Slab stiffness for lateral load analysis? 7

[PSR_1]

There is this argument around where I work which goes ' since post tensioned slabs don't crack during service loads, slab stiffness for lateral load computation can go as high as 0.5(eurocode, although it doesn't say for slabs) times the gross stiffness'. I amn't convinced with this statement as the contribution of the slab stiffness for lateral load resistance might demand special detailing. For RC slabs a value close to zero is usually used and am okay with that. But, I want to know your thoughts and practice regarding post tensioned slabs.

 

[hardbutmild]

It makes sense that some increase of the stiffness occurs due to post tensioning, but does it matter? Eurocode 8 states two things, a) - slab frame action should not be considered as a lateral resisting system and b) - any element can be called a secondary seismic element as long as the total stiffness hasn't changed by more than 15% when you remove all the secondary elements. Does the bending stiffness of your slab influence the lateral stiffness by more than 15%? I think that it should not, but you know your structure better. If it doesn't just proclaim it secondary seismic element and it only needs to "go for a ride" with the other elements. Of course, in plane stiffness is high, right?

 

[PSR_1]

Hardbutmild thanks, I am supposed to design the slab and so its upto me to recommend the stiffness modifiers for the lateral load resisting system designing guys and they say the modifier used for slabs is affecting the system critically . What I suggested was to use 15% and you have already mentioned in your post why 15% is my number and I got it from Michael N. Fardis book on seismic design based on EC.yet they demand more from PT slabs than what is suggested for RC once.

And yes, rigid diaphragm assumption is used.

 

[hardbutmild]

Yeah, in EN 1998-1 4.3.1 (7) "Unless a more accurate analysis of the cracked elements is performed, the elastic flexural and shear stiffness properties of concrete and masonry elements may be taken to be equal to one-half of the corresponding stiffness of the uncracked elements."
Since it says concrete, I guess it's equally applicable to reinforced and prestressed concrete. The only difference would be that PT would have a larger initial stiffness. Theoretically, you could calculate the cracking at quasipermanent load combination. This depends on the software you use and what output does it provide. I've never actually done it for a prestressed plate, but I don't see why it should differ. If you have strains at top and bottom, you can calculate the depth of compressive area from which you can calculate the stiffness, it just takes a bit of tinkering and a lot of calculation, but it's pretty basic. You could do this for each section, or you could divide the plate in part you find appropriate. I don't know, maybe your program can do the nonlinear anaylsis, or you might need to do this "by hand" using excel and modifying stiffness step by step. A lot of work, but shouldn't be to complex.

I know it's not an exact method, but given our lack of knowledge in regard to: level of actual vertical load during an earthquake, actual MoE (both the variation of inital value and its deterioration in time), the fact that the EI changes during an earthquake and depends on detailing, the fact that even when detailing is known, it's impossible to predict the stiffness degradation of the joint and a lot, lot more, I think this is good enough.
EDIT: Actually, now that I think about it, at quasipermanent, (if I remember correctly) you should have no tensile stresses, at least if you design it the right way. If a larger load comes, it'll crack a section, when it reduces back to quasipermanent, those cracks will close. The only question remains will this reduce any stiffness? I can't figure it out. So it's either full stiffness or some slightly reduced value in reality.
Another question is what is your main lateral resisting system? According to EN 1998-1 5.1.1 (2) "Concrete buildings with flat slab frames used as primary seismic elements in accordance with 4.2.2 are not fully covered by this section" plate frame action is not considered. You could use it, but the code gives no provisions because (I think) this system is not tested enough and no reliable directions could be given (I think that in US there are some provisions).
It seems to me that flat slab frames with pretensioned slabs would be a nightmare to detail (maybe someone who's done it can say) and I doubt that any other mechanisms than a soft sotrey one could develop (might be wrong, just a feeling).

 

[PSR_1]

In order to satisfy damage limitation requirement of EC number of shear walls around the perimeter of the building has been placed and it is the designers belief that this shear walls would limit the expected drift of the building well below certain limit that the column slab junction wouldn't be expected to transfer large amount of moment, hence resolving punching issues during design or frequent seismic event.

 

[KootK]

Firstly, keep in mind that it is interstory drift, rather than absolute drift, that will matter the most in this.

