Slab On Grade in ETABS.

First let's know what an SOG is. The full form is Slab on Grade/Ground. One use for it to create an equal level for construction. Imagine a large area foundation with minimal area at a lower level. It is easier to provide reinforcement in a single plane; hence the lower level can be raised by filling it with soil or some other substances. Then it acts as one level foundation.

I came across a scenario where I had to model an elliptical tank like structure, no columns in between. It was to be filled with soil. As you can see, I have attached an image, the slab span is quite large in between.

The plan of the model. Imagine an ellipse with R1 = 37 m and R2 = 65 m.

Now if you run the model as a normal slab, which it kinda is, one can easily guess the response. You can guess with experience that is, or a different case if you are a genius.

I will tell you how the response would look like if you run it as a normal slab. You would get lots of local modes (I am assuming you know what local modes are). Interestingly that would be the first mode too. And there's nothing wrong with the model response. It's just how it would react given the conditions. As you might have heard: Garbage In, Garbage Out. 

Modal Response

Mode 1

From above, one can easily deduce it's not the desired response. It has local modes all throughout its mode, till 21st mode. The 90% contribution is by the 23rd mode. Total number of modes is 24. The model didn't even run on p-delta. Now that isn't going to work, is it?

Don't fret. I am writing this blog to explain how I dealt with it. 

Understand first, what an SOG is. It's more like a mat or a raft than a slab. It has fillings below it unlike slabs which are suspended. So, it's only accurate to model it that way. And it structural terms, soil are taken as springs with certain stiffness which are computed by the Geotech guys. In SAFE, its subgrade modulus and in ETABS, it is defined as Area Springs. 

{In my experience, subgrade modulus is a better representative than the area springs. But that's ME with only around 3 months of experience in foundation design. This could be a topic for another blog.}

So, the initial error was sorted out. The SOG I modelled was simply too flexible. It had to be stiffened. Stiffness can be defined as the ability to resist deflection. 
One way to increase stiffness is by increasing the dimensions of an element. But that sure won't work here as you might have figured out by now. If it's already deflecting as much on 250mm, why would it deflect any less for 300mm or 500mm given the specific model. 
Thus, we go to the spring functions. And I definitely argue it's the better option. We are stiffening it by resisting the deflection, assuming there's a layer to stop the deflection.

At first, I used a stiffness of 1000 kN/m/m^2. It didn't help much with the response. It was not stiff enough. Then I went for 3500 kN/m/m^2. Gave a better response.

For 3500 kN/m/m^2;

Modal response.

Mode 1

Even this is not really convincing. The first mode is still local. But if you look closely at the mass ratios, one will notice the shift in the contribution. Now the summation of 14th mode contributes more than 90%. And that's how my iterations started.
Eventually I tried 7000 kN/m/m^2, 10000 kN/m/m^2 and finally 15000 kN/m/m^2.

For 10000 kN/m/m^2;

Modal Response

Mode 1


Mode 2

Mode 3
It was with 10000 kN/m/m^2 that I got the desired response. You know, the one where the first two modes should contribute more the 90% of the modal response. 

For 15000 kN/m/m^2; 

Modal Response

Mode 3.


If you increase it to 15000 kN/m/m^2, you even get the third mode as the torsional movement. Recommended as per IS 456. The third mode has RZ contribution of around 87%.

I can't tell you how I came with the magnitude, it was just trial and error and it worked for me. 
Please do note that the above area stiffness has nothing to do with the Geotechnical aspect, it was ME simply trying to stiffen my model. I can argue one doesn't need Geotech input as it is not actually a foundation.

Note: You can definitely share your approach of modelling SOG if it's different than this. And how you calculated the area stiffness if you used this approach.

Comments

Post a Comment

Popular posts from this blog

Ritz and Eigen.

Image
Ritz, not Rizz and Eigen Vector are two ways of solving a Modal Analysis problem. It is what ETABS use while doing the Modal Analysis. Today's blog will be about the difference between these two. EIGEN-VECTOR : It determines the undamped free-vibration mode shapes and frequencies of the system. What free-vibration means in our term is that there is no external loads acting on it for any period of time, just the initial conditions. The idea of bending a ruler and allowing it to reverberate. The natural modes obtained through this provide an excellent insight into the behaviour of the structure.  But remember, it's the free-vibration response while the structures will be under various different loads. What should be done then? Here comes the Ritz Vector. RITZ-VECTOR : Research has indicated that the natural free-vibration mode shapes are not the best basis for a mode-superposition analysis of structures subjected to dynamic loading : Wilson, Yuan and Dickens, 1982. I stole this l...
Read more

Modifiers.

Image
This is one of the coolest concepts I have properly learnt at my job. I do know I will learn lot more on this. It's the Stiffness Modifiers.  It is a modification factor that is generally used in the properties of cross-section such as Moment of Inertia, Shear Area, Torsional Constant etc. It can also be used for Mass and Weight as per requirement. Modifiers for a typical Beam. Now why is it used? As the loads act on the structure, it will tend to generate cracks on the tension zone. Thus, reducing the area of cross section and stiffness of the member. 1 means the structure would take all of the loads, while 0 won't be taking any. It is kind of a paradox; the structure would resist all the loads if it is not cracked, and we know it will crack. In other way, we want the structure to not take the load as it will eventually crack. Concrete is weak in Tension. As per codes, IS Code ACI Code Now I have two great examples for putting my case. One is related to a torsion modifier I st...
Read more