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

 

[Reo-Checka]

Tribby3d is looking better and better. Congrats Emil!

ReoChecka

https://reochecka.com.au/

 

[JoshPlumSE]

Your blog post is good. Some additional ideas to expand on it:
1) Another example with oddly spaced or non-orthogonal columns.
2) A extension from "Tributary are" to "influence area".
3) Other Odd cases. Maybe something like the following image where one of the edge columns is removed

 

[KootK]

Feel free to check it out or let me know if you have any comments or thoughts.

1) Firstly, I love what what you've accomplished with this technologically.

2) The app has one critical limitation that I didn't see mentioned in your blog: it does not account for floor system continuity over columns and walls and, therefore, will underestimate the true tributary area in many situations. It may well be that's an acceptable approximation in some scenarios but, given the nature of the tool, I feel that it is important to mention this in the associated documentation.

 

[JoelTXCive]

This is great.

Here's free input for improvement:

Instead of a concrete slab; calculate tributary area with steel joist supported by girders. The girders then deliver load to the columns.

Then, you can show the two ways to calculate the tributary area of the columns:

Method 1: As you have described above.
Method 2: Calculate the tributary area of the joist; and their point loads delivered to the girders. Then the girder loads going into the columns.

I read an article recently (which I cannot remember where) that said calculating the tributary area via Method 1 is always more conservative because some double counting happens.

It would nice to see the difference between the methods.

Keep up the good work!

 

[Tomfh]

This is neat, but as Kootk mentions the actual load going to each support depends a lot on slab continuity, as opposed to simple nearest neighbor calculation.

 

[tribby3d]

Tribby3d is looking better and better. Congrats Emil!

Thank you so much! Really appreciate it! Your stuff is amazing too, Nick.

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

Your blog post is good. Some additional ideas to expand on it:
1) Another example with oddly spaced or non-orthogonal columns.
2) A extension from "Tributary are" to "influence area".
3) Other Odd cases. Maybe something like the following image where one of the edge columns is removed

1 and 3 are really great ideas, thank you! I think these might become separate blog posts. For suggestion 2, can you elaborate a bit more on what you mean?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

1) Firstly, I love what what you've accomplished with this technologically.

2) The app has one critical limitation that I didn't see mentioned in your blog: it does not account for floor system continuity over columns and walls and, therefore, will underestimate the true tributary area in many situations. It may well be that's an acceptable approximation in some scenarios but, given the nature of the tool, I feel that it is important to mention this in the associated documentation.

Thank you KootK, really appreciate the feedback. Do you mean that in such scenario the support moments would affect the total accumulated area? Could you further explain how the mechanics around that works? I want to make sure I fully understand your point, so that it can be reflected properly in the documentation, as you say.

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

This is great.

Here's free input for improvement:

Instead of a concrete slab; calculate tributary area with steel joist supported by girders. The girders then deliver load to the columns.

Then, you can show the two ways to calculate the tributary area of the columns:

Method 1: As you have described above.
Method 2: Calculate the tributary area of the joist; and their point loads delivered to the girders. Then the girder loads going into the columns.

I read an article recently (which I cannot remember where) that said calculating the tributary area via Method 1 is always more conservative because some double counting happens.

It would nice to see the difference between the methods.

Keep up the good work!

Thank you JoelTXCive, I think this is super interesting. You and a few more have suggested to implement a sequenced tributary area solver, which would allow for analysis of one-way systems (like girder/joint systems) and much more. Exactly as you describe, it would calculate the tribs for the joists, which become point loads to the girders, which would become point loads to the columns etc.

The only significant downside I see with that approach is that the girders/joists would have to be modelled as well, which may slow down the process for the user to get the structure properly configured in tribby3d. Do you think it's still worth it? Feel free to reach out to me on tribby3d [at] gmail [dot com] if you'd be interested in discussing this feature further.

Cheers,
Emil


Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[tribby3d]

This is neat, but as Kootk mentions the actual load going to each support depends a lot on slab continuity, as opposed to simple nearest neighbor calculation.

Thanks a lot for the feedback Tomfh. Could you please help me understand how the continuity of the slab affects the tributary area? Does this have to do with moments induced if the slab isn't "released" at the supports? I am aware that slab directionality (like one-way systems) and column stiffness will affect the tributary area, but how does slab continuity affect it?

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[Tomfh]

Internal column can attract more load:

 

[tribby3d]

Internal column can attract more load:

You are right. The difference between continuous vs discontinuous could be up to 25% (0.625/0.5 = 1.25). However, I'm afraid that there is nothing that can be done to account for this with the current geometric approach that Tribby3d uses. Is this a deal-breaker in your opinion? Tribby3d is meant for early-stage approximations - FEA would be more appropriate if exact results are needed. Either way - I'll definitely improve the documentation to clarify this.

Many thanks for informing me about this.

Tribby3d
Structural loading software in the cloud

https://tribby3d.com

 

[Tomfh]

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).

 

[dik]

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

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

-Dik

 

[JoshPlumSE]

Internal column can attract more load.

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.

 

[bones206]

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

Tekla Video:

https://www.youtube.com/watch?v=pqf6-bX193Q

 

[dik]

????

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

-Dik

 

[dik]

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.

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

-Dik

 

[KootK]

Do you mean that in such scenario the support moments would affect the total accumulated area? Could you further explain how the mechanics around that works?

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).

c) 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.

d) 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.

You and a few more have suggested to implement a sequenced tributary area solver, which would allow for analysis of one-way system..

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.

Is this a deal-breaker in your opinion? Tribby3d is meant for early-stage approximations - FEA would be more appropriate if exact results are needed.

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.