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# Live Load Reduction for multi-story columns with different floor live loads3

## Live Load Reduction for multi-story columns with different floor live loads

(OP)
I'm trying to figure out how to use live load reduction (ASCE 7-10 section 4.7.2) in a multi-story column with different lives loads per floor. Specifically how to determine the tributary area. Would you consider the tributary area for all of the stories with the same live load above the story in question ignoring the other levels that have different values when determining the reduction? For instance, say you have a 10-story building. The top 2 stories are residential the next 4 levels are various (mechanical, storage etc) and the bottom 4 levels are residential with the ground floor being commercial let's say. Assuming the tributary area, At, for a specific column in question is the same at all levels would the 'effective' tributary area (for use in the LL reduction equation) for each of the residential levels be At and 2*At for the top two levels followed by 3*At, 4*At, 5*At and 6*At for the bottom 4 levels (basically ignoring the intermittent levels with differing live loads)? Thanks!

### RE: Live Load Reduction for multi-story columns with different floor live loads

The calculation as I understand it (I don't work specifically to ASCE codes, but the principle is similar in all codes) for determining the actual column load the live load reduction factor is based on the total area supported by the element.

So I would take the total area supported, then the live load reduction factor would be applied to all live loads on the levels above using the same number which is calculated.

You have a different live load reduction number for each storey as the area supported is reducing as you go up the structure.

It is not tied to the level of the load for the column design. It can be for elements to which the load is directly applied.

### RE: Live Load Reduction for multi-story columns with different floor live loads

I agree with Agent666: "then the live load reduction factor would be applied to all live loads on the levels above using the same number which is calculated."

But keep in mind that as the engineer you can always be more conservative in your design - you don't have to take the full LL reduction.
In some cases, one "type" of your live load may be more sustained over time and you might want to treat that as a non-reduced live load.

Also some live loads are not allowed to be reduced - check your local code (i.e. public assembly live loads).

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### RE: Live Load Reduction for multi-story columns with different floor live loads

(OP)
That makes sense. So basically you would calculate the reduction factor on every floor (with the At increasing each floor) and apply it to the respective unreduced live load, Lo, at each floor. I would skip any loads that can't be reduced (like heavy storage or public assembly loads). There are minimum values (0.5 and 0.4) for the factor so at some point the tributary area is moot since the minimum value controls. And I agree, normally I would be conservative and not use the reduction too much but I'm studying for the SE exam and I know they want us to apply the factors exactly to show that we understand them. Thanks for the help!

### RE: Live Load Reduction for multi-story columns with different floor live loads

(OP)
Re-reading this I think I misunderstood. What you're saying is to calculate the reduction factor at each floor considering the tributary areas of all the floors being supported and then apply that to all of the live loads above and including the floor being supported(that can be reduced obviously) to determine the column load at that specific floor? This would mean that the reduced live load on a floor can vary depending on which floor column is being considered at the moment. Am i understanding that correct?

### RE: Live Load Reduction for multi-story columns with different floor live loads

Yes. Each column at each level has a specific tributary area that it supports...basically the projected bay areas directly above it.

So that particular column (not the floor) has a specific live load reduction that is allowed by code.
That doesn't mean that you have to create a bookkeeping nightmare (unless you want to!).

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### RE: Live Load Reduction for multi-story columns with different floor live loads

(OP)
Thanks for the help! My boss says that if you ask 5 structural engineers a question you'll get 6 answers. I asked my instructor in my SE review course the same question and he believes the tributary areas should 'reset' depending on the loading being considered (I have his response below, I used office loading instead of residential in the bottom 4 floors). So basically all the floors with one particular live load (residential let's say) would be grouped together when determining the tributary area and reduction factor which falls in line with what my original post said. I will say that both methods have their merits and I'm not sure which would be more conservative. I shot an e-mail to ASCE asking their opinion.

The reason they have to "reset" the tributary area has to do with what we are accomplishing with live load reduction. Statistically we are unlikely to have the entire floor loaded fully to the uniformly distributed load (note that live load reduction only applies to uniform loads). The exceptions are places that by design tend to fill up (storage, assembly areas, garages, mechanical rooms, etc.).

