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Yield Line Vs, Strip method for RC slab analysis

Yield Line Vs, Strip method for RC slab analysis

Yield Line Vs, Strip method for RC slab analysis

(OP)
Gretings!
Im interested if someone could give me some insight on these two methods and how they compare to each other.
Im aware of FEM power when analyzing slab structures but when a calculation by hand is required wich one of these methods would you use and why? Wich are pros and cons, and also how they compare to elastic methods like FEM?
Some book recomendations, articles...
Many thanx!
 

RE: Yield Line Vs, Strip method for RC slab analysis

heya,
Usually strip method is being used for more regular and rectilinear kind of grids as the slab structutal layout.But, Yield Line method is used in more complex and rigorous layout with different boundary condiditions, such as triangular, circular, etc.
It is up to engineering judgment to predict the true failure mode of the plate which helps alot to setup a realistic set of calculations.
"Practical Yeild line Design" can help you alot to understand the philosophy behind this method:
http://www.concretecentre.com/PDF/PYLD240603a.pdf

cheers,
Sam

RE: Yield Line Vs, Strip method for RC slab analysis

An EXTREMELY important distinction, is that yield line is an "upper bound" solution, meaning you are inherently unconservative. That is to say, no matter what capacity you come up with, the real capacity is actually less than that. So it requires experience to postulate realistic failure lines. You really need to investigate all possible failure mechanisms.

Strip method is a "lower bound" method meaning that you are ALWAYS conservative. That is, if you postulate a certain load path and your steel is sufficient to withstand those loads, the slab will not fail. Note: this does not have anything to do with deflections. So with the strip method, you may get a slab that is perfectly safe but way too flexible or that has way too many cracks.

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
Ok
I read what you guys said, also SamETABS I looked at the book before posting here.
Seem that Ill start with Strip method, couse that method will give you moment distribution across the slab wich you can use and arrange reinforcement details.
Also it gives you egsact amount of load thats transfered to the beams wich you can use for designing beams later on.
And it also an "lower-bound" solution!

If I understand corectly these are all plastic method of analyzing slabs, correct?
FEM is an elastic method, correct, wich looks at the slab when the first crack appear opposite to plastic methods wich look at the slab when complete collaps happens.
Did I get this right?

RE: Yield Line Vs, Strip method for RC slab analysis

FEM is an elastic method but also it includes torsional moments (google Wood Armer). Some FEM programs can distribute these to design moments. The strip method (Hillerborg) explicitly sets these torsional moments to zero.

The strip method is more of a design method whereas the yield line method is more of an analysis method; i.e. pick a reinforcement pattern and find the collapse load.

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
sdz, thanx for the input!
I always thought that torsion basicly magnifies bending moments Mx and My in a plate member?! Is this statement correct?

Since the torsion moments are ignored in Strip and in Yield method, shouldnt both methods then be in the "upper bound" territory since theys will give you smaller bending moment values?
One thing more, I notice many FEM programs offer you to choose Poisson ratio number of concrete. Sincee FEM is elastic it should be 0.2.
But why not put it to 0 since it correspondes to the colapse moment?
Thank you

RE: Yield Line Vs, Strip method for RC slab analysis

Yield line is an upper bound method because there is always a possibility that a more critical pattern exists than the one assumed.

In a real slab the load is carried in bending Mx, My, and also in Torsion Mxy. If the torsion moment is "relaxed" and distributed to Mx and My these moments will increase. The strip method is a way of finding an acceptable pattern of Mx and My moments with Mxy set to zero. That's built into the method. The Mx and My pattern may not be the same as the pattern arising from an elastic analysis, nor might it be the most efficient, but it will be capable of carrying the applyed load. In practice the designer should aim for a pattern that is not too disimilar to the elastic moment distribution.

Does that help?

