Tributary areas of columns and how to best calculate them [blog post] 2

[tribby3d]

Hi all,

I wrote a blog post about calculating tributary areas of columns. Probably targeted more towards students and graduates, but thought someone in here might find it useful anyway Feel free to check it out or let me know if you have any comments or thoughts.

Read the full article here:

https://tribby3d.com/blog/tributary-areas-of-columns/

Previews:

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[KootK]

The blog also mentions column stiffness a few times. Too many times in my opinion given that columns are usually so much stiffer than the floor decks they support that the columns are effectively rigid. I might, instead, mention column stiffness one time and in conjunction with things like foundation settlement and column transfer structure deformation which are probably more relevant to the point that you're trying to make.

 

[dik]

and for irregular column spacing, Arnold Crosier showed me, going from the mid points of the lines joining columns... haven't done it for a long time, but used to sum all the tributary areas and compare that to the total area of the floor plate.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[MIStructE_IRE]

Firstly let me say, the presentation and graphics are excellent. Honestly however, while something like this could potentially be considered for initial scheme design estimates, which you ultimately have to redo anyway, I’m not sure when I would otherwise use this.

The only real answer for complex structures is FE. And of course if you do however go more complex than this then you become the same as any other software - and have to charge accordingly. So, I would ask, what exactly is your market?

 

[JoshPlumSE]

I've always used trib area for both... all part of the same spreadsheet... DL, LL, COL, and MECS (mech, elect, ceiling, and sprinklers)... why not if the trib area increases for loading, you should be able to use the same increase to reduce LL.

I always think of Trib Area (and influence area) for live load reduction as being independent of continuity. So, the interior column of a two bay frame beam would have the same Trib Area and Influence area whether the beam was continuous over the column or not.

I don't see a problem with this in the vast majority of circumstances. But, what is the definition of Tributary area and Influence area in the code. Something like "Area supported by an element". Look at the far support on the backspan of a cantilever beam. Is it reasonable to say that this support has a "negative" tributary area from the cantilever area? Or, a reduced trib area?

Not arguing that your method is flat out wrong. It's just not what I do. Take a look at the image below. The columns at Line A have the same Trib area (per my method) whether or not the cantilevers exist or don't exist. This becomes a much simpler calculation. And, I think LL Reduction is intended to be a relatively simple calculation.

 

[JoshPlumSE]

I should also point out that the code relationship (in ASCE-7) between Trib Area and Influence area probably makes more sense when you look at it this way. Though it doesn't make perfect sense.

A_I = 4*A_T for interior columns or edge columns without cantilevers
A_I = 2*A_T for corner columns with a cantilever, or for edge or interior beams. With no discussion of continuity.

 

[dik]

only used for flat slabs and plates... and for some column layouts you have to use a little judgement... generally, it works OK.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[JoshPlumSE]

I should also point out that my method is at least partly related to being a "generalized" method that could be used for any column layout in a steel framed floor. Like a certain software I was involved with developing.

 

[tribby3d]

A lot of buildings are designed using the tributary area method without any real consideration of this effect

Sometimes multipliers are used as a simple way of accounting for the effect, whilst still using tributary area method. Eg multiplying the first internal column load by 1.15 or 1.2 (depending on scenario).

Makes sense. Adjustment factors would be one way of dealing with this. Do you think that this is something that should be built into Tribby3d? Or is it better to deliver the "raw" areas, and let the users adjust the results based on their own judgement?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

1) Tomfh seems to have explained all that pretty well while I was sleeping. Do let us know if anything remains unclear however.

2) Some other situations that can result in interesting, and perhaps spurious, results include:

a) Cantilevers.

b) Alternating long and short spans as can be the case with rack storage and isle/stall parking layouts.

In the extreme, these things can produce what would effectively be negative tributary areas (uplift).

