Taro,
I will try and explain what I am referring to...it is a little difficult to put into words in a forum like this...and with no sketches...but I will try...
Just for argument sake, if we have an equal and multi-span flat plate structure in X and Y directions (i.e. square panels) and undertook an elastic analysis we would arrive at bending moments, shears and deflections, and the negative moments would peak over columns regions (in both directions) and be reduced in the middle strips (over the transverse column tendons), so we will see that the transverse distribution of the bending moments varies across the width of the slab panel. For positive moments, again we will see a varying distribution of moments across the panel width.
Now, if this was a RC flat plate we would provide rebar in column strips and middle strips in each direction, no questions asked.
For a PT flat plate, the elastic behavior is really one and the same as RC, and if anything, will behave more elastically as the onset of cracking is delayed due to the effects of the uplift and pre-compression by the prestress.
If we take a RC flat plate that we decide to only reinforce with rebar in the column strips (basically banded rebar, top and bottom) for 100% of the load, and in the orthogonal direction we provided top and bottom rebar that was uniformly spaced across the full panel width what would happen under load? (PS I am not advocating that this is a good method of reinforcing a structural slab! but I want to use it as an analogy). At service load levels it will crack, lots of cracking, and the type of cracking will be wide and somewhat UN-controlled and contrary to what we typically design and strive to achieve in a "good" design - why? Because there needs to be moment re-distribution (basically cracking) to take place so that the RC floor plate can "act" or behave as it was reinforced. Large areas of slab with significant moments have no reinforcement to resist those moments. For the slab to "work", these moments must redistribute to other areas where there is reinforcement. This effect can only happen if we provide a LOAD PATH to the supports, otherwise it will collapse. In this case, the elastic load path is 2-way but the reinforcement load path provided is one way, so the failure load path is one way. The elastic 2-way moments redistribute to a failure 1-way moment pattern. Unfortunately, for this to happen large cracks will develop and excessive deflections will occur to accommodate the redistribution of moments and actions. For "correctly" designed slabs (using column and middle strips both ways and adequate reinforcement) these cracks will be fine, well distributed and not full depth. Codes of practice control/limit the amount of moment re-distribution that can be assumed in design based upon the level of ductility of the section - an unreinforced section of concrete has no ductility! This is why we do not reinforce RC slabs in this way. At service, the redistribution has already commenced and excessive cracking and deflection will occur under normal service conditions. This is defined as structural serviceability failure. While the slab will not collapse (normally unless it is too non-ductile) it will have "failed" in terms of cracking and deflection.
Now if we take a similar flat plate but use P-T in the same banded/uniform distribution we would expect to see a similar behavior - however, depending on the level of balanced load and pre-compression, we will see a delay in the onset of cracking. Again, an unreinforced section of concrete with some P/A does not have much ductility.
But in P-T structures we use load-balancing? Load balancing is a very powerful tool for the engineer. Static's and equilibrium will tell us that we have to "balance" the full load in BOTH directions. From load-balancing view point, the panel tendons may be distributed between the X and Y directions arbitrarily provided the column line tendons satisfy static's and equilibrium. Load balancing can be achieved by band/uniform arrangements, or column/middle strip each way and at the BALANCED load level they will behave somewhat similarly. BUT, at loads other than the balanced load, and especially at overload, the banded/uniform tendons do not perform as well as those with column strips in each direction with corresponding middle strips.
If you look at the crack patterns in a banded/uniform slab at ultimate flexural limit state, after all cracking has occurred, moments have redistributed to where there are resisting moments etc, plastic hinges have formed, you will notice that the loads are all being carried by the equally spaced tendons to the banded tendons over the entire length and then to the support by the banded tendons. In other words, the load path to the support is a 1-way load path and is exactly the same as the load balancing load path. A 2-way load path requires middle strip reinforcement (of one type or another) and column strip reinforcement in both directions and this is not being provided, especially for the positive middle strip moments (between the banded tendons), in banded/uniform tendon design.
Also, when we consider a section's negative or positive moment capacity under ultimate (limit) strength state, the flat plate with banded tendons concentrated in a narrow width over the columns, is considered with the FULL panel width and no treatment of the "shear lag" effects are considered. Basically, it is permitting the use of mobilizing the full panel width, yet only reinforce (PT and/or rebar) in a narrow localized area. This, IMO, is wrong.
The "average" moment concept of banded/uniform tendons is just "assuming" the moment is uniform over the full panel width, and is very much simplifying the real situation.
Contrary to the PTI Manual statement "...forget about arbitrary column strip, middle strip and moment percentage tables which have been long familiar to the designer of the RC flat plates" P-T and RC plates are very similar in behavior. ACI has been slow in recognizing TRUE partial prestress, whilst other international codes have long permitted prestressed concrete as a “unified” material - "structural concrete", ranging from reinforced, to “partial" prestress, to “full” prestress.
The column/middle strip concept still uses average moments, but it is an average moment across the column or middle strips, respectively, NOT over the full panel width. Actual peak negative moments that over at the columns will be appreciably larger than the average column strip moments, and accordingly, the peak negative moments over the columns will be VERY significantly larger than the average of the full panel moments used in banded/uniform arrangements.
For banded/uniform tendon design, ACI 318 assumes the slab to be uncracked so its flexural tension levels are "hypothetical" stress levels - actual stresses are significantly different to these “hypothetical” values. The distribution of flexural stresses will approximately follow those of the elastic bending moments - bending moments that are based upon an assumed elastic material with a varying distribution across the panel width. All working stress calculations should be based on the actual stress distribution. Based on these correctly calculated stresses, banded/distributed tendon arrangements should not be allowed is the stresses are greater than in tension. The stress levels allowed in ACI should be compared to properly calculated stresses, not average moments/stresses, and the levels are far too high to provide correct crack control.
I have reviewed unbonded P-T flat plates, and often see cracks that are wide and not well distributed (sort of opposite to what we try and achieve in a "good" design) and these cracks are often full depth (unreinforced section cracks plus restraint effects can add to the net cracking situation). When I design partially prestressed slabs I ensure that there is sufficient mild steel rebar to control cracking in locations where flexural tensile stresses are exceeded, based upon a more rational (non-uniform) distribution of moments. For UN-bonded P-T flat plates with banded/uniform tendons where the design has assumed average moments across a full panel width the flexural stresses will be incorrect, there will be cracking, and the sections do not really have the ductility to be assuming this level of re-distribution that must occur. The result, if cracking does occur at service load levels, will be similar to the RC slab discussed above, large unrestrained cracks and excessive deflections compared to the calculated values.
Granted, many do not fail in a structural sense (secondary actions come into play), but in terms of serviceability criteria they will be cracked and will have deflected, and when one of the objective was to have controlled or no cracking they have "failed".
On a side note...(although it has little to do with P-T)… in early 1900's C.A.P Turner and his "mushroom" flat slabs were very controversial amongst engineers - there was significant disagreement about simply designing for 100% of static's - and even in ACI 1963 it was still permissible to design a RC flat slab for approximately 70% of static's!!!!
Sorry the above is so verbose.
