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Purely Theoretical Concrete Beam Question
2

Purely Theoretical Concrete Beam Question

Purely Theoretical Concrete Beam Question

(OP)
Let's say you have a mild reinforced concrete beam with post-tensioning cable cast in that is not stress.  Now say the beam is in service and it cracks.  Now you come back and and stress the post-tensioning such that the entire beam is in compression across the full cross-section for the entire length of the beam for the duration of its service life.  Is it reasonable to use the full Ig for deflection in this case?  I think so, but would like other opinions.  
 

RE: Purely Theoretical Concrete Beam Question

Since some of the conditions for a Timoshenko beam are violated better not count on the whole Ig; and all the estimates of deflection from reinforced concrete up show a number of parameters influencing deflection; in this case, for example, you wouldn't be starting from a complete section but a cracked one and some gained deflection; and our accuracy in predicting the final deflection will be severely dependant on how precisely we follow the situation as the loading progress to the one of our interest.

So in my view it will be more productive to follow any stated estimate by PCI, PTI, ACI and alike, of if not try at least follow the happenstances of the loading. For example, due to the formed cracks in the web, it will be showing lower shear stiffness and so the deflection will be bigger than if integral even if shear is being accounted.

RE: Purely Theoretical Concrete Beam Question

I would expect the full Ig to be operative after stressing but the majority of concrete strain takes place over time, so the amount of creep in the conventionally reinforced beam depends on its age when finally stressed.  Stressing does not reverse all creep, so deflection calculations would be a bit tricky.

BA

RE: Purely Theoretical Concrete Beam Question

(OP)
BA-
I agree that it wouldn't account for creep, and that wasn't my intention.  ACI accounts for creep by using a multiplier on the immediate deflection, which still makes sense to do.  I was just asking if the immediate deflection should be based on Ig or not.   

RE: Purely Theoretical Concrete Beam Question

Lion,

I believe it should.

BA

RE: Purely Theoretical Concrete Beam Question

2
Lion06

It could only be regarded as uncracked if the prestressing effects place the member completely in compression under the loading being considered for deflection. If there is any tension (any at all, not just above the cracking strength as it is already cracked, so cracking strength is technically 0), it is cracked if it cracked under the initial loading.

ACI does not account for creep and shrinkage in prestressed memebers using a multiplier. This only applies to RC members! This has always been the case. Unfortunately, certain software products created in and available in the USA have never been able to do these calculations properly and have used multiplier approaches, but it is not in accordance with ACI or any other design code that I know of (I work with all of the major concrete codes!).

RE: Purely Theoretical Concrete Beam Question

(OP)
rapt-
I agree that the concrete would need to be completely in compression, that was why I said that the post-tensioning was enough to cause the entire cross section to be in net compression along the entire length for the duration of its service life.

I do see in 9.5.4.3 that they don't tell you to use a multiplier.  Thanks for pointing that out.  Do you have any references that show the correct way to account for shrinkage, creep, and relaxation of the tendons?  Does using the multiplier get you close, at least?

RE: Purely Theoretical Concrete Beam Question

Lion06,

The multiplier method is not even close for RC members. It can easily be out by 50% or more for RC. I have seen calculations showing it as high as 6 - 8 for RC members in certain circumstances, instead of the codes 2. Then people assume com[pression reinforcement has a large effect in reducing this. In most cases it does not have much effect, simply because the reinforcement at the compression face is too close to the neutral axis or even on the tension side.

It is even worse for PT. Imagine a PT member where the PT exactly balances the permanent load. In this case, there is no short term deflection so there is no long term deflection. But there is still shrinkage restraint which causes stress and deflection and therefore creep deflection also. A multiplier approach would say there is no creep/shrinkage deflection.

There are several books that cover this. (Raymond) Ian Gilbert's Time Effects in Concrete Structures is one. He has released a new update of this recently, not sure of the name. I think Branson has a book that covers it, Deformations of Concrete Structures. British (Part 2) and Eurocode 2 give methods to calculate it.

Our software, RAPT, does it for you in 2D, as do some others such as Sofistik(probably wrong spelling) and RAM Concept now has a method built in for it if you use their highest level of deflection calculations (remember to turn on the Mxy moments as well in RAM).

RE: Purely Theoretical Concrete Beam Question

Sorry for jumping in here, but what approach does your software use?

EIT

RE: Purely Theoretical Concrete Beam Question

(OP)
We use two different P/T software programs.  RAM Concept and Adapt PT.  Adapt PT appears to use a multiplier.

RE: Purely Theoretical Concrete Beam Question

from RAPT's post: GILBERT, R.I. and RANZI, G. (2010), "Time-dependent Behaviour of Concrete Structures", in press, Taylor & Francis, London (A1).

