Area load distribution of closed polygon 2

[DanAndrews]

Does anyone know how to calculate the load distributed to the perimeter beams that form a closed polygon of any shape not just rectangular?
Any textbooks recommend? (I tried to search but no luck so far)

I read the support documents from RISA 3D and looks like they use finite meshes but I believe meshes method is not required for this issue?
Thank you.

 

[Celt83]

Assume you are talking about one-way distribution of loads and not considering continuity of slab over supports. Beams/Girders are straight and load areas are defined by straight lines.

Area loads:
1. Define span vector
2. Define points of intersections on beam lines of other beam ends and load region vertices, parallel to span vector.Add points at small distance before and after interior points to capture constant load regions.
3. At beam end and each point from above perform simple statics analysis to get reaction on beam.span for analysis is the distance from beam to nearest beam at span vector.
4. Connect results from above (since everything is defined with lines load will either be constant or vary linearly between the two points.

Point loads:
1. Define span vector
2. Find points of intersection of load point with beams.
3. Perform simple statics analysis to get reaction on beam.

Probably a way to program it so you apply the results to multiple beams at once to cut down on repeated calcs.

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[DanAndrews]

Thanks Celt83. I am actually more interested in two way load distribution mechanism. ie. calculate how much load each premier beam gets from a closed polygon with uniform area load.

The following is an example showing what I want to do. I couldn't find more resources explaining how load is distributed for a general closed polygon without using finite element approach. Is it based on yield line theory? (doesn't look like)

 

[Tomfh]

It’s nearest neighbour. Just bisect the angle between beams, and connect the dots between the intersections of the bisecting lines.

The regular rectangular beam method is the same
method, but appears simpler case due to 90/45 degree angles.


Note that this method (including the rectangular case) is a simplification that does not take into account actual stiffness behaviour. It’s not a “correct” method, but is merely a simple approximation to distribute loads to supports.

All but the simplest cases will give you slightly different results to a real analysis, or in some cases very different results, Eg if you have a very short backspan.

 

[DanAndrews]

Thanks Tomfh.
If it is based on 'nearest neighbour' to get the distributed load then I agree it is not the 'correct' way to get distributed loads but I am just wondering if this is the way all these FE softwares deal with load distribution (ETABS for example) when we assign 'membrane' or 'deck' to the slab instead of using 'shell' or they have other methods?

 

[Tomfh]

Finite element floor plate software will generally be using that method (finite element method) to distribute loads. That is what the programs do. They solve the stiffness equations and see where load is actually going.

Some software allows you to use the simple method though, when calculating loads going to line and point supports.

 

[1503-44]

Tomh has a point. It's not only the stiffness of the slab that determines where the load goes. The relative stiffness of the support mechanism also has a say in the matter, as would other effects. For example, a central support of a continuous beam we know reacts with 5/8ths of a uniform distributed load, whereas tributary load theory would only put 1/2 the load there. That simple case proves that tributary area theory is valid only for the simplest load cases with simply supported beams or slabs, The same would be true of a continuous slab with a central support beam. The beam could take 5/8ths of the distributed load on the slab, not 1/2.

 

[Celt83]

My experience when you use a two-way deck or panel as some programs call it is they use the trib area method which as tom noted us not “correct”.

Likely method of load region separation is Delaney Triangulation Link and Voronoi Diagram Link

You can test it in the programs by placing a point load in each of the regions you’ll tend to see 100% of the load going to one beam.

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[1503-44]

Delaney and Voroni just yield the same "tributary areas" for multifaceted polygons. Still wrong.
Point loads would still have to be proportioned (by square of?) distance to all edges.

 

[Celt83]

1503-44:
yes it is wrong but that is what these load panels are doing in many analysis packages they are doing simple trib areas to reduce computation time, otherwise you need to actually model a shell and give it all the appropriate stiffness matrix adjustments and edge releases.

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[1503-44]

Right. Would they correctly load a 1-way metal grating span, if it was framed by 4 channels?

 

[BAretired]

Hillerborg's strip method of design is a powerful and versatile technique for designing two-way reinforced concrete slabs and plates. The method is based on the lower bound theorem of plasticity, meaning that a design based on the strip method is always safe.

BA

 

[dik]

Other than the actual publication, is there a good *.pdf description of Hillerborg's strip method. I've noted the text on the internet, but $300 is a little pricey. I have a new project that it may be applicable. An existing structured flat slab with a 250 psf design load that has a mechanical equipment loading of nearly 400 psf over a significant area. It's been in operation for over 30 years... and they want to add a small jib crane to it.

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 read the support documents from RISA 3D and looks like they use finite meshes but I believe meshes method is not required for this issue?

To be clear, the methods used in RISA-3D and RISAFloor are different (at least they were 3 years ago when I worked for the company).

RISA-3D used a very "general" method for applying these loads. Essentially just converting the area load into a series of point loads and attributing those to the nearest beams in the direction of "area load attribution". That results in a series of internal member point loads on beams that then get converted into a series of distributed member loads on the beams. The accuracy of this method greatly depends on a user set value called "area load mesh size" which dictates how the area load is broken into smaller internal point loads during solution.

RISAFloor has a little more knowledge of the "framing" of floor system, so it usually uses a closed formed solution based on the assumption that the deck is simply supported wherever it lays on a beam. This tends to be a lot faster, and slightly more accurate.

Caveat:
While I worked for RISA for quite some time, my departure was less than cordial. As such, I feel the need to mention that I hold some personal bias against the current Nemetchuck management team over there. So, I'm not exactly a neutral observer when it comes to this product.

 

[Celt83]

RISAFloor has a little more knowledge of the "framing" of floor system, so it usually uses a closed formed solution based on the assumption that the deck is simply supported wherever it lays on a beam. This tends to be a lot faster, and slightly more accurate.

Are you able to share any more details about this? any white papers or other technical resources to google for?

My Personal Open Source Structural Applications:

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

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[BAretired]

Other than the actual publication, is there a good *.pdf description of Hillerborg's strip method. I've noted the text on the internet, but $300 is a little pricey.

I found file:///C:/Users/Owner/AppData/Local/Temp/Strip%20Method%20Design%20Handbook-1.pdf this morning. Can't comment on how "good" it is, but I will peruse it in the coming days.

Also found the following:

BA

 

[dik]

Thanks...

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

-Dik