The truthiness of the designer's assertion will depend on the height of the building and the character of its lateral deformation. In a shorter building, where the shear deformation drift approximation may hold true, beefy walls may well shield the slab/column joints as the designer suggests. However, owing to hybrid frame interaction effects, the walls may actually exacerbate the deformation demands on the slab column joints at the uppermost floors.

 

[r13]

KtooK,

Your assertion is valid for the effect of the shear wall, but I think they are quarreling the stiffness of the slab - more rigid (the designer) vs less rigid (the OP). I could be wrong though.

 

[KootK]

The slab stiffness is the primary issue but, per efr's last post, the interplay between the slab stiffness and the shear walls is also at issue. Will the shear walls shield the slab-column joints from excessive cracking or wont they? That's what informed my post.

 

[slickdeals]

The above information is from ACI 318-11. When they reworked the code in 2014, this part got lost in the shuffle. There is also some good information in ACI 318-11 Section 8.8.

For wind-controlled building, ignoring the slab stiffness and designing the shear walls to carry all the load without any frame action is a conservative assumption. Adding slab flexural stiffness improves overall building stiffness and reduces the building's dynamic response to wind. The contrary is true for seismic analysis, where a stiffer building has a higher base shear. Cracking a slab completely will make a building more flexible.

Your analysis shouldn't necessarily be dictated by what produces the least amount of reinforcement. It's about using assumptions that are consistent throughout the design process.
There may be scenarios where a column is near a shear core and that column will have a lot moment due to the slab coupling. Ignoring the slab stiffness there could lead to an issue with punching shear.

This is unfortunately a gray area in the American codes (and perhaps worldwide) and leaves a lot for the engineer to decipher.

 

[r13]

Very good reference and explanation.

 

[HTURKAK]

A strange topic. I am familiar with EC -8 bu i did not think till i read this thread. Below , copy and paste of some paragraphs of EC -8 EN 1998-1:2004 related with this topic;

5.1.1 (2)P Concrete buildings with flat slab frames used as primary seismic elements in accordance with 4.2.2 are not fully covered by this section.

5.2.1 Energy dissipation capacity and ductility classes (1)P The design of earthquake resistant concrete buildings shall provide the structure with an adequate capacity to dissipate energy without substantial reduction of its overall resistance against horizontal and vertical loading. To this end, the requirements and criteria of Section 2 apply

(2)P Concrete buildings may alternatively be designed for low dissipation capacity and low ductility, by applying only the rules of EN 1992-1-1:2004 for the seismic design situation, and neglecting the specific provisions given in this section, provided
the requirements set forth in 5.3 are met. For buildings which are not base-isolated (see Section 10), design with this alternative, termed ductility class L (low), is recommended only in low seismicity cases (see 3.2.1(4)).

5.3 Design to EN 1992-1-1
5.3.1 General
(1) Seismic design for low ductility (ductility class L), following EN 1992-1-1:2004 without any additional requirements other than those of 5.3.2, is recommended only for low seismicity cases (see 3.2.1(4)).

5.3.3 Behaviour factor
(1) A behaviour factor q of up to 1,5 may be used in deriving the seismic actions,regardless of the structural system and the regularity in elevation.

As far as I understand, according to Section 5 concrete buildings may include flat slabs or prestressed concrete beams,but these elements and columns connected to them shall be designed as secondary seismic elements.
In case of low-seismicity regions , concrete buildings with flat slabs or prestressed concrete beams may be designed considering all elements as primary seismic ones but for almost fully elastic response under the design seismic action, i.e. for Ductility Class Low (DCL) and a value of the behaviour factor q of not more than 1.5.

Another issue is the values of viscous damping. The spectra is in general prepared for 5% damping . This figure is O.K. for R.C. (which is 5.0–8.0 % for fully cracked R.C. ). However, damping is around 0.5% for Prestressed uncracked concrete .

One can say ; with q=1.5 and with spectra for 0.5% damping, and keeping the structure fully elastic, concrete buildings with flat slabs will not be feasible even for low seismic regions.

 

[rapt]

"since post tensioned slabs don't crack during service loads"

That is a rather broad statement. Many PT slabs crack under service loads, especially the "column strip " area near the column, which is the area that provides the stiffness.

 

[captain_slow]

Concrete tensioning does not really stiffen the slabs - it just changes the behaviour of the concrete section through introduction of an axial component. The fact that the end deflection is smaller is due to the effective uplift from PT, not due to increased slab stiffness. You could almost say that the slab is "effectively" stiffer, but not really.

