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Post-Tensioning Balancing Loads
- Thread starter jguer005
- Start date
While there are minimum prestrss guidelines, there are no minimum balancing requirements that I know of. Any deficiency in flexural strength could obviously be made up with mild reinforcing. There is a practical maximum balancing load however. You need to ensure that you don't accidentally over-balance (>100%) your system. If that happens, you'll end up with negative moments midspan, positive moments at your columns, and possibly a good deal of cracking.
Within the bounds of preventing over-balance, I've found it optimal to balance as much of the load as possible. I like to be closer to 85%. I'll push the balancing higher with FEM plate modelling than I will with 2D strip modelling because I have more confidence in the dead load estimation. I'll also back off a bit at the balconies to provide more of a margin of safety against water draining back into the occupied space (owners frown up that).
We have a PT expert here that goes by the handle Rapt. Hopefully you hear from him.
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
Within the bounds of preventing over-balance, I've found it optimal to balance as much of the load as possible. I like to be closer to 85%. I'll push the balancing higher with FEM plate modelling than I will with 2D strip modelling because I have more confidence in the dead load estimation. I'll also back off a bit at the balconies to provide more of a margin of safety against water draining back into the occupied space (owners frown up that).
We have a PT expert here that goes by the handle Rapt. Hopefully you hear from him.
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
It really depends on:
A) Type of slab support system that is being adopted (flat plate, flat slab, banded beam and slab, one-way beams & slab etc),
B) The superimposed dead and live loads,
C) Type of PT (BONDED or UNBonded tendons),
D) The applicable building code.
E) Supply & install cost or PT vs rebar
I am going to assume this is a US-based design, and therefore further assume UNBonded PT, ACI-318 code, and highly likely a flat plate system, under typical residential or parking LL.
Assuming so, you are not going to be able to do a partially prestressed PT slab design in the sense of exceeding flexural stresses and providing calculated bonded mild steel reinforcement (like those undertaken in Australia, for example). You are going to have to satisfy code-specified flexural stress limit for tension-zones.
I usually start by:
1) Determine a slab thickness based upon L/D ratios for the span and slab type. I now know my slab SW.
2) Then assume a PT balanced load of say 75-85% of SW. Now I have my prelim effective PT force.
3) Quick check of magnitude of P/A. Aim for >125 psi (absolute min) and <300 psi. Rule of thumb only.
4) Do a quick punching shear check based upon column size, adopted thickness, with calculated P/A.
4) Calc equivalent loads due to prestress, and do a quick frame run (BM distribution or plane frame) under working load AND ultimate load conditions.
5) check flexural stresses under working loads, and compare to code-specified values.
6) Adjust PT force and/or slab thickness if flexural stresses are not satisfied.
7) check ultimate flexural moments and determine magnitude of bonded reinforcement. Check code minimums.
8) Check punching shear in a more detailed manner.
9) Check deflections, allowing for creep and shrinkage effects.
Some engineers also do PT loss calcs, but the US practise (most especially for UNBonded PT) is to usually show effective Prestress forces on design drawings and assume an average loss allowance.
The above lends itself to computer software. But first timers should be doing it my hand the first few times, IMHO. Gives you a way better "feel" when your future designs are on the black-box.
A) Type of slab support system that is being adopted (flat plate, flat slab, banded beam and slab, one-way beams & slab etc),
B) The superimposed dead and live loads,
C) Type of PT (BONDED or UNBonded tendons),
D) The applicable building code.
E) Supply & install cost or PT vs rebar
I am going to assume this is a US-based design, and therefore further assume UNBonded PT, ACI-318 code, and highly likely a flat plate system, under typical residential or parking LL.
Assuming so, you are not going to be able to do a partially prestressed PT slab design in the sense of exceeding flexural stresses and providing calculated bonded mild steel reinforcement (like those undertaken in Australia, for example). You are going to have to satisfy code-specified flexural stress limit for tension-zones.
I usually start by:
1) Determine a slab thickness based upon L/D ratios for the span and slab type. I now know my slab SW.
2) Then assume a PT balanced load of say 75-85% of SW. Now I have my prelim effective PT force.
3) Quick check of magnitude of P/A. Aim for >125 psi (absolute min) and <300 psi. Rule of thumb only.
4) Do a quick punching shear check based upon column size, adopted thickness, with calculated P/A.
4) Calc equivalent loads due to prestress, and do a quick frame run (BM distribution or plane frame) under working load AND ultimate load conditions.
