Yield Line Vs, Strip method for RC slab analysis 1

[mar2805]

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!

 

[SamETABS]

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

 

[frv]

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.

 

[mar2805]

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?

 

[sdz]

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.

 

[mar2805]

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

 

[sdz]

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?

 

[mar2805]

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?

 

[asixth]

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.

 

[NS4U]

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.

 

[hokie66]

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.

 

[NS4U]

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.

 

[hokie66]

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.

 

[NS4U]

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.

 

[hokie66]

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.

 

[sdz]

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.

 

[hokie66]

sdz,

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

 

[mar2805]

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

 

[asixth]

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.

 

[NS4U]

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