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
Ok. I understand that these are the plastic method of analyzing, meaning that you look at the constructon at its faliure.
In our egsample, the formation of  plastic hinges wich then turns structure to a mechanism.
If plastic methods are used for analyzing, one must be very carefull and ansure high ductility and rotational capacity of cross section wich is achived by limiting the neutral axsis depth.
Elastic methods look at the structure to the moment when the first cracks appear. In slab case there are bending moments and torsional moments wich have to be find.
From you answers theis is easiest achived by using FEM programs wich I also use.
But how to obtain valid results without using computer programs, when you dont have computer in front of you, and when you dont have those tables of coefficents wich you use to get bending moments in a plate?
I only see solution using strip method or yield line method, and these methods neglect torsional moments!
This might sound stupid, but is this dangerous?
These methods have been used for lot of years and the structures are stll in one piece?!
Is there maybe another way?

 

RE: Yield Line Vs, Strip method for RC slab analysis

I recently posted a question where I perform a computer analysis by reducing the torsional stiffness (J) of my concrete elements so I will only get answers that are either Mxx or Myy (Mxy~=0). So I don't think it is dangerous to ignore torsional moments as long as they have been redistributed to orthogonal bending moments.

RE: Yield Line Vs, Strip method for RC slab analysis

asixth, you are correct.

This is the reason the strip method can be used.  If you look at the differential equation for plate bending, (crudely) it is something like this:

Mxx + Myy + Mxy = q

where q is the applied load.  The equation essentially says your applied force has to be resisted by a combination of your internal moments.  

If you set Mxy equal to zero, this means Mxx and Myy have to carry the difference, but the differential equation is still satisfied, and everything is in equilibrium.  As a side note: If you wanted to treat this as a one-way slab (ie beam) you could set Myy and Mxy equal to zero and just design for Mxx.  You would need a lot of steel for the Mxx moments, and the slab would crack significantly in the Y direction, but eventually everything would redistribute and be carried by the Mxx steel.  

The only upside to designing for Mxy is to reduce cracking at the corners. When designing for Mxy you will be able to provide the proper amount of reinforcement at the corners to reduce torsional cracking.  ACI 318 addresses this though by making the designer add a certain amount of corner reinforcement in the slab.  

RE: Yield Line Vs, Strip method for RC slab analysis

I agree with asixth and NS4U that Mxx and Myy are all you need to ensure that a flat slab is designed adequately, but I don't agree with NS4U that you can design a flat slab as a one way slab.  It will not necessarily redistribute enough in the other direction to prevent collapse.  Depends on dimensions.

RE: Yield Line Vs, Strip method for RC slab analysis

do the math... i have...

Is it the proper thing to do? No.

Is is a positive load path (provided enough reinforcement is sufficient)? Yes.

Will there be a lot of deflection/cracks? Yes.

Will it fail under the designed load? No.  

RE: Yield Line Vs, Strip method for RC slab analysis

Well, if there is enough reinforcement in the secondary direction, it is a two way slab.  The slab determines how it bends, not the designer.

RE: Yield Line Vs, Strip method for RC slab analysis

I disagree, the slab will initially want to bend as it naturally would (via Mxx, Myy and Mxy).  if the slab doesn't have the ability to generate an internal Myy (ie no secondary reinforcement) the slab will eventually behave as a one way slab.

This is the heart of yield line theory: as long as the designer provides a positive load path the structure will not fail.  Thus, if you provided only Mxx reinforcement the slab will not fail.

Don't get me wrong I 100% disagree with only providing reinforcement in one direction for slab that is clearly two-way.  I was merely trying to show an example.


my point is that if there's no secondary reinforcement it a stable one-way slab and will not fail.
 

RE: Yield Line Vs, Strip method for RC slab analysis

You are correct within limits, but try that philosophy with a slab where the column spacing in the y direction is 4 times the spacing in the x direction.  That is what I mean by it depends on the dimensions.  

RE: Yield Line Vs, Strip method for RC slab analysis

NS4U & hokie66,
NS4U is correct for a slab supported on fours sides. For a slab supported on columns you can't eliminate the moment in one direction by increasing reinforcement in the other.  

RE: Yield Line Vs, Strip method for RC slab analysis

sdz,

To a degree you can redistribute the reinforcement in a slab supported on columns.  After cracking, the moments will chase the reinforcement.  

