T beam minimum Reinforcing

[nickky]

Hi Guys,

Currently I am designing a one way slab which has beams (T-beams).

We know that when the neutral axis is in the flange the beam acts like a regular (bf x d) rectangular beam (bf is the effective flange width). In this case if the calculated reinforcement ratio is less than RHOmin then we must use RHOmin to calculate the minimum rebar.

I remember from the school time (and also saw in "Winter" concrete design) where it says the bw (web width) must be used for min reinforcement calculation but here is the problem:

If we use the bw then the available flexural strength of the beam will be way lower than the demand. How this could be explained? Why we must use the bw for Asmin?

Thanks

 

[asixth]

Yes. 0.2-0.3%

 

[rowingengineer]

Hokie,
What I was trying to say is if you have a slab design with minimum steel at 32mpa and then you get results from the concrete at 60mpa this slab could qualify as un-reinforced design. As your tensile strength would be increase by about 40% making Mcr>.6M* meeting the requirements of the code.

But since we are heading down the theory discussion I will put something out there for discussion; the requirement to have steel greater than 1.2 Mcr, based on the tensile strength to ensure ductility is a miss leading requirement. This is due to the fact that the tensile strains in the concrete due to what is ignored (restraint by reo and supports, plastic shrinkage strains ect). The Mcr defined for minimum strength is different to the Mcr used for deflexion calculations. Thus the minimum steel requirement is not for ductility at all, it is there for basic strength and stiffness, however for a slab or beam to behave in a ductile manner you only need the points at which the hinge would form to be ductile. So i put out there that the 1.2 is a safety factor only and nothing much to do with ductility of the cross section, only to ensure inherent strength and stiffness such that the slab can form hinges and at those points behave in a ductile manner.


Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[nickky]

Gentlemen,

With all respect I would be thankful if you would try to concentrate on the main question which is the following:

Which width - bf(flange) or bw(web)- must be used when calculating the minimum Ast for a T-beam which neutral axis has fallen within the flange (i.e. acting as a bf x d rectangular beam). Please note that I am a practicing engineer in the United States and therefore I prefer the answers to be based on ACI code.

Thank you again!

 

[rapt]

Nickky,

My original posting explained how to do this. Using Bw or Bf is not logical. You should calculate the cracking moment, multiply it by 1.2 and use this as the minimum Ultimate moment for the section for design. This will then satisfy the logic of Clause 10.5 for you for any section shape. This is discussed in the ACI318 commentary and also in 18.8.2 (for bonded prestressed sections but the same logic apoplies for RC sections).

My following postings will answer some of the questions from above!

 

[rapt]

RE,

Compression ductility is only required at plastic hinge locations, tension ductility is required everywhere.

The logic is that at any point where the concrete cracks, there must be a certain tension force applied to make it crack and as the concrete can no longer carry that force, sufficient reinforceemnt must be supplied to carrty that tension force. The Mcr approach is logical for this and works ok. It also allows for to calculate minimums for multiple reinforcement types and complicated shapes.

The second part of the tension ductility problem (related to my answer to Hokie66 below) is that the strain in the reinfoprcement should be limited. Unfortunately no design codes require this (except EC2 where you do not assume a pure elastic/plastic stress strain diagram). Realistically the strain in the reinforcement should be limited to below the failure strain. The Mcr approach could be used for this limit as well for rectangular sections. It does not work for sections such as T sections (it is completely reverse to the Mcr logic for these shapes).


Hokie66,

I would agree with RE on this. The problem is with the level of strain in the reinforcement and reinforcement ductility itself. If the reinforceemnt is very ductile (class E), there would be no problem. If it was class N, you would probably still be ok, unless you got some class N reinforcement right on the lower limit, but the reinforcemrnt could fracture prematurely. If it was Class L steel, you would be in lots of trouble.

Re RAPT
I have thought about a 3D modeller (for about the last 18 years). But modelling is so easy in RAPT in most cases I have put other things first. You never know what might happen one day.

 

[hokie66]

nickky,

The ACI provisions for minimum reinforcement for beams specifically use bw. The top steel would be based on bw, so I think it is not logical to use more steel in the bottom than in the top, when the top moments are greater.