Thus, we can say that each residential floor is going to be loaded only X amount of it's full uniform load per square foot based on how typical residential floors are loaded. Each subsequent story increases the amount of residential square footage the column takes and thus reduces the probability that that stories column experiences the full uniform load.

Essentially an increase in the square footage of the residential load reduces the residential design uniform load for the column. The first column to see residential load supports much less area and thus has a higher chance to see the full design load. The second column has more residential area and thus sees a even lower design residential load.

We can do the same for the office areas. However, they will be loaded with a different load so we can't count the residential floors above when we consider the office loads. Thus, the first column to support an office load will support the reduced residential loads (and all the other stories) but the chances are the first office story is fully loaded are higher as there is less office square feet being supported. You calculate the office live load reduction per square feet of office live load.

### RE: Live Load Reduction for multi-story columns with different floor live loads

#### Quote:

You calculate the office live load reduction per square feet of office live load.

I don't believe that is what the code says. I'll have to look but I've never done that ever.

Now not reducing storage live loads makes sense of course. But I've never heard of using different tributary areas for different types of live loads.

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### RE: Live Load Reduction for multi-story columns with different floor live loads

Something to be aware of:- I was reading up on LLRF's to see if anyone did it the way you are suggesting and noted that ASCE uses what it terms the influence area. This is not the tributary area! It is 4 times the tributary area for a column, or the total area supported by the members that the column supports.

The code I work to uses the tributary area, and you also referred to tributary a area so just pointing out the distinction between the two.

I don't know the exact answer to your question given the ambiguity raised in the approach. However, consider the case if you had a building with a different occupancy on every single level, then by your argument for the entire structure there would be no live load reduction or no reduction due to the statistics/probabilities of floor loading at each floor. This in my mind is unrealistic for the entire building and for individual column design, it is more realistic to consider the whole building as just a supported area irrespective of the individual occupancy.

The chances of having every different level in this scenario fully loaded is likely to be similar to having all of the levels fully loaded when there is the same occupancy throughout. The statical stuff still applies!

Therefore I believe LLRF's should apply irrespective of the occupancy provided, and they should be based on a cumulative area approach for each individual area that qualifies for a reduction. (heavier or certain types of occupancy loads may not allow a reduction)

It will be interesting to see what ASCE come back with, so much ambiguity in something that I'm sure was intended to be straightforward!

### RE: Live Load Reduction for multi-story columns with different floor live loads

Agent666 - every time I typed "tributary" I wondered when someone would comment. You are correct in the distinction between tributary and influence.

While I use the correct areas - the older method of LL reduction (0.08(A-150) used the tributary area so it is just habit with me term-wise.

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### RE: Live Load Reduction for multi-story columns with different floor live loads

Figure I'll chime in since I am the aforementioned instructor, and am curious about this topic as well as I've yet to find an official resolution to it.

#### Quote (JAE)

I don't believe that is what the code says. I'll have to look but I've never done that ever.

Now not reducing storage live loads makes sense of course. But I've never heard of using different tributary areas for different types of live loads.

I based this off of my interpretation of ASCE 7-10 4.7.2 (and fully suggest that I could be incorrect, this is just how I read it).

The definition of Lo = unreduced design live load per ft2 of area supported by the member. (Essentially Lo = design pounds per square foot)
The definition of At = tributary area in ft2

Now I take the ft2 from Lo's definition to be equivalent to the ft2 in At's definition. This is because the definition of Lo states that it refers design load per square foot of area supported by the member but if we take this "area supported by the member" as the entire tributary area for a multi-story column with differing loading at each story then it's not correct. Thus, I interpret this as we have to calculate L (reduced) for each loading type. I further rationalize this as what if KLL changes types between stories? For example a column is located centrally in a lower story but the building tapers as you go up in height so at some point this column becomes an edge column. In that case it seems clear to me that you must calculate KLL*At for each KLL region and it would not make sense to use the total At for these two calculations.

My one final rational is that each loaded area will have different statistical probabilities for maximum load. For example, let us say we have a building with mixed offices and residential floors. The chances of all residential floors being loaded up fully in a building is low; so we reduce the live load for the residential floors as we would expect. Now, the offices below will likely be loaded at different times than residential (but will have some long-term live load in each). Thus, the chances that all the residential floors are fully loaded AND the office floors are fully load is low, but I'd say it to be no lower than each area analyzed separately.

