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Post tensioned concrete 2
- Thread starter pat2
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2
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rapt,
Would you elaborate, please? I assume you are referring to the provisions for partial prestressing. Because of cracking, the deflections increase and must be accounted for. Is the referenced PCI method for deflection calculation of cracked members indadequate or impractical?
It has been a few years since I have been heavily involved with PT design, but I for one am interested in trying out the revised provisions in certain situations. They can have real benefits for members that have high live loads, etc. where too much prestress can be a bad thing.
Would you elaborate, please? I assume you are referring to the provisions for partial prestressing. Because of cracking, the deflections increase and must be accounted for. Is the referenced PCI method for deflection calculation of cracked members indadequate or impractical?
It has been a few years since I have been heavily involved with PT design, but I for one am interested in trying out the revised provisions in certain situations. They can have real benefits for members that have high live loads, etc. where too much prestress can be a bad thing.
Taro,
The allowable stress provisions now allow you to assume that the member is uncracked if the stress in the concrete is less than the tensile strength of the concrete.
The whole idea of this rule has always been that, while concrete (even with PT) does crack we can assume that the cracking will not be a problem if the stress in the concrete is limited to a certain value. If the cracking calculations are actually done it will be found that the crack widths will be ok so do not worry about doing the calculations. This does work as long as there is sufficient bonded reinforcement (stressed or not) to restrain the crack when it does happen.
For members with bonded PT, this logic does normally work at the old 6rootf'c limit. For unbonded PT it did not even work then. Now the limit has been increased to 7.2rootf'c so we can only assume that the situation is now worse. This logic only works if bonded steel is placed in areas where there is a possibility of a crack forming (tension in the concrete, see banded discussion below).
Add to this the fact that much of the PT design in the USA and to PTI design rules is done on the basis of average moment design for 2-way slabs and the actual levels of stress are actually about 50% higher than the designers are calculating if based on a logical column/middle strip distribution of elastic stresses and probably 3 to 5 times higher in a zone located near the column. So your calculations tell you that the stress in the concrete is 7.2rootf'c or less and the concrete is uncracked but the concrete knows the stress is actually closer to 15 to 30root f'c and it is cracked.
Add to this the fact that all slabs are restrained in some way and many are heavily restrained. The stresses induced by this restraint need to be added to the applied stresses.
Add to this the fact that people are reinforcing these slabs based on an one-way ultimate failure load path (banded tendon arrangement in the slab) while the cracking and deflection are dependent on the elastic stress and moment distribution which is a 2-way distribution. There are heavily stressed areas of slab that have no reinforcement at all to provide crack control and redistribution to the failure load path.
Add to this the temperature and shrinkage differentials between top and bottom of the slab (colder on top puts tension on top).
And the code is telling you that you can consider this member to be uncracked for both crack control and deflection calculations.
Also, for deflection calculations, kcs does not apply to prestressed members. In fact is is completely wrong for all slabs, RC or PT because it should be dependent on a lot more things like member depth, concrete properties etc.
Add all this together and then make sure your insurance is paid up and your wife owns the house and car because your slabs are probably going to crack and deflect far more than you are being led to believe if they are ever loaded (which we are supposed to design for).
The allowable stress provisions now allow you to assume that the member is uncracked if the stress in the concrete is less than the tensile strength of the concrete.
The whole idea of this rule has always been that, while concrete (even with PT) does crack we can assume that the cracking will not be a problem if the stress in the concrete is limited to a certain value. If the cracking calculations are actually done it will be found that the crack widths will be ok so do not worry about doing the calculations. This does work as long as there is sufficient bonded reinforcement (stressed or not) to restrain the crack when it does happen.
For members with bonded PT, this logic does normally work at the old 6rootf'c limit. For unbonded PT it did not even work then. Now the limit has been increased to 7.2rootf'c so we can only assume that the situation is now worse. This logic only works if bonded steel is placed in areas where there is a possibility of a crack forming (tension in the concrete, see banded discussion below).
Add to this the fact that much of the PT design in the USA and to PTI design rules is done on the basis of average moment design for 2-way slabs and the actual levels of stress are actually about 50% higher than the designers are calculating if based on a logical column/middle strip distribution of elastic stresses and probably 3 to 5 times higher in a zone located near the column. So your calculations tell you that the stress in the concrete is 7.2rootf'c or less and the concrete is uncracked but the concrete knows the stress is actually closer to 15 to 30root f'c and it is cracked.
Add to this the fact that all slabs are restrained in some way and many are heavily restrained. The stresses induced by this restraint need to be added to the applied stresses.
Add to this the fact that people are reinforcing these slabs based on an one-way ultimate failure load path (banded tendon arrangement in the slab) while the cracking and deflection are dependent on the elastic stress and moment distribution which is a 2-way distribution. There are heavily stressed areas of slab that have no reinforcement at all to provide crack control and redistribution to the failure load path.
Add to this the temperature and shrinkage differentials between top and bottom of the slab (colder on top puts tension on top).
And the code is telling you that you can consider this member to be uncracked for both crack control and deflection calculations.
Also, for deflection calculations, kcs does not apply to prestressed members. In fact is is completely wrong for all slabs, RC or PT because it should be dependent on a lot more things like member depth, concrete properties etc.
