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.
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Purely Theoretical Concrete Beam Question 2
- Thread starter Lion06
- Start date
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.
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.
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
BA
- Thread starter
- #4
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.
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.
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2
- #6
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!).
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!).
- Thread starter
- #7
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?
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?
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).
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).
- Thread starter
- #10
rowingengineer
Structural
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.”
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.”
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!
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!
- Thread starter
- #13
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?
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?
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
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
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!!
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!!
- Thread starter
- #17
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!!).
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."
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!!).
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."
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
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
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.
"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.
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