P/T Question

[ron9876]

I have a condition with a heavily loaded two way pt slab with 3 spans both directions and beams along the perimeter in one direction. The slab has a P/A of about 225 psi. Bands run parallel to the beams. The beam is an L beam with a relatively small flange.

The beam will be stressed as required. This leaves a portion of the slab adjacent to the beam without pt. I would think that some of the stress from both the beam and the band will go to prestress this area. This means that the beam and band don't have as much P/A as designed. I am thinking about adding some cables in the slab parallel to the beam to make up the difference but this doesn't look right. Does anyone have any input into this condition?

 

[strucguy]

Can you please provide a simple sketch. ACI 318-05 does provide some guidance on providing additional steel (rebar or PT) for the portion the slab beyond effect slab widtd. This will take care of shrinkage or temperature stresses in that zone. Refer to page 92 of ACI 318-05 for additional info.

 

[AUCE98]

You should consider the perimeter beam flange as being 1/2 the length between column lines. Propotion the pt in the beam to accomodate the area of this design strip. The precompression from the beam will distribute into the flange, propogating at a 45 degree angle from the stress end. The only area which you will end up without precompression will be a triangular area between the bandlines at the edge. This area can be mildly reinforced, or provide additional pt tendons.

 

[ron9876]

Yes but ACI has limits for the size of the effective flange. That's where the problem comes in.

 

[rapt]

Ron,

In a purely elastic homogenous material what AUCE98 says is correct in terms of the lateral distribution of the prestress. Not on the vertical design of the beam because you cannot use that flange width as you have already said. There was some very misleading information on this over the last 20 years from some PT experts and they were very wrong.

Concrete is not that material mentioned above. Concrete shrinks differently depending on the section depth and it cracks.

The end result of this is that the axial prestress in a beam will normally be confined to the beam and the proper effective flange width you have calculated.

The remainder of the slab between the beams needs extra shrinkage and temperature reinforcement. The minimum to achieve moderate crack control would be about 1.3MPa, but this will not ensure reasonable crack widths if the concrete cracks as the prestress will be at wide spacings if bonded and thus to far apart for crack control once the concrete cracks, and if you are using unbonded, it is useless for crack control.

I would provide normal RC concrete minimum reinforcement, about .18% in the slab parallel to be beams for good crack control.

 

[ron9876]

rapt I agree with what you say. My concern is the slab that I am designing is very heavily loaded and will have salt water over it quite often. The area in question can't have zero prestress since the slab will shorten and the area must shorten with it. That means that some of the prestress from the adjacent band or the beam will bleed over leaving these members with less than design prestress. Thus the idea of adding pt in this area even though it will look crazy.

 

[hokie66]

I don't think it is crazy. In your case, with salt water over it, you can't be too conservative. I would use at least 2.5 MPa of bonded prestress figured on the gross area, and also add bars in the slab areas which will tend to crack due to differential shrinkage.

 

[rapt]

Ron,

Actually, it can have zero prestress.

You need to consider the effects of differential shrinkage within your arguement. The slab, having a much smaller thickness than the beam/band, with shrink a lot more than the beam/band and the slab area immediately attached to the beam. This shrinkage differential will induce more compression into the beam and tension into the slab. If this is more than the P/A in the slab, you will have direct tension in the slab between the beams.

Add to this the effect of the P/A drawing into the beam at supports where the top section (the slab flange) is in tension and probably cracked under service loads. because of this the P/A is contained withing the web in this area.

The combination of the 2 gives basically no P/A in the slab from the beam and probably direct tension stress due to the shrtinkage differential.

For your situation, with salt water above, I would agree with Hokie and put in about 2.5Mpa plus about .2% reinforceemnt in the top of the slab. And I might use a water proof membrane as well as/instead of the P/A tendons if the structure is to last a long time!