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Post-Tensioned Transfer Beam in One-Way Slab Design

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jgwdea

Structural
Dec 21, 2010
8
My main question is whether or not a post-tensioned transfer beam parallel to the direction of slab post-tensioning tendons should be designed as a T-Beam (using slab as flange) or Rectangular beam.

Here is an example to illustrate the question:

Let’s say I have a 180 (north-south direction) foot by 540 (east-west direction) foot elevated slab. The columns are spaced at 20’ centers in the long direction (east-west) and 60’ centers in the short direction (north-south). For a typical PT beam perpendicular to the slab span, I would have a 3-span (60 feet per span in the north-south direction) beam with a 20’ flange width (effective flange width of 106” based on ACI). So these beams are spaced at 20 foot centers typically. Now let’s say the architect wants to eliminate a column, which requires me to add a 40 foot transfer beam running east-west to provide support for the beam line running north-south. It seems to me, I should design this transfer beam as a rectangular beam instead of a T-beam. If I were to design it as a T-Beam, the added flange width would reduce my P/A stress, so I could add quite a bit more PT without overloading precompression. However, it doesn’t seem like I should be able to use slab beyond the width of the transfer beam as flange material since the one-way slab will be post-tensioned parallel to this beam (it will already have its own precompression stress.)

Thanks,
jgwdea
 
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jgwdea,

Precompression is one minor aspect of design. It does not tell you how anything actually works.

Think how the whole beam performs. It is a T beam!

The slab beside the beam will actually be supported by the beam. It is not going to span the whole distance and the beam is so much stiffer the slab will simply be part of the beam. So include that part of the slab load in the beam.
 
Thanks,

It has a 60' flange, so would you use the effective width (per ACI for bending stress check) or the full 60' to check P/A.

-jgwdea
 
Lets say you have a 10" thick slab and a 24" wide transfer beam.

then Per ACI 318-05, 8.10.2::

(a) (16 x 10" slab) x 2 sides + 24" = 344" or 28.67'

(b) (1/2 x 60'x12"/')x2sides = 720" or 60'

Hence (a) controls and your effective flange width is 344" not the 60' you are considering.

Look at figure R7.12.3 on top of page 92. It clearly defines the flange width for a prestressing beam while it is describing how to determing T & S tendons.

P.S. Be careful with this one. This is a situation where staged prestressing would be an ideal solution since it will be difficult to control top fiber stresses at mid-span prior to application of your transfer loads. Consider partial prestressing to avoid ridiculously deep transfer beams.
 
Thank you all.

I appreciate it!

-jgwdea
 
Point of clarification. You are likely using the equivalent frame methodology for design which would have you use 1/2 the slab span on either side of the beam. But I caution you to think about what is happening here. Read up on St. Venant's principle. This basically states that a point load applied to a shell will distribute out at a 2:1 ratio on each side of the point load (the 2 is parallel to the applied load and the 1 is perpendicular). If you were to apply this logic you would find that after 20' into the span you would be able to distribute the point load to 10' on either side of the beam center line. This would give you a 20' or 240" wide flange width which is relatively close to what you get with section 8.10.2.

 
Always the effective flange width for design. Even for the P/A calculations. The full panel width only defines the load on the beam. it has nothing to do with how the beam actually acts.
 
I think you need to consider the sequence of construction. Will the transfer beam be post-tensioned before the slab is placed? In that case, you are limited to the allowable fci when you post tension the transfer beam minus the compression that will occur due to dead load once the slab is placed. Then, if the slab has shear connection to the transfer beam, you need to watch out for the affects of post-tensioning the slab.

On the other hand, if everything will be shored and post-tensioned at the same time, you should be able to use the composite section of the transfer beam and the effective slab width.
 
graybeach,
I think it is clear from the OP that the beam and slab are monolithic.
 
Thanks to all the responses.

Correct me if I'm wrong...so to correctly check the maximum precompression in the transfer girder, I would need to sum the precompression I get from the PT slab design and the precompression I get from the PT transfer beam design since the post-tensioning of each results in additive precompression in the slab/flange.

Does anyone have any references for maximum precompression in transfer beams? I don't see any code limits.

Thanks,
jgwdea
 
Another concern I have is overly high precompression in the slab due to high P/A in the transfer beam. I am concerned that excessive P/A could cause excessive shortening of the slab in this area, resulting in columns at the edges being pulled inward.

Any thoughts?

