Concrete Podium Design Live Load Reduction 2

[DavitBek]

Hi All

Long time follower of the forum, and first time poster, as usually I find the answer to the question I have from posts in the past

I was looking to understand the acceptable procedure for reducing the live load on a concrete podium from wooden stories above. Specifically, a 6 story mixed use structure, a two story two way concrete podium (one underground garage, one commercial above), and four wooden stories residential sitting on top of the commercial level.

I am using a two stage analysis, designing the wooden stories separately, and superimposing the loads on a concrete podium.

Using that procedure, summing the forces in four wooden stories I would have a total of 180 lb/sqft (4x40lb/sqft+20lb/sqft) sitting on the concrete podium. And specifically 160 lb/sqft floor live load.

As you likely know, the ASCE 7-10 (Chapter 4.7) prescribed live load reduction is

L=Lo(.25+15/((KLL*AT)^.5))

L=reduced live load
Lo=unreduced live load
KLL=live load element factor (KLL=1 in the case of a slab)
AT=tributary area

(Max reduction allowed is L=0.4Lo)

I'm looking to reduce this 160lb/sqft floor live load in my design of the concrete podium, as all four stories will never be packed to capacity.

Specifically, what I am not sure of is what AT value to use.

Both in my office and on the forum I've found a lot of conflicting answers ranging from using the entire footprint of the wooden stories(16,000 sqft in this case), the area between four columns supporting the slab multiplied by the number of stories (30ft*30ft*4=3,600 sqft), and the area between four columns supporting the slab (30ft*30ft=900 sqft).

Needless to say, those three values produce wildly different reduction factors

16,000 sqft: L=.37Lo=.4Lo
3,600 sqft: L=.50Lo
900 sqft: L=.75Lo

In all past projects of this nature I have used a 25% reduction to be on the safe side, however it would nice to get a firm answer to this question and to know whether I am over designing, and if I would be okay using a 40% reduction factor recommended by the owner of a company- a very experienced and respected engineer.

 

[BAretired]

AT = 30*30*4 =3600 SF would seem to be the correct interpretation of the code as that is the area of live load supported by the slab panel under consideration.

BA

 

[CURVEB]

I agree, although to add a different perspective we often use the alternate live load reduction provisions which say that A is the area of floor supported by the member. In the case of a transfer slab, that area includes the slab itself as well as the floors above that it supports. That would be the 3,600 SF option in your case, although depending on the layout you might even have a reducible live load on your transfer slab, so 5 floors would get you to 4500 sqft.

It helps to think of the slab as a transfer girder supporting a column load. The reduced live load in the column will be the load you apply to the transfer girder. It doesn't get bigger just because you go from a column to a beam.

I'm not sure how the 16,000 SF option would make ever make sense for a live load reduction. I could maybe see using the area of 4 bays instead of just 1, because in theory, you have to have all 4 bays around a column fully loaded in order to see the maximum slab moments, punching shear, etc.

 

[BAretired]

I am not current with the latest Live Load reduction formulas, but it is possible that the factor for live load on the slab itself is different than that for the residential floors above. If live load on the slab is for commercial use, the reduction may be different than noted above.

BA

 

[DavitBek]

Thank you both very much for taking the time to respond. It's much appreciated.

3600 sqft it is

 

[KootK]

I think that you can do way better than 3600 sf. And you probably should to stay competitive.

Walk with me...

1) Erase the continuous slab business from your mind and, for now, think of simple span beams running between your columns and supporting infill. We'll come back to this.

2) Abandon this ridiculous notion of Kll and At being separate variables because ASCE thinks that you're a helpless child. Instead, consider them one variable and define it like this:

A_influence = Every damn square foot that could be loaded and would result in some load winding up where you're concerned about it. Trust me... this is better. And righter.

3) Imagine your slab as simple span girders as described in #1. Infinite continuity will make your brain explode for this stuff and isn't necessary.

4) For slab flexure and one way shear, A_inf = 30' x 60' x 4 = 7,200 SF

5) For the axial component of punching shear, A_inf = 60' x 60' x4 = 14,400 SF.

All this said, there are some bearing wall layouts where it may be innapropriate to treat things as though uniformly loaded at the transfer slab level. Fectum emptor.



HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[CURVEB]

Koot - I'm not following the 60x60x4 for the influence area. For axial punching shear wouldn't it be 30x30x4 (given the bay size of 30x30)? Otherwise, I agree with your analysis.

 

[KootK]

For axial punching shear wouldn't it be 30x30x4 (given the bay size of 30x30)?

How so? We're both considering an interior column, right? If so, it seems to me that 30x30x4 is actually the tributary area rather than the influence area. I believe that the influence area would always be more than the tributary area for a column except, perhaps, if the structure somehow only had a single column. Certainly, it would seem odd to me for the column influence area to be less than that for one of the imaginary girders tying into it.

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[BAretired]

I do not agree with KootK's reasoning. Live load reductions for any structural element should be made on the basis of tributary area, not so called "influence area". It is not reasonable to assign a reduction to live load not carried by the structural element.

