Who among you thinks flat slab design is boring? Anyone besides myself?
I thought so too myself before. But don’t worry though, you will change your mind after this and hopefully you will be entertained like myself on this fundamental concept regarding moment transfer between column and slab. And yes you were right when you read fundamental, so you might want to overlearn this one.
Time to set that imagination again in motion.
Before, we just used pin supports to represent a column under the slab. So with this modelling approach, we can be assured that the bending moment on the other side will be equal to the bending moment on the opposite side. So this is as if we have a ball joint on the pin-supported part of the slab and the bending moments are just passing through the slab with the support doing nothing but to restrict the vertical displacement.
But this type of model is incorrect. First, because there is no such thing as an unyielding support. Second, the bending moments do not just pass through the slab to eventually balance itself. So continuing the first argument, instead of a rigid support, in reality we have a finite spring type of support provided by the column to resist the vertical displacement and the out-of-plane rotations (remember that we are only dealing with gravity forces here, that is, we don’t take into account the in-plane forces that the joint is subjected into). Not all of the bending moments in the slab pass through the joint and get redistributed to the other side. Some of these unbalanced bending moments get resisted by the columns thereby inducing rotation on the columns. This aint a bridge where you have rollers as support on one end so the ball joint model is totally incorrect!
So now let us deal with these bending moments one by one and see what we’re up against:
- Bending moments in the column. This should be properly captured using a 3D analysis model like ETABS. The good news is, if we have regularly-shaped columns on top of another, then this is almost always accounted for. Otherwise if you have, say a circular column below and an L-type column above, then you might want to make sure that the bending moments above can be sensibly passed to the column below.
- Bending moments in the slab. If you are using SAFE or ROBOT or RAM Concept or any other software capable of slab analysis, you always got this covered. Just a friendly reminder: the critical section for bending is on the face of support and not on the joint where you provided a stick model of the column!
- The unbalanced bending moment. Even if you have a kilometer of tributary width of slab for your column, only a portion of the slab is effective to transfer the unbalanced bending moment to the column. Yes, we must make sure that the slab is capable of supporting such bending moment before it can pass it to a stiffer column. You get the picture? This unbalanced moment in the slab is NOT, and I repeat, IS NOT captured by SAFE (I’m not sure for the other software out there). Hence, this is a must-do supplementary manual check.
What supplementary manual check am I referring to? for ACI318, this is under the provisions of 13.5.3.2 and for BS 8110, this is under 3.7.4.2 I will not dig into BS in my sample calculation though.
Now let’s break down the requirements of ACI318 13.5.3.2
The unbalanced bending moment is the bending moment in the column that can be derived in the analysis. Note that for equilibrium, you will not really get a zero-unbalanced bending moment in the column. We can have a negligible amount of bending moment but never a zero.
Only a percentage of the unbalanced bending moment will be resisted by the slab through bending. This is given by the factor γf, where f denotes flexure. The remaining percentage of the unbalanced bending moment will be converted as shear which is given by equation 11-37. So don’t rejoice just yet that you only have a small percentage of the unbalanced moment resisted as bending moment in the slab. Wait ‘till you see the punching shear calculations. Note also that the parameters b1 and b2 in the computation for γf are the same nomenclatures in the computation for punching shear
So the effective slab width to be considered to transfer this unbalanced bending moment is only 1.5 times the thickness of the slab or drop panel on each side of the column face.
Let’s get to my favorite part which is the manual calculation. So in the attached handcalc, we have a blade column supporting a relatively thin slab of 250mm. In the example, you can see that the effective width is reduced due to the presence of an opening. The total reinforcement of 2 layers of T12-100 for the hogging moment (negative bending moment) may seem too much when checking the design via SAFE but upon checking 13.5.3.2, we found out that the provided reinforcement is insufficient. So the reinforcement derived by the slab bending moments at the supports is not a guarantee that it can always adequately transfer the unbalanced bending moment to the column. READ: this will always require a detailed check in order to be sure.
In case you missed that manual check, you can check it below.
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Turns out, it seems that the set up where this check would be critical, is when you have, say blade columns which can resist a relatively large bending moment in its strong axis; and a relatively thin slab punctuated with openings. That’s just a personal assessment though.
Nonetheless, it will always take a detailed check to be sure.
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