Thanks again,
jgwdea
 
Compression of a 40' beam in a 540' long slab is a very minor part of the overall shortening. Probably 70 or 80% will be from drying shrinkage of the slab.
 
jgwdea

Yes, if the precompression inthe T beam from the flange tendons plus the beam tensons is high, you will need to consider the effect. But simply stating that it is high does not make it possible for us to comment. What is "high"?

As Hokie has said, shrinkage will be higher and so will temperature change. All need to be considered, especially if your beam is 180' long.

So work out the effects of all axial shortening and take them into account. I do not see the problem.
 
I do not know what the current ACI code says about the flange width of a T-Beam. Here is what ACI 318-63 had to say: The effective flange width to be used in the design of symmetrical T-Beams shall not exceed one-fourth of the span length of the beam, and its overhanging width on either side of the beam shall not exceed eight times the thickness of the slab nor one half the clear distance to the next beam.

I have always thought that to be a very sensible criteria. It means that your flange width for the 40' transfer beam should not exceed 10'.

BA
 
Using ADAPT PT 8.00,

A 24" wide by 36" deep, 40' transfer beam with a 720" wide (x5.5" deep) flange (112" effective flange width) results in a P/A of 147 psi. With the exact same loading conditions, and only changing the actual flange width from 720" to 112", I get a P/A of 512 psi. The slab P/A due to its post-tensioning in this area is about 250 psi. (I spoke to an engineer with ADAPT to ask about the use of the total flange width in their P/A calculation vs. the effective flange width...he said they use the full flange width for P/A and effective for everything else (stress calc's, etc.))

So the slab P/A in the effective width of the transfer beam would be 250 psi + 512 psi = 762 psi. Correct?

It sounds like most of those who have replied do not see any concern for these P/A levels. I just wanted to make sure since this is my first PT design and did not see any specific literature on this.

-jgwdea
 
jqwidea,

Don't believe everything you hear. The beam should be designed for its P/A within the effective flange width, not the full slab width as suggested by the Adapt person. Adapt has always had this problem and its developers/support staff do not understand what they are doing!

Tha slab beside the beam will be doing nothing in the direction of the transfer beam. There is no bending there. The beam is so stiff, the slab beside it can only be acting one way perpendicular to the beam. Putting tendons in the slab parallel to the beam and saying the slab is spanning that way is not a logical assumption. The tendons will not be doing anything useful. Yes you are getting a load balance, but in terms of resisting moments in a slab, you cannot generate any bending moment there from the slab so why do you want a resisting moment there. You cannot design the slab as a two way slab and then shove a gigantic beam in the middle of it and still say the slab acts as the same 2way slab. The spanning actions of the slab will be significantly modified and needs to be designed accordingly (your Adapt man will probably not understand this either).

Regarding your P/A levels indicated above, yes they are too high for a long length of beam and in a situation where there is a lot of indeterminancy. There is going to be a lot of shortening that you will have to allow for in designing the remainder of the structure, both short term and long term.

As I said at the end of my last post, So work out the effects of all axial shortening and take them into account!!
 
Quoting again from ACI 318-63 Article 906 (e): Where the principal reinforcement in a slab is parallel to the beam, transverse reinforcement shall be provided in the top of the slab. This reinforcement shall be designed to carry the load on the portion of the slab required for the flange of the T-beam. The flange shall be assumed to act as a cantilever. The spacing of the bars shall not exceed five times the thickness of the flange, nor in any case, 18 in.

It may be better to omit post-tensioning tendons for the width of beam flange and provide nominal conventional reinforcement instead.

BA
 
BAretired,

Though most of us are not old enough to have a copy of the 63 code, I agree entirely. Reinforce the slab beside the beam as a beam flange.

A PT slab acts the same as an RC slab and should be reinfroced in a sim ilar manner. The slab beside a very stiff beam cannot have secondary bending in the difecxtion parallel to the beam. The beam controls the stresses in that area of the lsab and that is how it should be reinforced.

In all designs, it is logical to determine how the slab/beam system is going to deflect and distribute load and reinforce it accordingly. It is no use putting reinforcement (including tendons) where there are no bending stress if the stresses are in another area because of relative stiffnesses of other elements in the structure.

The fact that a column has been removed and replaced by a transfer beam completely changes the way this slab is going to act. It is no use having tendons parallel to and close to the beam draping to a bending moment pattern that would exist if the beam was not there and the column was. The beam is there and the 2way slab bending pattern you would get assuming a column cannot occur.
 
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