BA

 

[CURVEB]

Koot - for an interior column, I would think you have 4 30x30 bays, 1 at each corner of the column, like so:

 

[Celt83]

This discussion seems to have ended up based around the live load reduction at the columns, For the actual transfer slab design I would look at a bay or column/middle strip and determine the supported wood floor area. I usually end up around 0.6Lo when looking at it this way.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[slickdeals]

Agree with BA. For two-way slabs, it's the panel area of the slab under consideration. For a 30' x 30' bay, it would be 900 SF.
While you are at it, there is an "alternative approach" for live load reduction in IBC that gives a slightly better reduction value. You should look into that.

 

[KootK]

I do not agree with KootK's reasoning. Live load reductions for any structural element should be made on the basis of tributary area, not so called "influence area".

I object strongly.

Firstly, whether or not you think that live load reductions ought to be based on influence area, they most definitely are based on influence area in ASCE7. KLL x AT, the very parameter that enters into the live load reduction calculation, IS the influence area. So there's that.

Secondly, from a theoretical standpoint, I believe that it is much more rational to base live load reduction on influence area as opposed to tributary area. Live load reduction is obviously a statistical thing. The more loaded area that contributes demand to a member, the lower the likelihood that that all of those loaded areas will see their maximum load concurrently.

Since influence area, by definition, represents every square foot of area that would contribute demand to a member when loaded, it's the perfect tool for such a statistical analysis. And, by contrast, tributary area would be a more flawed tool for such a statistical analysis precisely because, on it's own, it does not reflect the total loaded area that would contribute to member demand.

It is not reasonable to assign a reduction to live load not carried by the structural element.

I believe that there is a fundamental logical error in that statement. It seems to assume that live load reduction is a probabilistic function of load. It's not. Rather, live load reduction is a probabilistic function of loaded area contributing demand. And that's a fundamentally different thing for which the influence area is the correct metric.

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[KootK]

Koot - for an interior column, I would think you have 4 30x30 bays, 1 at each corner of the column, like so:

I disagree. Let's try it another way. The sketch below is taken from ASCE7 commentary. Do you not agree that it suggests that the influence area for our case would be 4 x 60 x 60? I certainly believe that it does. And this would be entirely consistent with the KLL = 4.0 commonly used for interior columns and specified in ASCE7.

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[KootK]

Agree with BA. For two-way slabs, it's the panel area of the slab under consideration. For a 30' x 30' bay, it would be 900 SF.

I disagree. Again I think that this is to mistake tributary area as the appropriate tool for statistical, live load reduction analysis when it should rightly be influence area.

ASCE7 table 4.7-1 lumps two way slabs into the category of "other crap" with a Kll = 1.0 (trib area) unless you go and calculate KLL. I take that to simply mean that live load reduction for a two way slab is a bit complex and requires one to put their thinking cap on based on a fundamental understanding of live load reduction. So Kll = 1.0 unless you go and put your thinking cap on which is, of course, what we're doing here. I'll note also, that per the table below, a two-way slab does indeed have the ability transfer shear perpendicular to its span as that is the very definition of a two-way slab.

Again referring to the ASCE7 commentary sketch, does the clip below not suggest that the influence area for slab design for a 30' x 30' layout would be based 60' x 30'? It does to me. Yeah, it's beams rather than flat plate. But, as I mentioned at the top, you pretty much need to think in terms of beams in order to make rational sense of this stuff.

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[slickdeals]

This is from ICC's document on loads

 

[KootK]

I'm not sure what that proves slick. That IBC LLR method is for roofs and is specifically indexed to tributary area rather than influence area. And, presumably, it's stochastically calibrated to that metric. The basic ASCE method is not. Apples and oranges.

It's not as though LLR methods cannot be developed unless they're indexed to influence area. Heck, I think that old NYC provisions exist that index live load reduction to nothing more than the number of floors, as surely suits that market. But these things should not be construed to mean that influence area is an invalid index or even an inferior one. And for the sake of the ASCE method, influence area is the correct index in my opinion. Otherwise, how does one explain all of the >1 KLL values that result in one entering the equation with input that is not tributary area?

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[CURVEB]

Do you not agree that it suggests that the influence area for our case would be 4 x 60 x 60?

I think we are in agreement that 4 bays contribute to the influence area for a column axial load, what I'm not following is why you are using 60x60 for the bay size. With columns spaced 30' apart, I think the next bay starts beyond this point, so I don't get how you can include it. I would think no portion of the slab beyond 30' from the element you are looking at (the column in this case) has an influence on the load, unless you start to consider slab continuity.

 

[KootK]

...what I'm not following is why you are using 60x60 for the bay size.

I'm not. 60x60 is the size of the influence area. Think of it as (2x30)x(2x30) if you prefer. For an interior column, the influence area is bounded by a box two bay sizes long in each direction.

I would think no portion of the slab beyond 30' from the element you are looking at (the column in this case) has an influence on the load, unless you start to consider slab continuity

I generally agree, but that gives you an influence area width of 60' (2 bays) does it not?

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235

 

[KootK]

Perhaps there has been some confusion in formulas that include the number 4 where that number reflects the number of floors rather than the number of bays? I've been trying to keep this consistent with OP's question but this all would get much simpler with the four floors bit stripped out.

I think we are in agreement that 4 bays contribute to the influence area for a column axial load

Yes, we are in agreement on that. Those four, 30' bays will with result in an influence perimeter 60' x 60'.

HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me:

http://www.eng-tips.com/viewthread.cfm?qid=456235