Do the statistics of typical office loading change based on how many apartments are occupied above it? In my opinion I don't believe so. Is there a larger tributary area that the column supports when we include both the office stories and residential stories? Yes, which ignoring type of live load, statistically should have be lower uniform load. So, this is why I could see this working both ways.

Again though, I've yet to find any official clarification and I do agree that I've seen a few examples do it my way (though I question these examples quality as we found other errors in it) and a few examples do it the other way.

Professional and Structural Engineer (ME, NH)
American Concrete Industries
www.americanconcrete.com

### RE: Live Load Reduction for multi-story columns with different floor live loads

TME,
I would keep it simple. ASCE 7-10 commentary says, "For multiple ï¬‚oors, areas for members supporting more than one floor are summed." There is no mention to restart with different occupancies. This makes sense because there is only two types of loads to consider, those that can be reduced and those that can not. For the example with residential on one floor and office on another, it would be more likely that two floors of residential or two floors of office would be fully loaded at the same time. So it makes no sense to have less reduction for mixed occupancies. But, as JAE above, the engineer can always be more conservative in the design.

A more interesting question is whether one should include the influence area of occupancies with no live load reduction for elements supporting mixed occupancies. Consider a building with assembly at the top and offices below. Would it be appropriate to include the assembly influence area to further reduce the office live loads on the lower columns? I think the code says yes. But, I would be hesitant to do this.

The part that I find frustrating is partition live loads. Section 4.7.1 says live loads in Table 4-1 may be reduced. Partitions are in 4.3.2 and not in the table. So, I chase partition live loads separate from the reducible live loads. It would be more convenient if the partitions loads were reducible so they could be included with the other live loads.

### RE: Live Load Reduction for multi-story columns with different floor live loads

I agree with the above (by wannabeSE) - with respect to LL Reduction there are two types of live loads: reducible and non-reducible.
Thus, only the reducible live loads (and areas associated with reducible live loads) are involved in live load reduction calculations.

Partition live loads were some time ago described in a commentary as dealing with the aspect of moving office partitions where the corridor exitway would possibly move around the space under different configurations of walls. Thus the exitway (with a live load of 100 psf) would affect the floor design so a 20 psf (now 15 psf) added "live" load was used to account for the moving 100 psf exit way.

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### RE: Live Load Reduction for multi-story columns with different floor live loads

So, I've spent the past half-hour staring at the commentary of 4.7.1 and I can't find anything that says my concept isn't correct.

However, I'm beginning to feel that I agree with you guys on what the intent of ASCE section 4.7.1 is. I'm not saying at all that my method is correct; I'm simply trying to find what the most accurate interpretation of section 4.7.1 is so as to advise people how to properly apply live load reduction in regard to SE exam.

wannabeSE: That's a good quote. I don't think that alone invalidates my concept of how to apply 4.7.1 but when you combine that with the commentary above, "the influence area is defined as that floor area over which the influence surface for structural effects in significantly different from zero." Below that they define KLL = AI/AT. This seems to imply to me that you have to have AI and AT be the full tributary areas for all loads. That said, I could still see this applying in my concept.

I also am not clear on how best to address members that change KLL values as you go up or down the structure without having two different regions of live load reduction or using the lower of the two applicable KLL values. Either approach seems appropriate but will wildly change the result depending on which approach is chosen.

So, in the end, I'm almost convinced you folks are correct. I think the only thing holding me back from converting to your camp is my concept is more conservative. I might just have to dig up the original paper cited in the commentary regarding live load reduction.

Professional and Structural Engineer (ME, NH)
American Concrete Industries
www.americanconcrete.com

### RE: Live Load Reduction for multi-story columns with different floor live loads

I think for multiple floors with different conditions (i.e. an interior column changing to an edge column above) I would be tempted to calculate a weighted average of the KLL factor for the column.
As the commentary suggests, the KLL factor is simply a way for the code-writers to allow use of tributary area (more convenient to designers) but tie the math and statistics into the influence area.

Using an average value for KLL simply seems consistent with this math.

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### RE: Live Load Reduction for multi-story columns with different floor live loads

I took a glance through the structural analysis textbook I have on hand (by Leet and Uang) and it agrees with JAE and wannabeSE.

