long span two way PT

[CoreyGuo]

I have a long span two way slab situation and the basic info is like this: the slab is 120 feet by 90 feet and the slab is supported only by perimeter walls or columns. There are three PT beams in the short direction and two PT beams in long direction and therefore the spaning between beams or between beam and slab perimeter is 30 feet. Note that there are only perimeter supports and no intermediate supports.

Apparently the PT beams in both directions work in two-way reaction to share all the loads. Has anyone have experience on such a structure? Any comments or suggestions are welcome.

Thanks!

 

[csd72]

Never designed one this way, but the loads would be distributed in accordance with strain compatibility, i.e. beams will take loads in proportion to their stiffness.

 

[rapt]

CoreyGuo,

It is a two way grillage of beams. Nothing special about it.

Obviously, the longer 120' spanning beams will be partly supported by the shorter spanning beams if they are the same stiffness.

You will beed to do a grillage analysis to determine the relative supporting effects of the beams. As long as you are designing it all as basically uncracked, this could be an elastic analysis to get some reactions to apply to the shorter span beams and supporting loads to apply to the longer span beams.

Then the slab is simply designed as multiple 30' spans of two way slab (on continuous supports) with half the load carried in each direction.

 

[CoreyGuo]

Thanks all for the response.

Rapt,

Actually there are two spans in the long direction, 120 feet and 90 feet, therefore the total structure is about 210 feet by 90 feet.

Currently only the beams in both directions are post tensioned and slabs are not. After the grillage analysis, we can see that at some locations short beams provide support for long beam and sometimes long beams provide support for short beams. The reasons are that long PT beams are continuous and short beams are tapered from one side to another.

As we are expecting, portion of the PT compression force is dissipated into slab and therefore it would be inappropriate to take one individual beams out and analysis it in 2-D program. I think that this is really the time when 3-D FEM based programs, such as Ram Concept or ADAPT, is required. Besides, it would be very hard to design the beams without cracking and I only managed to bring the stress below 12*sqrt(fc’). For each design strip, I only include the effective width for each beam in the design strip. The portion of the slab close to perimeter is left out.

For the slab design, there are two choices: 1. design the slabs as two way slabs by assuming that slabs are supported by PT beams in both directions; 2. design the slabs according to the results from 3-D programs. The first approach does not consider the PT effects due to PT tendons in beams and also does not consider the large deflection curvature in the middle of the bay because the supports from PT beams are assumed being rigid. So it looks like that the second approach should be used.

If you disagree with any of the description above, please comment on.

 

[rapt]

CoreyGuo,

That is where everyone is being misled in their thinking with FEM programs. For a start they do not even have beam elements, only thickened slabs (unless they have changed recently). Secondly, they are still only doing an elastic analysis of an inelastic material with very variable properties, with variations depending on shape, stress and a lot of other factors.

The P/A only distributes evenly over the full width if the concrete is elastic and if there is no membrane action and if the shrinkage of the concrete is the same for all of the concrete involved, slabs and beams, etc. None of these conditions are true for your slab system. Depending on their shapes, the beam shrinkage could be 1/2 to 1/3 of the slab shrinkage. This causes tension in the slab and compression in the beams, effectively pulling the axial prestress out of the slab and into the beams. If you analysis this effect on a real FEM program you will see the effects.

You cannot rely on an elastic FEM analysis telling you where the prestress is going, no matter what certain FEM suppliers and self proclaimed experts tell you.

Any PT experts I talk to flatly refuse to use those programs for beam design after checking their results, and modify the default approach for slab design significantly also, and then ignore part of the results anyway. Their Torsional stiffnesses are questionable, they ignore Mxy moments in design and often effects which are distributed in 3D in the analysis are then merged together to give the design actions for the beams ignoring the initial elastic analysis distribution. And their fudged attempts at deflection calculations are just that, a guess. None of this is correct and much of it results in under-design.

Yes, use a real FEM/grillage analysis to decide the relative support reactions of the different beams, but make sure it is being analysed and designed properly.

RE the slab panels, I would have no problems with designing them as 2way slabs supported by the beams. You can allow for support settlement in this if you want to allow for the beams deflecting. And I would design the beams for the contributing slab to each beam plus whatever support/applied reactions there are from other beams. Just make sure that whatever design tool you are using is actually doing it properly!!

 

[rapt]

CoreyGuo,

I forgot to add,

if the beams are cracked as is likely with these span lengths, you need to account for this in the crack control calculations and the deflection calculations as well as accounting for creep and shrinkage effects properly. None of the FEM software will do this properly for you. RAPT, a 2D program, is the only PT program that will attempt to do this properly for you.