Yes, really good points. The backspan/cantilever effect is also tricky, and also more or less impossible to account for with the current geometric approach. I didn't realize alternating short and long spans could bring similar effects. I'll include this in the documentation. Thank you!

As with all tools used professionally, it will incumbent upon your professional users to employ their own judgment when deciding whether or not Tribby represents valid approximation. I think that your path forward with something like this is to be user friendly in making it reasonably clear what Tribby does and does not do but, at the same time, don't go nuts with hand holding.

This is so important. I'm planning a couple of more blog posts on the topic. Will definitely do what I can to clarify the assumptions and potential scenarios where the results can be misleading in the documentation.

An interesting case might be the one shown below from your blog. A useful approach for your blog might be to take some of these interesting cases and run them with a true FEM program to see how they compare to your Tribby results.

Great idea. I read a white paper that did this comparison a while ago. Would be interesting to reproduce some of the results presented in it, but also include some special cases like the one you brought up with cantilevering effects from walls.

One way treatment can be surprising complex with respect to automated calculation, as you mentioned. You might take a look at RISA Floor which handles this.

Thank you, will do.

What's your end game here? Is this to be a revenue generating thing used by practicing engineers? Or an exploratory tool for students etc? I think that we'll be able to do a much better job of advising you on this once we know the direction that you plan to go with it.

To be honest, I don't know. Currently the focus is to make a user-friendly and robust tool that practicing engineers find useful. Tribby3d is sort of an expensive hobby project at the moment (both in terms of hosting costs and man hours), so I would love to find a way to keep the project running sustainably in the long run (given that people DO find it useful). But before any of that the main focus will be to iterate and validate it to make sure it's up to snuff with what's expected from a professional engineering software. Does that make sense?

The blog also mentions column stiffness a few times. Too many times in my opinion given that columns are usually so much stiffer than the floor decks they support that the columns are effectively rigid. I might, instead, mention column stiffness one time and in conjunction with things like foundation settlement and column transfer structure deformation which are probably more relevant to the point that you're trying to make.

Excellent feedback. Glad you understood the point I was trying to make I'll update the text. Thank you!

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

We always increased the first interior support by 10% to accommodate the increase in area... also used 0.9 for the exterior columns.

Good to know! I suppose that assumes that the entire floor is continuous then? Otherwise I suppose you would have to do a similar redistribution wherever the floor continuity is broken.

and for irregular column spacing, Arnold Crosier showed me, going from the mid points of the lines joining columns... haven't done it for a long time, but used to sum all the tributary areas and compare that to the total area of the floor plate.

Not sure if I understand this fully. Isn't this what Tribby3d does?

Thanks for the feedback dik. Appreciate it!






Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

I think Tekla Structural Designer has something similar to what JoelTXCive proposed. They call it a grillage chase-down.

Interesting. I'll have a look at this. I heard that RAM Concept also has a similar graph-based approach for solving one-way systems without FE. Do you know anything about that?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

Firstly let me say, the presentation and graphics are excellent. Honestly however, while something like this could potentially be considered for initial scheme design estimates, which you ultimately have to redo anyway, I’m not sure when I would otherwise use this.

Thank you! Good to know. It is a fine balance between making the tool sufficiently accurate and simple enough to use. I'm constantly trying to find this balance with Tribby3d.

The only real answer for complex structures is FE. And of course if you do however go more complex than this then you become the same as any other software - and have to charge accordingly. So, I would ask, what exactly is your market?

As mentioned in the answer to KootK - I don't know. The focus right now is to make Tribby3d a useful and valuable tool for early-stage load-take down analysis, and along with that understand if this solves a sufficiently big problem for it to be worth it. What's your take on that?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

I don't see a problem with this in the vast majority of circumstances. But, what is the definition of Tributary area and Influence area in the code. Something like "Area supported by an element". Look at the far support on the backspan of a cantilever beam. Is it reasonable to say that this support has a "negative" tributary area from the cantilever area? Or, a reduced trib area?