The closest book I can find that would give an "official" response from ASCE is Structural Loads: 2012 IBC And ASCE/SEI 7-10 by David A. Fanella which I believe addresses live load reduction and was sponsored by ASCE. Unfortunately I don't have a copy of this text and not sure if this is worth spending $65 on. Anyone have a copy of this text? JAE: That would make sense, I'd agree with that given the commentary in ASCE about how to derive KLL. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads I believe that there's a more accurate, and less confusing, way to handle LLR: 1) Toss the KLL concept out the window. All that matters is the square footage of influence area. And that can be envisioned as the sum of all of the square feet that are loaded with reducible live load and contributing load to the member being considered. 2) Use the influence area dertermined in step one to work out the coefficient that can be applied to each and every square foot of tributary, reducible load to account for the improbability of all those square feet being loaded at once. That's it. That's my interpretation of ASCE and It makes rock solid probabilistic sense in my opinion. If you accept that: 1) No reset. 2) Upper floor assembly area would not contribute to lower column influence area. 3) An average KLL would usually work but, truly, why bother? Just go straight to influence area. I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it. ### RE: Live Load Reduction for multi-story columns with different floor live loads Well, KootK, I value your opinion a lot but more than that I value simplicity when it makes sense and that makes a lot of sense. I also agree that your approach matches what the commentary describes for the calculation of KLL and I believe section 4.7.1 (don't have ASCE 7 with me) mentions that KLL can be computed by a rational analysis. I still am not 100% convinced that my approach isn't the intent of the code but it definitely doesn't seem to match the general consensus of everyone here. As my ultimate goal is to properly advise the engineers in the review course on how best to approach the SE exam I will flip-flop and recommend they follow either KootK's method (which would be the easiest to apply on the exam) or the "traditional" method that JAE and wannabeSE (and others) discussed. Thanks for everyone's input on this. I'd love to see more info if anyone has it. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads A couple of additional thoughts, none of which I can "prove": 1) My understanding is that ASCE live load reduction gives no nod to temporal effects. It is assumed that peak loading occurs in all areas at the same time and that any available reductions are a result of partial floor load utilization at those peak loading times. In my mind, that implies that you'd rationally have a greater ability to reduce loads for a mixed occupancy than you would for a single occupancy structure since, obviously, the peak utilization might be out of phase for the various occupancies (offices peak during the day and homes peak in the evenings etc)). I believe that wannabeSE was essentially making the same point above. In conclusion, I feel that using full LLr in mixed occupancy structures is probably more conservative than the same practice would be in single occupancy structures. 2) Would we all agree that the live load reductions should be applied on a design action by design action basis rather than on a member by member basis? Case in point: in multi story column design, different levels of live load reduction would apply to column axial demand and column flexural demand, even for the same column design? I often see junior engineers apply the same reduction to column moments as they do to column axial loads. I feel that is inappropriate as the column moments often arise from a much smaller loaded influence area. 3) I feel that multistory column design should include consideration of partial live loading cases, whether we deal with them explicitly or not. If some combination of office only live load -- and a corresponding lower LL reduction -- would produce a more critical effect than all stories (office & res) loaded, that should be considered in the design. I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it. ### RE: Live Load Reduction for multi-story columns with different floor live loads 1) I would agree with this but only if the intent of ASCE 7's was to use the total tributary area and not break the tributary areas up for each occupancy load type. If the total tributary area is used then, yes, I would agree. Though, you could of course have live loads that peak at the same time. Classrooms and a Library for example so this is such a case-by-case basis that I would find it had to ever take advantage of. 2) I would actually not agree but only in regard to how best to apply the KLL factor. In reality I believe you are correct that we "should" take this into consideration but ASCE 7 makes no distinction for design action when they present the prescriptive KLL factors and only consider live load reduction on a member by member basis. They do however give the engineer the option of calculating their own KLL through rational analysis so I don't see anything wrong with your approach, only that it's not required and would be highly tedious. 3) Wait, isn't this what I was saying about having tributary areas based on same-type occupancy loaded areas? My approach would be more conservative as it includes maximum force effects with a minimal live load reduction but otherwise is a similar concept. