With two way PT slabs-when the initial tensile stress exceeds the maximum should the reinforcement be placed at columns or spread across the trib width?
Is this an existing structure that has had an initial stress applied that exceeds 10% (or whatever your code stipulates)? Or are you designing a structure where a larger then normal initial stress is required, if so why?
Use a partially prestressed slab and make up the deficit with conventional reinforcement, increasing the slab depth if desired to control tensile stresses.
ohhhh, sorry missed my coffee yesterday. You've got a high negative moment over the columns and it needs a bit more reo. Well I'd spread the reo across the column width and then chuck in a bit extra over the columns, have you checked your punching?
I don't think we are addressing the same problem. As I understand it, the loads are very heavy, requiring a lot of post-tension cables to resist them. However, when the loads are not present, the large pretension force causes excessive tensile stresses at midspan.
It is the tensile stresses that occur at the time of stressing before any losses. Top reinforement for normal loading goes over the columns and bottom is spread over full width. ACI gives a method to calculate the area of steel but doesn't mention if placement is the same as for the standard condition.
You should place and distribute the required tensile steel in the same manner as prescriptive steel outlined in ACI 318-05, sections 18.9.3.2 and 18.9.3.3. The negative moment steel should be concentrated at the columns because the restraint of the columns draws and concentrates the negative moment to this location (ie 1.5h from each face of the column). At mid-span you should distribute the steel evenly across the slab width since the moment will be more evenly distributed across this region due to the flexibility inherent at mid-span.
Since your moments are from the P/T (primary and secondary) the moment diagram is the opposite of the typical gravity load diagram. Thus the tensile region at the columns is the bottom of the slab and the tensile region at the center of the span will be at the top of the slab and this is where you should locate your mild steel. This will look somewhat unusual since at the columns you will need to place mild steel at the top and bottom of the slab (top for prescriptive requirements and bottom for initial stresses).
If possible, I highly recommend either increasing your slab depth or your concrete strength to avoid exceeding the allowable intial stresses. Also, be careful that your service load stresses do not exceed 6(f'c)^1/2 since this is a two way slab and should be designed as class U. Also, be careful of your long term deflection.
Out of curiousity, what is your average prestress?
larsacious thanks for the input. That was my first impression since it is really only upside down loading but it doesn't feel right to have a tension zone without reinforcement at the supports.
If it does crack (which we are assuming since we are adding reinforcement)the cracks will close with shrinkage, creep and the addition of loads.
This is an unusual condition. It is a tunnel under a street with 4'-5' of soil, ground water and truck loading. The slab is 17"-19" thick with 6,000 psi concrete. It works well everywhere except one edge conditon where there is a longer diagonal span.
It is one of those conditions where the band in question tapers and merges with the adjacent band. The total P/A in that area is about 480 psi so don't want to add more cable. Wish I could.
Partial Prestressing in flat slabs is not allowed by ACI318. This is because the real stress distribution in the slab and the concentrations of stress in certain areas is not being considered (average stress over the full width is considered). It is not possible to do proper partial prestress calculations if you are not dealing with the real stress distribution.
Ron, My initial comment was because your initial question was so general it was impossible to answer logically.
The reinforcement should be placed where the stresses are going to cause the cracks. Unfortunately the ACI code logic does not tell you where the cracks are going to be because it does not consider stress concentrations in slabs. You need to go back to engineering logic and decide where the possible cracks will be. This will definitely be near the column in your case, but could spread out further than the ACI nominal placing limits for "support" reinforcement. If you are doing an FEM analysis, it will give the stress distributions. I would place the reinfrocement anywhere where the transfer stresses are greater than about 100psi stress. This is much lower than the normal code rule and it is because those rules are unconservative in cases where there are no bonded tendons (I know ebverything there is unbonded)near the tension face.