In my experience relying on frame action from the slab is just poor practice that you never want to rely on from the onset. If you do choose to do something like this you have to (at the very least):

1. Design the slab for the additional moments.
2. Detail the slab-column (or slab-wall) connections to transfer the moment action from lateral loads.

These two things above are quite unusual and will attract questions from the independent reviewer; I would certainly ask questions. The unexpected upside of such approach is that your slab now has fixed connections and so should deflect slightly less...


@rapt - you are completely right; even properly designed PT members may experience hairline cracking in service because the PT is only ever meant to zero-out the self-weight.

 

[hardbutmild]

you are completely right; even properly designed PT members may experience hairline cracking in service because the PT is only ever meant to zero-out the self-weight.

It depends, as rapt said, it's a rather broad statement. I believe that in eurocode it zeroes-out the self-weight + 30% of characteristic service load, but you can still prestress it to a lower or higher level, no one is stopping you. That's (DL + 0,3LL) also what you design seismic for, so it's a valid question. I'd agree that cracking will occur, but it's rather hard to determine the proper stiffness because it will be larger than for RC (it doesn't matter if you call it real or effective stiffness increase, a less cracked section is a less cracked section no matter the cause).

One can say ; with q=1.5 and with spectra for 0.5% damping, and keeping the structure fully elastic, concrete buildings with flat slabs will not be feasible even for low seismic regions.

Certainly, but as I understand it, he has walls... They probably take a large chunk of the force. I'd say that 1,5 is too low a behaviour factor for such a structure that mainly relies on walls and slightly on slab frames. I also think that damping level should be defined by elements that actually dissipate the energy (I might be wrong, I've never thought about it till now) and dissipating energy in plates is a bad idea. The only question is how to keep the slab frame elastic while walls dissipate the energy.

 

[HTURKAK]

Certainly, but as I understand it, he has walls... They probably take a large chunk of the force. I'd say that 1,5 is too low a behaviour factor for such a structure that mainly relies on walls and slightly on slab frames. I also think that damping level should be defined by elements that actually dissipate the energy (I might be wrong, I've never thought about it till now) and dissipating energy in plates is a bad idea. The only question is how to keep the slab frame elastic while walls dissipate the energy.

Dear hardbutmild, if the LFRS has shear walls, the slabs and prestressed elements certainly will be secondary elements. The initial energy dissipation for LFRS should be plastic hinging at beams (coupling beams etc) connected to walls. If thread is a real question, efr (Civil/Environmental) may publish the structural plan ,and so our discussion can be more objective. In past, i designed flat slab systems for low rise buildings but , i always used drop spandrel beams all around the building.

 

[r13]

Follow this thread up to this point, I am getting quite confused as what is the I_eff to be used for a post-tensioned slab in the frame analysis, either it be 0.5Ig, or less, or no difference at all? And what is the base of your opinion. Admittedly, I didn't read all responses thoroughly.

 

[PSR_1]

Retired, the main topic is far gone.

HTURKAK,here is the picture of part of the building

 

[r13]

IMO, I don't understand/deserve the pink star, but thanks anyway, and good to know the question is resolved.

 

[hokie66]

That floor plan is designed to create cracking, whether it is prestressed or not. So use the slab as a diaphragm only, and the walls to resist the shear. Provide enough deformed bar reinforcement to limit cracking to an acceptable level.

 

[HTURKAK]

Dear efr (Civil/Environmental), i looked to the plan of the bldg that you released.
IMO , one of the concerns should be loss of prestress to the shear walls rather than the effective EI is 0.3 or 0.5 for the slab .I think , the approach of not considering the flat slab to be part of the lateral force resisting system is a must .

I will suggest, to run two cases ; one case column joints pin connected (moment released for the columns ) and the other case with column Joints moment is not released. Use behavior factor q=1 for both cases and design the elements with different q values. Use the first analysis f or shear wall and foundation design, with q=4. The second analysis,use uncracked sections and use q=1.5 for moments transfered to the PT slab and for column design use q=4.
Moreover i will suggest ;
i) provide minimum bottom steel in slab-column connection to prevent sudden collapse,
ii) discuss with PT vendor(s) to ensure post tension is not lost to shear walls
iii) some of the PT tendons shall run through the column cage in both directions ..
Good Luck...