Live Load Reduction & Influence Area

[KimWT]

Hi!

When I tried to apply live load reduction, I was not sure I understood KLL (Live Load Element Factor) correctly.
It is not clear how exterior columns called as (2), edge columns (3) and corner columns (4) are defined.
[I attached respective conditions with (1) to (5).]
How much slab should be projecting beyond column when it is called cantilevered?

Can I say C1/C4/C9 belongs to corner columns (4), C10/C11/C12 to exterior columns (2), and C2/C3/C5 to edge columns (3)?
If this is true, C9 has KLL*AT=2*26*15-780SF while its influence area is 36*30=1080SF.
This means KLL*AT and AI (influence area) can be different.
Why does ASCE7 use KLL*AT instead of influence area?

 

[steele6707]

The attached sketch is from ASCE 7-05. This may help you. I believe this to still be accurate.

 

[KootK]

Why does ASCE7 use KLL*AT instead of influence area?

I do not know. I think that this is handled terribly in ASCE7 and feel that it's best to toss out K_LL altogether and, instead, handle it like this:

1) IA = Influence Area = K_LL x AT. And we shall mention K_LL x AT no more. Well, until the end.

2) For now, consider only a system in which there is no continuity other than at the cantilevers. Replace your slab by an analogous steel beam layout.

3) IA = the sum of every square foot over which you could place some load and have some fraction of it make it's way to the column under consideration. One consequence of this is that all of your cantilever load will count towards IA at the adjacent columns.

4) This gets a bit muddier once slab continuity is considered since, in theory, one could place load anywhere on the floor plate and it would have some impact on the column being considered. In the interest of simplicity and rationality, I believe that most engineers simply treat continuous slabs similar to non-continuous framing systems. It's not perfect but, then, what the hell is.

5) If your effective K_LL is not 2, 3, 4, or even a damn whole number, lose no sleep at all over that. Rest easy in the knowledge that you actually understand what's going on rather that having followed some oversimplified code equation.

 

[OldBldgGuy]

That's why this guy advises God...

 

[JoshPlumSE]

My guess is ASCE does that just because it's so much easier to define tributary area than influence area. Nothing more complicated than that.

In reality, they're really just telling you to use a simplified version of the influence area. That way we don't have to worry about all the little areas that might influence a column just a tiny bit; areas where we have multi-span continuity, or areas where the framing might get weird and influence area might be hard to compute.