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
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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.
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.
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
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.
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.
- Thread starter
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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.
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.
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.
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.
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
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
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!
"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!
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
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.
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.
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
Doug Jenkins
Interactive Design Services
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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