 

[csd72]

So I take it you have 6 beams spanning 90' and 2 beams spanning 210' (with edge walls/supports all around the perimeter).

At the middle of the slab, the stffness of the 90' beams is about 30 times that of the 210' beams therefore the 90' beams will be taking virtually all of the load.

So if these beams work, then so should the ones towards the ends.

So why not save your client some money and remove the 210' beams so that the formwork can be greatly simplified. You could then partially post-tension the slabs with the tendons that were not used for the beams.

 

[hokie66]

The way I read his post, the 210' side is two spans, 120' and 90'. He did say the support was by edge walls and columns, but the support is not continuous.

 

[CoreyGuo]

Rapt,

Thanks a lot for your response. I raised the following questions for your thoughts:

1. You recommended the use of a real FEM analysis. If the analysis is elastic and does not take creep, shrinkage factors into consideration, then the results would have no difference from the other 3-D PT software.
2. Are you saying that you would analysis the beam only to meet stress and strength criteria? I would think that most engineer will analysis the beam as T beam with slab effective width.
3. Do you think that no P/A is dissipated into surrounding slabs? Have you used this approach for your projects? I agree that theoretically slabs shorten more and may apply compression force to beams. But I’ve never seen one case where beams are analyzed independently from effective slab width.
4. We do not have RAPT 2-D program. What is the approach the program use to calculate the cracked section and deflection? Does it take creep and shrinkage into consideration? How the program is different from other PT programs in stress and strength design results? I would like to know the theory and possible results before I suggest IT dept to buy RAPT 2-D.

Thanks again!

 

[CoreyGuo]

CSD72,

Hokie66 is right, the two beams in the 210’ direction has two spans, 120’ plus 90’ and in the middle there are two column, one for each beam. The two beams will be cast monolithically with the column support.

Preliminary FEM analysis indicates that the beams in the 210’ direction take about the 1/2 to 1/3 (depending on the short beam location) of the moments of the beams in the 90’ direction. Therefore the beams in the 210’ direction contribute significantly. Besides, the panel ratio 120’:90’ qualifies the slab as two-way slab.

Do you ever (or heard from someone) take creep, shrinkage factors into your PT design?

Anyone has recommendations regarding to the vibration issue for long span concrete?

Thanks!

 

[csd72]

Creep, shrinkage, loss of prestress, e.t.c. all have to be taken into account.

http://vibration.shef.ac.uk/pubs/jou_2002.html

 

[rapt]

CoreyGuo,

Answering in order,

1 I suggested using specialist FEM analysis programs which at least allow you to model grillages of beams properly. Some of these can also model creep but not cracking and creep and shrinkage effects for deflections. At least the stiffness models from these programs will be more correct than you will get from the design FEM programs that only have plate/shell elements (again unless they have added more recently that I do not know about). Agreed you will not get the effects of cracking or long term effects. But, after doing the design, you could rerun the analysis with reduced stiffness on these members to try to match the total long term deflection from the design if you want to check the variation on the reactions from the long term effects.

2 No, I would use a T beam with the effective flange width but I would assume the full PT from the beam tendons is contained within that width.

3 It depends on the load condition and the age of the concrete. At the time of stressing with basically no shrinkage and balanced load similar to the dead load, yes the axial prestress will dissipate over the full width. If you are doing partial prestress design, then at the supports the prestress will be in the web under service loads and at ultimate so no dissipation after the flange cracks. At midspan, it will dissipate over the effective flange width under all of these situations. Under long term effects, over the full length there would be little or no dissipation to the slabs.

As per 2, I assume dissipation over the width of the effectiove flange, no further. I and many others have used this approach over the last 33 years in my experience and before my time also. This is the standard approach used for design in most parts of the world for PT members. Some PT programs that assume dissipation over the full width only do so for the service stresses. Ultimate strength logic is putting the full prestress force in the effective flange anyway.

Some people suggest that FEM proves the full dissipation but as I mentioned in earlier posts, this would only apply if concrete were an elastic homogeneous material. It is not, it cracks, creeps and shrinks and these properties vary with concrete shape.

With the size of beams you are going to need for this project, I would expect no dissipation past the effective flange.

4 RAPT allows for cracking and does a creep and shrinkage analysis for deflection calculations allowing for concrete properties, reinforcement and prestress and short term and permanent load conditions. Similar to the method prescribed in Part 2 of BS8110. All of its section calculations are by strain compatibility (except for unbonded PT tendons) and allow for variable concrete properties as well as cracking and normal stress/strain relationships for concrete and steel (no rectangular stress blocks for concrete).

For any further discussion on this that is not of interest to or relevant to list members can be done direct to me via email. My email address is available on the

http://www.raptsoftware.com

website.