploying the bars required by calculation, without a minimum?

 

[darkjmf1]

It seemed out of line to me as well but for different reasons. Frankly, I question whether or not that's been calculated correctly. I've designed my share of concrete beams and don't recall every having such an extreme situation arise. This means what... 50 bars around the perimeter? That's at least 40 bars more than I'd consider to be typical

As I said in the original post, the problem here is that the beam is oversized due to architectural reasons.
My first thought was to reduce sizes so the As,min would not gobern the design of the reinforcements, but I was not allowed to.
Is not there in ACI any clause for these situations? I am thinking about something similar to 10.3.1.2 for columns.