Add all this together and then make sure your insurance is paid up and your wife owns the house and car because your slabs are probably going to crack and deflect far more than you are being led to believe if they are ever loaded (which we are supposed to design for).
rapt,
Thanks for clarifying your comment. The root issue is that the engineer should realistically evaluate whether cracking will occur at service load levels and make sure that deflection calculations are accurate (especially for 2-way slabs). This is a valid issue for any concrete design under any code. I agree that it is probably unwise to try to "push the envelope" of allowable stresses for traditional slab designs where the old system (with all its idiosyncrasies) gives reasonable performance.
The upside of the new provisions is that you don't need to "fully" prestress for high live loads which occur rarely. Under the old system, beams were often loaded up with dozens of tendons in an attempt to meet the service stress limits. This led to anchorage congestion, excessive camber, additional shrinkage, etc. The new system permits one to basically use a conventional reinforced concrete design approach but also benefit from the prestress.
Thanks for clarifying your comment. The root issue is that the engineer should realistically evaluate whether cracking will occur at service load levels and make sure that deflection calculations are accurate (especially for 2-way slabs). This is a valid issue for any concrete design under any code. I agree that it is probably unwise to try to "push the envelope" of allowable stresses for traditional slab designs where the old system (with all its idiosyncrasies) gives reasonable performance.
The upside of the new provisions is that you don't need to "fully" prestress for high live loads which occur rarely. Under the old system, beams were often loaded up with dozens of tendons in an attempt to meet the service stress limits. This led to anchorage congestion, excessive camber, additional shrinkage, etc. The new system permits one to basically use a conventional reinforced concrete design approach but also benefit from the prestress.
Taro,
The old method always allowed you to design for stresses above 6roo6f'c as long as you designed it allowing for cracking. I have been doing this for 27 years to Australian, British, European and ACI codes. There is no problem with designing partially prestressed members and allowing them to crack. Any designer who is doing otherwise, except in cases where cracking must be avoided (eg roofs), is wasting his clients money. I do not think I have ever designed a "fully" prestressed member except when attempting to waterproof a roof.
But, if you are desinging for cracked prestressed members, you must do them properly. The moments at service which cause the cracking are the elastic moments and they must be allowed for where they occur in the slab.
The standard practice in USA/PTI design practice has always been to average these moments over the full width. In cases where the stress levels were kept low enough at service this worked and cracking did not occur. Unfortunately, in many cases ther stress levels have not been kept low enough either because of the extra effects I mentioned which designers ignored or because they allow the average stresses to reach 6rootf'c which cracked the slab in the negative moment region near the columns as well as other places. In these cases cracking has occured and is is bad because it is unrestrained by bonded reinforcement which has not been placed to the elastic moment/stress pattern.
USA/PTI design practice and designer's interpretation of the ACI code still allows for these calculations to be done based on average moments. If this practice is used for cracked prestressed slabs then there will be problems. Bonded reinforcement must be placed at any point where a crack might occur. This is completely different to the layout of prestressing and reinforcement that is currently being used.
Also, with unbonded tendons, the 7.2rootf'c limit is too high to ensure crack control without calculation. It should be significantly lower.
Unfortunately, the "realistic" evaluation of stress and possible cracking is being based on the new ACI provisions combined with the old design methods and this is not logical or correct. Designers need to start thing of the way a two-way slab really acts rather than using the simplified logic that has been used for so long and only worked because of the limitations placed on it.
The old method always allowed you to design for stresses above 6roo6f'c as long as you designed it allowing for cracking. I have been doing this for 27 years to Australian, British, European and ACI codes. There is no problem with designing partially prestressed members and allowing them to crack. Any designer who is doing otherwise, except in cases where cracking must be avoided (eg roofs), is wasting his clients money. I do not think I have ever designed a "fully" prestressed member except when attempting to waterproof a roof.
But, if you are desinging for cracked prestressed members, you must do them properly. The moments at service which cause the cracking are the elastic moments and they must be allowed for where they occur in the slab.
The standard practice in USA/PTI design practice has always been to average these moments over the full width. In cases where the stress levels were kept low enough at service this worked and cracking did not occur. Unfortunately, in many cases ther stress levels have not been kept low enough either because of the extra effects I mentioned which designers ignored or because they allow the average stresses to reach 6rootf'c which cracked the slab in the negative moment region near the columns as well as other places. In these cases cracking has occured and is is bad because it is unrestrained by bonded reinforcement which has not been placed to the elastic moment/stress pattern.
USA/PTI design practice and designer's interpretation of the ACI code still allows for these calculations to be done based on average moments. If this practice is used for cracked prestressed slabs then there will be problems. Bonded reinforcement must be placed at any point where a crack might occur. This is completely different to the layout of prestressing and reinforcement that is currently being used.
Also, with unbonded tendons, the 7.2rootf'c limit is too high to ensure crack control without calculation. It should be significantly lower.
Unfortunately, the "realistic" evaluation of stress and possible cracking is being based on the new ACI provisions combined with the old design methods and this is not logical or correct. Designers need to start thing of the way a two-way slab really acts rather than using the simplified logic that has been used for so long and only worked because of the limitations placed on it.
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