 

[rapt]

Nickky/Hokie66,

Actually ACI318 clause 10.5.2 , bw is set to 2bw when the flange is in tension, for statically determinant members. Logically this should apply for statically indeterminant members also.

 

[hokie66]

The condition of a flange in tension in statically determinant members is uncommon in buildings. I see the logic for simple spans, but why do you think it should also apply to continuous spans?

At any rate, I think Nickky's question was for beams where the flange is in compression.

 

[rapt]

Nickky,

Just went back to the top and read your question again. Why will the available flexural strength be lower than the demand? This clause is defining the absolute minimum area of reinforcement required. You still have to do the calculations to determine the area of reinforcement required to satisfy the actual applied moments. Clause 10.5 is just setting a minimum area of reinforcement in case your calculated area to satisfy the applied moments is too low.

Hokie66,

Because the background logic to this cluase is exactly what I have explained above regarding Mcr. In regions with the flange in tension, Z will be much larger than for zones with the flange in compression. So the minimum area of reinforcement should be corrrspondingly larger.

For a T section , the Zt and Zb values will both be significantly higher than they would be for the web treated by a rectangular section by itself, which is what you are doing if you use Bw in this calculation. You are completely ignoring the presence of a flange on the cracking moment of the section.

This whole problem is caused by stupid code simplifications. We would not be having this discussion if the correct Mcr formula had been put in there in the first place. Everyone would have accepted it. But they wanted something really simple so they made it 1.4/fsy. Then over time thay have realised that this is too simple and have made it more and more complex. They have now got it to the point where it is basically correct for rectangular sections. Their next realisation will be that it is wrong for non-rectangular sections and that the easiest way to do it is by calculating Mcr, like they should have in the first place.

 

[rowingengineer]

Nickky,
Sorry for the diversion, but 1.2 Mcr is the one i would use, while it is not perfect, it is better than % for a T-beam.

Rapt,
Rapt: The modelling is the easy part, having to get the loads out of one program to another program that is the part that I don't like, but I will give you this, your loads are a lot easier to generate as patterning is looked after.

Mcr:
While I agree the Mcr is a useful equation for getting the minimum reo, and i also agree that tension ductility is required, could it not be that concrete can provided this required tension ductility. I base this on observations in a few articles where the increased steel reo decreased the ductility of the concrete, I will concede I can’t remember it they has ratios below Mcr. While we are educated by many that concrete has no tensile ability, the higher strength concrete are showing repeatable tensile results these days
Mcr value is based on the tensile strength at 28 days however the real value could be + 10 to 40% of this, meaning if you were looking for ductility due to reinforcement at every section it is highly unlikely to be provided by the steel if just working on Mcr (I note that the lastest code is changing this I believe), more likely the concrete. However the other possibility is also true in that the Mcr required for flexural cracking is reduced significantly due to restraining effects causing tensile stress to build up, the restraints could lead to really high tensile stress’s that caus a crack then you would want the reo, of some amount.

All in all I think the safety factor is if it has to high rupture strength, then the 1.2 ensures it acts like unreinforced concrete.

Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that them like it

 

[rapt]

RE,

Send me an email about your load transfer problems and we can discuss it in private. We will get in trouble doing it here.

You cannot rely on the tensile strength of normal concretes, even high strength ones. The Super High strength concretes like Ductal and those discussed at the CIA conference by the Europeans actually have a fairly high percentage of steel fibre and they are showing reasonably reliable tensile strengths. But they are not what we are using in buyildings. The steel fibre is giving them the tensile strength, not the concrete.

For the normal concretes we are using, reinforcement of some sort is required to take the tension force. I have had discussu=ions with code committees regarding the value of Mcr that we use (lower bound tensile strength) and they are happy with it. If you look at it on a steel strain basis as I suggested above to hokie66, then it gives reasonable strains in the reinforcement as long as the reinforcement ductility is not too low (no Class L).

Increased tension steel ratio will never reduce under reinforced ductility (tension ductility). It will reduce over reinfroced ductility (compression ductility).

All codes limit compression ductility by limiting the maximum steel ratio of the maximum neutral axis depth or the minimum strain in the reinforcement, forcing the steel to yield before the concrete crushes.

Most codes limit tension ductility indirectly by limiting the minimum reinforceemnt level which indirectly limits the maximum steel strain, but not all that well for non-rectangular sections as I mentioned earlier.