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads #### Quote (TME) I would agree with this but only if the intent of ASCE 7's was to use the total tributary area and not break the tributary areas up for each occupancy load type. I guess I don't understand what has led you to believe that ASCE intends for us to break up tributary areas by occupancy. Can you point to a particular statement? I see it as wannabe seems to: there are only two kinds of load in this context, reducible and unreducible. #### Quote (TME) Though, you could of course have live loads that peak at the same time. Classrooms and a Library for example so this is such a case-by-case basis that I would find it had to ever take advantage of. Agreed. I wasn't suggesting that the temporal effect be taken advantage of so much as suggesting that, because of the temporal effect, I see no rationale for introducing additional conservatism in to the live load reduction calculation. You know, other than individual designer preference. #### Quote (TME) Wait, isn't this what I was saying about having tributary areas based on same-type occupancy loaded areas? My approach would be more conservative as it includes maximum force effects with a minimal live load reduction but otherwise is a similar concept. It is similar which is why I tabled it. The snippet below, applicable to one and two family dwellings, conveys a similar sentiment I believe. I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it. ### RE: Live Load Reduction for multi-story columns with different floor live loads #### Quote (KootK) It is similar which is why I tabled it. The snippet below, applicable to one and two family dwellings, conveys a similar sentiment I believe. Interesting, what is that snipped from as I don't recognize it. #### Quote (KootK) I guess I don't understand what has led you to believe that ASCE intends for us to break up tributary areas by occupancy. Can you point to a particular statement? I see it as wannabe seems to: there are only two kinds of load in this context, reducible and unreducible. I initially based my concept off of a PPI example, the fact that it was most conservative, and the ASCE 7 definition of Lo (see my first post from March 13th above). Since then wannabeSE and JAE convinced me that my interpretation didn't match what the commentary implied. Ignoring the PPI example, the only thing I have is the fact that it's more conservative and I see nothing in ASCE 7 that says that we're not supposed to break it up by occupancy load. But, I've conceded that this probably is not the intent of ASCE 7-10 4.7.1 nor is it what would be expected on the SE exam. #### Quote (KootK) Agreed. I wasn't suggesting that the temporal effect be taken advantage of so much as suggesting that, because of the temporal effect, I see no rationale for introducing additional conservatism in to the live load reduction calculation. You know, other than individual designer preference. Ah, that makes sense. I could see that balancing out some other un-conservative area of the live load reduction process. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads (OP) Thanks for all the helps guys. It's been very informative reading these posts! If I ever get a response back from ASCE I'll be sure to pass it on but for now I'll move forward with the interpreation given originally by Agent666 and JAE. ### RE: Live Load Reduction for multi-story columns with different floor live loads #### Quote (TME) Interesting, what is that snipped from as I don't recognize it. That's actually the tail end of ASCE 7-10 4.7.2. I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it. ### RE: Live Load Reduction for multi-story columns with different floor live loads Eh? Not in my edition. Third printing w/ supplement 1. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads (OP) That section was removed in the errata for the 2nd printing. With that said I think it shows what they were thinking for reduced live load on multiple floors. ### RE: Live Load Reduction for multi-story columns with different floor live loads Agreed! That does seem to settle it even if they removed it. Professional and Structural Engineer (ME, NH) American Concrete Industries www.americanconcrete.com ### RE: Live Load Reduction for multi-story columns with different floor live loads A solution to an example in the book TehMightyEngineer mentioned addresses this specific topic. Although, he uses IBC and IBC states that a LL >100psf cannot be reduced.The exception in ASCE 4.7.3 says you can. What would you use on the SE exam? ### RE: Live Load Reduction for multi-story columns with different floor live loads Thanks for posting that! Saves me$65 and that's a good example of a lot of the topics discussed. I think we can finally put this to rest as I consider that example official enough for my purposes.

IBC 2012 has an exception for the live load reduction of heavy loads (Lo > 100 PSF) in 1607.10.1.2 similar to ASCE 7 where if more than 2 floors are supported the heavy load can be reduced 20%.

On the SE exam I would reduce the heavy live load by 20% because they may be trying to see if you know about this exception.

Professional and Structural Engineer (ME, NH)
American Concrete Industries
www.americanconcrete.com

### RE: Live Load Reduction for multi-story columns with different floor live loads

(OP)
Awesome! Thanks! I think we can finally put this to bed.

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