Sorry to say but I'm a bit conservative, and for beams I would limit my Ieff to 0.6 Ig-0.7 Ig. I'm a little concerned about restraint forces.

 

ANY FOOL CAN DESIGN A STRUCTURE. IT TAKES AN ENGINEER TO DESIGN A CONNECTION."
 

RE: Purely Theoretical Concrete Beam Question

RFruend,

RAPT uses a bit of a mixture. We use the British Concrete Society method for tension stiffening, allowing a variable tensile stress in the concrete depending on the tension strain in the concrete (this is an improved version of the BS8110 tension stiffening logic), the Age Adjusted Modulus Method from Gilbert,s books (he did not invent it, just discusses it) for creep and normal shrinkage warping calculations. When you get back to first principles, the logic for shrinkage and creep effects should not vary that much. The variation comes more in concrete properties for different codes/countries.

Lion06,

yes, Adapt PT uses a multiplier approach and makes a lot of other approximations for PT also!!

RAPT Concept offers several different approaches, from multiplier (the default method) to full shrinkage/creep if you want to take the time to get better answers. So you can get a wide variety of answers from RAM Concept depending on how much effort you put into the design. Many designers take the easy route and use the default multiplier option not realising how wrong they can be. You also need to make sure you turn on the Include Mxy moments in design in RAM Concept because by default it ignores them and this is grossly unconservative!

RE: Purely Theoretical Concrete Beam Question

(OP)
rapt-

I wish I could give you more than the one star!  

So the bottom line is I just shouldn't believe a deflection anser from Adapt PT?  

Regarding RAM Concept, I'll make sure to find the "Include Mxy moments" box.  It seems strange that they would make the default option the UNconservative option.  

It sounds from your earlier post, like the multiplier gives wrong answers even for mild RC beams.  Is that correct?  Is the % of difference between multiplier and a more rational approach different for RC systems than for P/T systems?

RE: Purely Theoretical Concrete Beam Question

I will loosely quote a pearl of former head of ACI's deflection chapter:

There are 10 steps in the calculation of deflections... if the probability of error in every step is ... 5%, then the probability of error in the deflection estimate will be of 40%

Author: Russell S. Fling, ex Presidente de ACI y de su comité 435 Deflexiones
Artículo: Practical Considerations in Computing Deflection of Reinforced Concrete
Publicación: ACI SP-133 (Serviceability and Safety) -4, page 71
Editor: ACI American Concrete Institute, Detroit, 1992

 

RE: Purely Theoretical Concrete Beam Question

What above if you know what you are doing. It will be unlikely to meet 5% error by step if not. I have seen deflections overpredicted ten times actual deflection purportedly following the spanish code estimate.

RE: Purely Theoretical Concrete Beam Question

Lion06,

Thanks for the star.  I never used to get any at school so this helps to make up for it.

RE Mxy, it is unfortunate that some people who are advising others how to design do not know what they are talking about!

The accuracy of the multiplier approach varies for different members depending on member shape, stress levels, concrete properties, loading patterns and a lot of other things. It cannot be quantified as 2 (A bit like the number 42!!!! representing 'the meaning of life, the universe, and everything'). It can vary from 1-1.5 to 6-9 depending on the situation.

Ishvaag,

You can keep your head in the sand as long a you like. I prefer to have a reasonable ball park guess as to my expected deflections, rather than not knowing which ball park I am actually in by using a multiplier method. And compared to test results in experimental studies and comparisons with buildings done by others, RAPT's answers are in the right ball park at least!
In a test at UNSW by Gilbert and others, reported in ACI several years ago, ACI expected deflection after 270 odd days was about 9mm. Actual was 29.1mm. RAPT was 30.5mm. I much prefer RAPT's answer to ACI code, even if it is over-estimating the deflections!!

RE: Purely Theoretical Concrete Beam Question

(OP)
Do you have any literature on the more accurate creep deflections calculations?

RE: Purely Theoretical Concrete Beam Question

Lion06

If you do a Bing search for "Creep deflections + R.I Gilbert", you will get 3070 hits. The link below is to the 2nd one. It is talking about AS3600 rules but fortunately concrete does not know about codes!! But it is a good summary and the developemnt of the AS3600 rules over time (which ACI has not caught up with!!).

http://www.ejse.org/Archives/Fulltext/200101/02/20010102.htm

Quote below from the above article.