5) check flexural stresses under working loads, and compare to code-specified values.
6) Adjust PT force and/or slab thickness if flexural stresses are not satisfied.
7) check ultimate flexural moments and determine magnitude of bonded reinforcement. Check code minimums.
8) Check punching shear in a more detailed manner.
9) Check deflections, allowing for creep and shrinkage effects.
Some engineers also do PT loss calcs, but the US practise (most especially for UNBonded PT) is to usually show effective Prestress forces on design drawings and assume an average loss allowance.
The above lends itself to computer software. But first timers should be doing it my hand the first few times, IMHO. Gives you a way better "feel" when your future designs are on the black-box.
Load balancing is not a design requirement, it is a tool for determining the number of tendons to suit a specific condition. For normal slab loads (2.5-5KPa) balancing 60-80% is normally logical, but depends on the L/D ratio chosen (thinner slab requires more load balanced) and the design objective.
Ingenuity has given the logic for ACI code average moment logic where partial prestressing cannot be used and hypothetical stress limits must be met.
If you work to more sensible logic using column/middle strip moment patterns (yes PT flat slabs actually do work this way, same as RC flat slabs, ACI/PTI has simply ignored it for the sake of simplification of the process, thus forcing designers to adopt a more basic design procedure and not get the best out of their designs), then partial prestressing can be used and there is no logical limit to the amount of load to balance. many designers in this case will balance sufficient load to ensure that no bottom reinforcement is required (with bonded PT slabs and proper 2way tendon layouts, not banded/distributed which should always have extra reinforcement added to handle the redistributions required).
For slabs with heavier loads, more load should be balanced.
The more important objective is to make sure that the load balance is consistent in the 2 directions to provide a load path to the supports. PTI has put out a paper that suggests there are 4 different possible tendon patterns. Unfortunately, 2 of these do not provide a load path to the supports and should not be used unless the design is done using FEM analysis and design considering different strips picking up the areas of higher stress with the appropriate tendons in that width, I.e. a proper partial prestress design. This is not the default design that you get out of the FEM slab PT programs, it takes a lot of work by the designer to get the right design in these cases. These two patterns are
- distributed tendons in both directions
- banded tendons in both directions.
In both cases, it is important to design for the different areas of slab (no averaging of whole panels) and add the extra reinforcement where it is needed for both crack control and strength, for distributed in both directions, a lot of reinforcement over the columns, and for banded in both directions, and lot of bottom reinforcement in both directions. Also, you must use proper deflection calculations allowing for cracking and long term effects (no fudge multipliers!
The other 2 patterns are really the 2 extremes of a correct tendon layout. The more general one is a column/middle strip layout, (all of my description of % below applies to flat plates. They will vary where there are drop panels.) where 75% of the tendons are in the column strips in each direction and 25% in the middle strips. This gives a pure 2 way load balance for a square grid of columns. The easiest way to think of it and lay it out is to place 50% of the tendons in each direction as equally spaced distributed tendons in each direction (you 2 way slab tendons assuming continuous supports) with the remaining 50% concentrated in bands on the support lines (your support strips). Once you think of it this way, you can vary these %'s for rectangular panels to more logically match the shape. The extreme is for slabs with very close columns in one direction where the distributed tendons would be in the long span direction with 100% distributed in that direction and the band in the short span direction with 100% in the band. This is the way the slab wants to work, so go with it.
The other pattern, often used in USA with unbonded PT, is to use the banded distributed tendon pattern in any slab independent of the slab spans. Unfortunately a lot of the advice I have seen in this suggests the band should be in the long span direction, but this is completely illogical based on the argument above, always try to work the way the slabs wants to, there is less redistribution that way. This layout can be justified as long as you either follow the advice above regarding analysis and design considering all of the different strips, or use the ACI code logic and add all of the extra reinforcement it requires.
The biggest problem with this method is the amount of redistribution you are allowing without considering its effects, assuming that the code simplifications for strength, crack control and deflection are covering you. This is ok for lightly loaded slabs where the stresses will be low anyway but I do not agree that it is ok for heavily loaded slabs or slabs where there is a very irregular support layout. The method is basically providing a yield line result, based on an elastic analysis. This is ok for regular column layouts but not for extremely irregular layouts where a true yield line analysis should be performed.
Ingenuity has given the logic for ACI code average moment logic where partial prestressing cannot be used and hypothetical stress limits must be met.