Yes, the tributary area method certainly has its flaws, like, you say, scenarios with backspans and cantilevers.

There is a difference between calculating column loads and calculating the column's tributary area. Just because an interior column may have more load, doesn't mean it's tributary area increases in the same manner.

To me, tributary area is mostly related to calculating live load reduction factors. Sure, it can used for early design approximation. But, I don't use it for actual design loading.

If you don't use the tributary area method for calculating design loads in early stage concept design, how do you else do it? Do you build an early stage FE model, even for preliminary calcs?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[JoshPlumSE]

If you don't use the tributary area method for calculating design loads in early stage concept design, how do you else do it? Do you build an early stage FE model, even for preliminary calcs?

Well, keep in mind that my background is with structural software more than design. I've had a number of years of design experience as well. But, much more of my career has been spent with RISA and CSi.

As such, I've not been as concerned about preliminary design. But, more with developing routines that will programmatically work for all cases. Especially the weird ones. That's why Trib area is most important for me only in LL reduction.

That being said, Trib area calcs are pretty easy in the early stage. And, I don't feel the need to get them 100% correct. As long as I'm in the ballpark with my initial / conceptual design.

 

[dik]

Floor plates generally are... but with all engineering stuff, you have to use a little 'educated' judgement.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

and you can take a look at your slab moment design output and get more correct PZS locations... for a more 'correct' tributary area.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[KootK]

Tribby3d is sort of an expensive hobby project at the moment (both in terms of hosting costs and man hours)

I don't doubt it on the hours front. The effort shows.

May I ask the approximate scale of the hosting costs? I've got some software ambitions of my own and that would be useful information for me.

My gut feel on this is that your path might be a free service supported by advertising. Then your primary customers can be students, people on Eng-Tips who discuss these things, and small scale practicing engineers without access to a full blown, plate FEM programs. I don't see that allowing you to quit your day job but, as you say, it might make the project self sustaining.

In offices that do a lot of concrete highrise work, I've seen tools that look like this:

1) For a repeating floor, your run an FEM model to get accurate column loads and moments.

2) You plug the results from that one floor into a big spreadsheet that extrapolates that to the loads on all of your repeating floors.

3) The big spreadsheet designs all of the associated columns and column to slap connections, including punching shear and stud rails.

In this way, one can design all of the columns and column connections for fifteen stories worth of concrete columns in an afternoon.

I mention this because this might represent a path to market for Tribby3d, especially if you could do it more cleanly and more transparently than your typical firm's big spreadsheet. My concern with this, however, is that many firms that do a lot of highrise work like this are likely to already have the big spreadsheet and will likely prefer to use that because they control it and understand it well.

 

[tribby3d]

That being said, Trib area calcs are pretty easy in the early stage. And, I don't feel the need to get them 100% correct. As long as I'm in the ballpark with my initial / conceptual design.

Makes sense! Ballpark is what we're going after here

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

and you can take a look at your slab moment design output and get more correct PZS locations... for a more 'correct' tributary area.

What's a PZS location? Is that the inflection point for the moment diagram?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

May I ask the approximate scale of the hosting costs? I've got some software ambitions of my own and that would be useful information for me.

Sure, I'm very happy to share these details with you, but would prefer to avoid posting that information here. Feel free to reach out via email (tribby3d at gmail dot com) and I'll tell you more.

In this way, one can design all of the columns and column connections for fifteen stories worth of concrete columns in an afternoon.

I suppose the assumption here is that every floor is identical?

I mention this because this might represent a path to market for Tribby3d, especially if you could do it more cleanly and more transparently than your typical firm's big spreadsheet. My concern with this, however, is that many firms that do a lot of highrise work like this are likely to already have the big spreadsheet and will likely prefer to use that because they control it and understand it well.

Appreciate this input, thank you! I agree that transparency is key.

Tribby3d
Structural loading software in the cloud

https://tribby3d.com