"The use of the deflection multiplier kcs to calculate time-dependent deflections is simple and convenient and, provided the section is initially cracked under short term loads, it sometimes provides a 'ball-park' estimate of final deflection. However, to calculate the shrinkage induced deflection by multiplying the load induced short-term deflection by a long-term deflection multiplier is fundamentally wrong. Shrinkage can cause significant deflection even in unloaded members (where the short-term deflection is zero). The approach ignores the creep and shrinkage characteristics of the concrete, the environment, the age at first loading and so on. At best, it provides a very approximate estimate. At worst, it is not worth the time involved in making the calculation."

RE: Purely Theoretical Concrete Beam Question

The rational methods of deflection calculation (i.e. allowing for, cracking (including differential temperature and differential creep and shrinkage effects), tension stiffening, loss of tension stiffening, creep and shrinkage) will give an upper bound estimate of deflection.  If the service load in a beam is just over the cracking moment, and if a particular beam does not crack, then the deflection in that beam will be much less than predicted.  Nontheless, it is the upper bound deflection that is required in design, because some nominally identical beams will crack, and will deflect to the extent predicted.

The paper linked below looks at deflections in an actual structure that were 5x greater than indicated by a simplistic code based analysis, and 3x greater than a reasonably careful application of code simplified methods, but were acurately predicted by consideration of all the factors listed above.

 

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Purely Theoretical Concrete Beam Question

P.S.

"At best, it provides a very approximate estimate. At worst, it is not worth the time involved in making the calculation."

He is talking about RC members in the comments above about accuracy. He agrees that such methods can NEVER be used for PT members.

 

RE: Purely Theoretical Concrete Beam Question

Hi Lion06,

To calculate the immediate deflection, what you want to do is find the moment which causes the stress at the bottom of the beam to be 0 MPa. (The point at which the crack is just about to open, let's call it Mcr)  
Any deflection caused by that moment or less should be calculated by the full Ig value.

If you want to calculate the immediate deflection caused by a moment greater than the Mcr, you should use the I-cracked value.  The fully cracked value of I will be conservative.  For a closer estimate, it's probably worth the while to take an interpolation between Ig and Icrack.


With regards to long-term deflections, (I see there's been some discussions on the validity of multipliers etc), you may wish to take a look at the Australian Standard 3600.  They've nicely presented values for shrinkage, relaxation, creep etc in a way where the designer can modify a 'basic' value of strain to get a 'design' value of strain wrt to specific environmental and situational criteria.
These strains can then be used to calculate deflections etc.  Nevertheless, as the general gist of the previous posts go, concrete long term deflections are more or less of a gamble.


Hope that helped a bit.

RE: Purely Theoretical Concrete Beam Question

Quote:

Let's say you have a mild reinforced concrete beam with post-tensioning cable cast in that is not stress.  Now say the beam is in service and it cracks.  Now you come back and and stress the post-tensioning such that the entire beam is in compression across the full cross-section for the entire length of the beam for the duration of its service life.  Is it reasonable to use the full Ig for deflection in this case?  I think so, but would like other opinions.

To make an intelligent estimate of the immediate deflection as a result of post-tensioning, all of the cracks will close which, by itself will cause deflection.

The full Ig will be effective after the cracks have closed, but the age of the beam when it is stressed is an important variable because creep and shrinkage which took place in the unstressed beam will be partially reversed.

Without knowing the age of the concrete and the extent of cracking, it is not possible to arrive at an accurate estimate of immediate deflection.

BA

RE: Purely Theoretical Concrete Beam Question

well, rapt, I was not quoting Fling to say that there's no chance to get some good predictions of deflections; I am well aware of where I am in technical standup and thousands of publications make of me a shenanigan of the state of the art of so many professional things; for sure I wouldn't stand a head-on encounter with one Gilbert or one of the main programmers of one of the programs on the matter, like rapt, even with some significant previous dedication to the matter.

I was pointing mainly that the typical designer is not, as an average, in the conditions of making a good prediction; specially because they don't care to use something that can help him to do such thing, as good software.

For example, the one that made the 10 (or more!) times prediction was one of the Heads of the department of mechanical -here called industrial- engineering career in town. And no matter his entitlements reality showed him wrong, because the beam under study was built and working, and in place, not showing even such tenth of his aduced deflection.

That said, I also have seen 8" deflections in one member of scarce depth and about 20 ft span. It was quite likely a failed or nearly so member maybe as old as 60 yr old or more that was already working in catenary way, but who knows. These things, I also point, were not by the seventies' the realm of just minor construction, a whole Ministry of Commerce in Madrid, one of the tall buildings at the Castellana, maybe 40 or more stories tall had at construction time near 5" deflections -on 12 meter spans- plate with abaqus- entirely visible and it didn't enjoy even the charity of then receiving a technical floor, but just -it was told us, I don't know if it corresponds to the truth- was just to be filled with pavement mortar to level the surface.