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
Guys Im sorry but I was wrong in my earlier statements.
Torsional moments in a 2 way slab decrease bending moments in x and y direction!
Thats why the bending moments in x dirction for a simply suported slab are not ql2/16 and in y direction gl2/16. They are smaller,something around ql2/27 in one and in other direction.
What torsion moment do is to change direction of main bending moments, and because of that are not orthogonal like in x and y direction but are rather inclined and directed diagonaly to the slab.
Main moments also change sign convenion from positve to negative at corners if the uplift of the slab is prevented, so you have to provide "torsional" reinforcement at the corners

RE: Yield Line Vs, Strip method for RC slab analysis

Mx=q*Lx^2/16
My=q*Ly^2/16

If the slab is simply supported on 4 sides and Lx=Ly.

I don't have access to my concrete code at the moment but I do remember a clause that talks about torsional moment and the corners and negative moment as the slab wants to lift at the corners. I will have to look further into it before I can comment.

 

RE: Yield Line Vs, Strip method for RC slab analysis

hokie, point taken.  I was thinking of a slab supported on four sides.

You are correct, if it's on columns its a totally different ball game

RE: Yield Line Vs, Strip method for RC slab analysis

You can ignore torsion for the slab design itself through using strip or yield line method, but I am not sure that it is always safe to ignore the transfer of torsion from a slab system to the supporting vertical elements.

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
"Mx=q*Lx^2/16
My=q*Ly^2/16
If the slab is simply supported on 4 sides and Lx=Ly."

Is valid if the slab is not restarined against uplifting e.g. if there are no beams under the slab edges!

If there are beams under the slab edges, beams will have its torsional stifness wich will couse negative bending moments in the corners of the slab.
Uplifting is prvented, torsion is present in the slab, bending moments reduce in both direction, but negative momets appear at the corners where the torsion is at max.

RE: Yield Line Vs, Strip method for RC slab analysis

mar2805,

I agree. The beams will go into torsion causing negative bending moment in the slab at the supports.

What are the dimensions of the edge beams and how have you calcuated the torsional stiffness.

RE: Yield Line Vs, Strip method for RC slab analysis

(OP)
Thats a good question and more importantly how to calculate value of negative bending moments (due the torsion) that appear at the corners?

...I think yield line method has offered an solution to negative moments at the corners (negative yield line), but dont know if elastic methods have somekind of formula for this...also dont know if strip method can calculate these moments due torsion.
 

RE: Yield Line Vs, Strip method for RC slab analysis


Hokie66,Thanks for sorting out the NS4U's problem. I only just returned from a training trip plus holidays and have not been checking Engtips. You are definitely correct with flat slabs as distinct from 2way slabs (British definition Flat slab -slab system supported on columns 2way slab - slab system with continuous supports in 2 directions.).

RE Mxy moments, they cannot be ignored in design. They are not Torsion as is defined as compatibility torsion, they, combined with the Mxx and Myy moments on an element, are required to define moment condition on an element when using Orthoginal moments. If you design on principal moments, Mxy is zero but you cannot reinforce based on principal moments as their angle is different for every element. For design for flat slabs, Mxy must be combined with Mxx and Myy in the 2 design directions using Wood Ahmer or similar to get proper design moments. FEM design programs that ignore Mxy in design are definitely wrong and significantly unconservative.
I do not think that setting torsional constant to 0 or a low value is correct either. if you are going to do an FEM analysis you should do it, not fudge it into something meaningless, but then you need to design for all of the effects from it.
When Mxy moments are included, the design moments from FEM are the same as from strip analysis.

Elastic Analysis:
Strip methods should be used logically to model as close as possible to the actual elastic action of the slab, as should Yield Line if you want reasonable performance for crack control and deflections. Otherwise as stated by someone above, you will get large cracks and larger than expected deflections.

The same is true for FEM analysis and design. One problem with FEM is that some people are basivally doing a Yield Line reinforcing layout based on an FEM analysis (eg PT flat slabs based on banded/distributed average designs). This is not logical. You cannot base a Yield Line solution on an FEM analysis.

RE Deflections:
You can get very good estimates of long term deflections from strip analysis/design if you reinforce to the elastic moment pattern for the slab and allow for the transverse distributions of moments. Much better than most FEM programs give if you use RAPT to do it, but you have to understand what you are doing.

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