If you work to more sensible logic using column/middle strip moment patterns (yes PT flat slabs actually do work this way, same as RC flat slabs, ACI/PTI has simply ignored it for the sake of simplification of the process, thus forcing designers to adopt a more basic design procedure and not get the best out of their designs), then partial prestressing can be used and there is no logical limit to the amount of load to balance. many designers in this case will balance sufficient load to ensure that no bottom reinforcement is required (with bonded PT slabs and proper 2way tendon layouts, not banded/distributed which should always have extra reinforcement added to handle the redistributions required).
For slabs with heavier loads, more load should be balanced.
The more important objective is to make sure that the load balance is consistent in the 2 directions to provide a load path to the supports. PTI has put out a paper that suggests there are 4 different possible tendon patterns. Unfortunately, 2 of these do not provide a load path to the supports and should not be used unless the design is done using FEM analysis and design considering different strips picking up the areas of higher stress with the appropriate tendons in that width, I.e. a proper partial prestress design. This is not the default design that you get out of the FEM slab PT programs, it takes a lot of work by the designer to get the right design in these cases. These two patterns are
- distributed tendons in both directions
- banded tendons in both directions.
In both cases, it is important to design for the different areas of slab (no averaging of whole panels) and add the extra reinforcement where it is needed for both crack control and strength, for distributed in both directions, a lot of reinforcement over the columns, and for banded in both directions, and lot of bottom reinforcement in both directions. Also, you must use proper deflection calculations allowing for cracking and long term effects (no fudge multipliers!
The other 2 patterns are really the 2 extremes of a correct tendon layout. The more general one is a column/middle strip layout, (all of my description of % below applies to flat plates. They will vary where there are drop panels.) where 75% of the tendons are in the column strips in each direction and 25% in the middle strips. This gives a pure 2 way load balance for a square grid of columns. The easiest way to think of it and lay it out is to place 50% of the tendons in each direction as equally spaced distributed tendons in each direction (you 2 way slab tendons assuming continuous supports) with the remaining 50% concentrated in bands on the support lines (your support strips). Once you think of it this way, you can vary these %'s for rectangular panels to more logically match the shape. The extreme is for slabs with very close columns in one direction where the distributed tendons would be in the long span direction with 100% distributed in that direction and the band in the short span direction with 100% in the band. This is the way the slab wants to work, so go with it.
The other pattern, often used in USA with unbonded PT, is to use the banded distributed tendon pattern in any slab independent of the slab spans. Unfortunately a lot of the advice I have seen in this suggests the band should be in the long span direction, but this is completely illogical based on the argument above, always try to work the way the slabs wants to, there is less redistribution that way. This layout can be justified as long as you either follow the advice above regarding analysis and design considering all of the different strips, or use the ACI code logic and add all of the extra reinforcement it requires.
The biggest problem with this method is the amount of redistribution you are allowing without considering its effects, assuming that the code simplifications for strength, crack control and deflection are covering you. This is ok for lightly loaded slabs where the stresses will be low anyway but I do not agree that it is ok for heavily loaded slabs or slabs where there is a very irregular support layout. The method is basically providing a yield line result, based on an elastic analysis. This is ok for regular column layouts but not for extremely irregular layouts where a true yield line analysis should be performed.
@ rapt: I'm steeped in North American practice. Could you point me to any books or technical documents that follow the design philosophies that you ascribe to? I'm curious to know more, particularly about the column strip / middle strip business. I haven't found many texts that deal with PT floor slabs comprehensively.
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
KootK,
I have not read a text book on PT slabs for about 35 years, so am not sure what the current ones say. Everything I have said above is based on engineering logic. What we are supposed to be trained to do! It is all statics and equilibrium!
The reason RAPT is basically not sold in USA is because of the code and designers interpretation of it and the PTI literature. I have no desire to waste my time arguing against the illogic of PT design in USA!
Prof Ian Gilbert is working on a new version of his book at the moment. I will check to see what he is saying on flat slabs in it.
I have not read a text book on PT slabs for about 35 years, so am not sure what the current ones say. Everything I have said above is based on engineering logic. What we are supposed to be trained to do! It is all statics and equilibrium!
The reason RAPT is basically not sold in USA is because of the code and designers interpretation of it and the PTI literature. I have no desire to waste my time arguing against the illogic of PT design in USA!
Prof Ian Gilbert is working on a new version of his book at the moment. I will check to see what he is saying on flat slabs in it.
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