Moment to edge column

As per ACI Direct Design Method, the moment on the exterior column is given as a fraction of the total (factored) static moment on the panel - total load on the panel * clear span / 8. For slabs without edge beam, it is given as 0.26 * total static moment. After distributing this moment in proportion to the stiffnesses of the columns above and below, the moment may be combined with the factored axial load for design of the exterior column. You may also search posts on this forum or refer to text book on design of concrete structures for limitations and applicability of simplified design methods.

I find that, for a single storey building, the edge columns need slightly more reinforcement than the internal columns carrying half the load, if the same column sections are used.

Does this sound correct? If however it is a multistorey building, the moment get shared by the column above and below, and basically halved. So edge columns in a single storey building attract a bending moment almost twice as much as an equivalent loaded multi storey building edge column.

Just seems odd that sometimes an edge column needs more rebar than in internal one.

Is the slab and columns forming your lateral force resisting system? Or do you have some shear walls somewhere resisting your lateral loads? Either way I'd urge you to stop assuming that slab/beam joints at columns in cast-in-place concrete are hinged/pinned. It will give you a slightly conservative positive flexural moment in the span of the column strip, but it is erroneous to assume that there isn't flexural continuity into your columns. The way I see it you have three possible paths forward:

-Your slab and columns are your LFRS. You need to perform an indeterminate frame analysis using your column strips. You can simplify that down to a 2D beam-element analysis for each column line.
-You have a separate LFRS AND your slab system and building parameters will conform to the Direct Design Method requirements. No need for a frame analysis. See DST148's post.
-You have a separate LFRS and your slab system/building parameters don't conform to the Direct Design Method. You need to perform an indeterminate frame analysis, again, simplified down to 2D beam-elements for each column line.

theonlynamenottaken,
There is nothing wrong with sybie99's approach, and she isn't assuming no continuity, she is just wanting some guidance on how much. Hers is a tried and true method, and as long as she provides adequate top reinforcement at the exterior and allows for the moment in the column, the design will be satisfactory. She said it is a "simple flat slab", so I think that rules out the slab being part of a moment frame.

Yes - many times edge and corner columns require more reinforcement than interior columns due to applied moments.

Per the Direct Design Method edge column strips in flat plate slabs must be designed for 0.26Mo. In addition, enough of the slab reinforcement needs to be concentrated around the column to meet Section 13.6.3.6 ('08 code) for transferring the unbalanced moment by flexure.

With regard to the moment in the column, the PCA notes say: "At exterior column or wall supports, the total exterior negative factored moment from the slab system is transferred directly to the supporting member." So the column must resist 0.26Mo as well.

If you don't want moment in the edge column the Direct Design Method is off the table.

What is being missed so far in this discussion is punching shear. If the end column will attract a certain moment, punching hsear must be designed for that moment. You cannot make arbitrary redistributions from columns in the case pf punching shear design.

Until the column cracks, it will attract a moment relative to its full uncracked stiffness. So the absolute minimum moment the end column must be designed for is its cracking moment (considering also axial force effects) if it can attract that moment. If it cannot attract the cracking moment, then it must be designed for the full moment it will attract.

Once the moment is greater than the cracking moment, the stiffness of the end column will reduce. But the reduction will not be 95 or 100% as some assume. The moment of inertian of a minimum reinforced section with no axial forces is about 25 - 30% of the full stiffness. generaly it will be closer to 50-60% of full stiffness. So it should not be reduced to less then this.

but, remember also that the slab is cracking and also has reduced stiffenss 9depending on RC/PT). if it is an RC slab and it has a normal level of cracking, its stiffness will also be reduced to in the order of 25-50% of full stiffness. With no axial forces and a much lower minimum reinforcement than the columns, 25% is possible.

So if both the slab and column are cracked, the stiffness of both should be reduced. So simply design for full stiffness in most cases and you will be close to correct. that is why codes says to use full stiffness!

Unless of course you provide a properly detailed pin connection at the ends of the columns. i still do not believe this to be possible. So, my logic in most cases would be full stiffness and design the column for the moment ot will attract. Unless you can justify otherwise using my logic from above. And this would only ever be possible with a PT slab designed to be uncracked.

rapt is certainly correct in all respects. Back to the OP's question, she is asking about a flat slab on a 10m x 10m grid. I wouldn't do a flat slab with column spacings that great. Banded slabs or, if a flat slab is a requirement, at least spandrel beams should be considered in conjuntion. The edge beams take away most of the moment induced punching shear problems.

I"m confused. Hokie66 said in his first post above that "hers is a tried and true method", yet agrees that rapt's post is correct, in which he/she recommends using the stiffness of the column - i.e. an indeterminate frame analysis. My understanding of ACI 318 Chapter 8 (in the U.S.) is that you have to account for "the relative stiffnesses and conditions of restraint" (8.84) and to design "for the maximum effects of factored loads as determined by the theory of elastic analysis" (8.3.1). I thought the only way around an indeterminate frame analysis was to have a layout/design that conformed to the requirements for approximate analysis (one-way slabs/beams by 8.3.3) or to the requirements of the Direct Design Method (two-way slabs 13.6). Is there a way that is ok by the code to design a cast-in-place slab or beam system and assume it's simply supported?

In my first post, I was referring only to the flexural design of the slab with a pin at the edge support. For the moment to be taken by the column, and for punching shear in the slab, another assessment is required, and as rapt pointed out, it requires judgment in addition to experience with code provisions.