RE: Purely Theoretical Concrete Beam Question

(OP)
BA-
Points well taken, but that's a little more nuanced than my original intent.

Let's say for purposes of this discussion that the beam initially cracks along the entire length (Ma>Mcr for the entire length).  Now say the beam is shored back to perfectly level and external P/T is applied at the centroid of the section only (to make sure there is no deflection related to the P/T).  Also, assume for the loads under consideration that the P/T force is such that the beam cross section is in full compression for the entire length of the beam.

RE: Purely Theoretical Concrete Beam Question

Equal from a theoretical standpoint the deflections won't be because the material beams the deflections of which are to be calculated -one including the cracks- are not.

Stresses would be in the zones adjacent to the cracks different to the case without cracks, and integration of the respective deformations to ascertain a deflection, also will.

This without considering further stages of upper loading that might mean, upon the onset of buckling on the growing always compressive load, the degraded stiffness may show in the lower value that would correspond to the case in which the buckling might have the cracks again opening.

Note that the ordinary loading of the beam would try to open the cracks as the described buckling would do, and the sections at the cracks wouldn't be able to show stiffness in the cracked part to oppose the attempt of opening, so, not as if was continuos.

This lesser stiffness will show in the deflection, irrespective of the fact that the loading may include a compressive load enough to close -but not glue to continuity- the cracks.

RE: Purely Theoretical Concrete Beam Question

I don't believe that shoring the beam back to perfectly level makes any difference.  If the prestress force is kept at the c.g. of the section throughout its length, the initial deflection after stressing and removing the shores will be identical to the deflection prior to stressing except for the deflection resulting from closing the cracks.
 
Long term deflection is a different matter and would depend on the age of the concrete when stressed because some concrete was previously compressed and some was either unstressed or only slightly stressed in tension.  Differential creep would enter the picture because of the variable history of previous stress.

BA

RE: Purely Theoretical Concrete Beam Question

Ishvaaag,

"I was pointing mainly that the typical designer is not, as an average, in the conditions of making a good prediction; specially because they don't care to use something that can help him to do such thing, as good software."

This is getting to the real problem. They quite often are misled by the software they do use. Many designers are using FEM software for design of concrete members and getting deflection estimates from them. Unfortunately, in a lot of cases, those deflection estimates are meaningless as they do not allow for cracking and long term effects at all or do so as a guess based on a factored approach.

I am sure there are many buildings in the world with deflection problems like those you mentioned. And a lot of them have been designed based on very sophisticated FEM software. We have been seeing a lot of very shallow concrete members over the last 10 years or so, much more slender than previously. I think a lot of the casue is designers not understanding the results they are getting from software they are using or really understanding deflection calculation logic and what a software program needs to do to get it right.  

So they are using software, but not software appropriate for the task!  

RE: Purely Theoretical Concrete Beam Question

Quote:

For example, the one that made the 10 (or more!) times prediction was one of the Heads of the department of mechanical -here called industrial- engineering career in town. And no matter his entitlements reality showed him wrong, because the beam under study was built and working, and in place, not showing even such tenth of his aduced deflection.

It may be he got it wrong, and it may be he calculated the correct upper bound deflection, and this particular beam deflected much less than the upper bound.  Structures deflecting less than expected is not usually a problem.  Structures deflecting more than expected can be a very big and expensive problem.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Purely Theoretical Concrete Beam Question

IDS,

I can add, this was in a legal report for one litigation of the eighties for a problem that really had not that cause (exorbitant deflection), and he was unprofessionally partisan in portraying intently something that reality showed was not there, nor is now, for the building, once corrected the constructive façade problen that had, continues to perform perfectly respect deflection anywhere today. 274 dwelling units attest.

Worth mentioning, the problem on one very common error to three cases of sizable scale (irreflective and of unsuspected consequences suppression of constructive backup to some fragile façade component) was adjudicated to repair to

Case 1. the technical parties
Case 2. the construction firm
Case 3. The developer, that had to eat the problem

so you can expect statistical justice, be happy.

RE: Purely Theoretical Concrete Beam Question

ishvaag - I can't comment on the case in question, but my point was that while it is impossible to accurately predict how much any given member will deflect, it is possible to give an excellent prediction of the maximum amount it might deflect, and that is what is important, at least in the design context.

 

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Purely Theoretical Concrete Beam Question

I have long been in somewhat the same camp as ishvaaag on this...prediction of deflections in concrete is a lottery.  Use of the appropriate software, like RAPT, now makes this less so.  Regardless of the software, as a baseline I still won't deviate from the span/depth criteria which have served me well.  As rapt said, there are too many shallow concrete member designs these day, and therein lies the problem.

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