Making triangular "concrete bricks" for a 3V dome in sketch up

[Juan Bidegain]

Hello everyone, I am new to this group but I have been through most of the posts in here and I am amazed by the level of understanding some ppl have about domes.

 I am trying to see if I can build a triangular brick that will have half the beveled angle included on it to make a hubless concrete 3v dome, I recently started using sketch up to help my project along before I start making concrete and I was able to get the hexagon brick done in scketch up, the way I did it, is by taking a 3v dome model from the 3d warehous and expanding it (down) 5.5" depth. That creates some overlaping with I then proceeded to divide using the line tool to make the bricks from the hexagon figure after cleaining up with the eraser all the overlaps that hang out of the figure. After that I just rotated the brick on the center axis and made the hexagon. The specs for the triangle for the hexagon are the followin. 

An isoceles triangle where the 2 equal sides are 60.7° and the top is 58.6° ( the lenght of the sides is not important as when scaling to size the angles will remain the same) and the bevel angle that I need on the 2 equal sides is 6.8° and on the base(the board oposite to the top angle) is 7.2°.

 See attached brick and hexagon.

Now the problem I am having is because the triangle that I need to use for the pentagon is very particular as it should add to 181.1° which is not a normal triangle, I checked several models on the 3d warehouse and all the triangles for the pentagon are slightly different and the work as long as you dont add any depth to it, I tried to do the same that I did with the hexagon and I keep finding that there is always one wall that wont close as it is not paralel to all sides so it wont crate a face, I tried building the pentagon with the missing face but it compounds to a wide gap at the end after the error adds up with every brick. 
I dont know if there is any way to do something like this in sketch up, the specs for the pentagon triangle are

An isoceles triangle where the 2 equal sides are 55.1° and the top is 70.9° (again the lenght of the sides is not important) and the beveled angel on the 2 equal sides is 7.2°  and on the base (side oposite to the top angle) is 4.1°

Even a close approximation of this triangle but one that doesnt leave me with a wide gap in one side of the pentagon would be great, I mean in case someone knows how to bypass the 181.1° degrees needed for this triangle yet still making a 5.5" deep pentagon overall.

Thank you all for sharing all your knowledge if this plan works I will be posting my findings on the warehouse for ppl to try it out, the plan is to print the triangle with a 3D printer and see how weel the fit together to make a mini dome. 

[Ashok Mathur]

Dear Jaun,

This is just a guess.

Try these three set of angles that add up to 180.

70 degree 32 minutes; 54 degree and 44 minutes; 54 degree and 44 minutes.

Source Page 4 of Polyhedron Models By MJ Wenninger.

Note on these pages the discussion is about spherical triangles.

See also Page 5 and 6 Figures 5 and Fig.6

These are just guesses.

Regards

Ashok

Regards

Ashok

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[TaffGoch]

Juan,

What is the desired diameter (or radius) of the dome? (The ones that I have posted to the 3D Warehouse have a unit [1.0] radius.)

From SketchUp measurement, the radius in your models appears to be ~32 inches. I created a new model that may be of interest to you, where the hexagonal tiles have equal edges and angles. The same with the pentagonal tiles. As with your models, the tiles are 5½"-thick. See what you think:

-Taff

[Juan Bidegain]

Hi Taffgoch, thanks for building that you are seriously talented on sketch up I spent 4 hours yesterday using Ashok's angles and I got pretty close but still had a gap when I put my pentagon triangles together to make the actual pentagon. 
I havent had time to play with the models you sent me but I wanted to thank you for taking the time, they look amazing, I will see if I have time in the next couple of days and I will let you know. 
I am looking to make a model tha I can scale up or down to suit my needs, I plan to make a dome first of small dimensions (sort of a dog kenel size) I am thinking 4 feet diameter, I know how to calculate the sturt lenght using the chord factors to build the size I need but I will also have to know adjust my dimensions to my 5 inch deep walls. 
But like I said on my first post I will probably 3D print this mold to use it as a reference for future molds and also to see how the briks work. 
I will keep you posted on my progress and again thank you so much for taking the time to build the model and to share it. 

[Juan Bidegain]

Hi Ahsok, thanks for the quick reply I havent had much time to read that book but I noticed your angles only add to 179.1° which still doesnt work for sketch up. I tried your angles with the closes aproximation posible. I ended up with a 70.6° by 54.7° isoceles triangle that is almost perfect but still have a little gap on my pentagon when I put the 5 triangles together. TaffGoch sent me a model that works and it is really close to the angles you mention so I am going to try his model. 
I will probably end up getting that book anyway as all this dome related math is quiet fascinating. Thanks for your reply I will keep posting my progress here to show you guys how things are working. 

Regards

Ashok

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[Ashok Mathur]

Dear Juan,

Pay far more attention to what Taff sends as that is likely to quickly yield you the results that you want.

I have no ability in SketchUp and am just beginning my enquiry into spherical triangles.

A few things that I have learnt so far are:

* A sphere always has a radius of 1. You get all the dimensions of the brick from this sphere and just multiply by the desired radius to get the final dimensions.

* Lengths are often stated as angles. Lengths are of arcs that extend that angle to the center of the sphere.

*You can choose the depth of the triangle at any stage. It can range from zero to the radius of the circle. So if you want to cover the surface of the sphere with a ferro-cement shell, the depth cpuld be 1 inch.If you want a convential brick, the depth could be  4 inches.

* The three angles that I sent you correspond to the following three sides of a spherical brick.
70.533 = 3.142*70.533/180 = 1.2311
54.733 = 3.142*54.733/180 = 0.95539

*None of the above would make any sense were it not for the fact that just 24 of these bricks cover the spherical surface completly and smoothly.

 You can make a paprer model in about one hours time to see it for yourself.Or  a model in SketchUp would show the same.

Still, these are very large bricks and you may want an alternate solution.

Wenninger has the following solution

20 degrees 54 minutes; 31 degrees 43 minutes and 37 degrees and 23 minutes

You need 120 of these bricks.Ten bricks make a pentagonal section and you need 12 of them to make the sphere.

No probleeem if you use Sketch Up.

Regards

Ashok

Regards

Ashok

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[Juan Bidegain]

Hello Ashok and Taff, sorry I havent got back to you earlier, it is hard to find time sometimes to get all my projects worked on :) Also I am still learning how to use sketch up so everything takes a lot longer for me. 

I have used Taff's Hexagon and Pentagon bricks and they worked amazing, I cant thank you enough for sending those. I was able to break them down to single bricks and also to build a full dome with perfect seems. see attached images.

My plan now is to develop a mold based on the single bricks to cast my concrete shapes and then mount them togehter with some mortar, after that I will coat the whole structure with stucco or something like that and see if it works, my first concrete model will be 3 feet wide at the base of a 5/8 3V dome. 
I will come back once that is done and show you guys if it worked out the way I envision. 
Again, thank you Taff you save me several painfull hours in sketch up :) 

[Juan Bidegain]

Hello, I just wanted to thank you both for helping out, it has been a long time since I logged in to update you guys but I have been trying and learning to work with this new bricks and their angles and how to build them properly and finally got a dome out of it, It is small but the scaling up should not be a problem. I am currently working in making a bigger dome and see how that works. This is the link to my youtube timelapse of how I put the bricks together. At that point my aircrete bricks were still to britle and didnt hold to good but I have since made a much better aircrete recipe and it feels like it should be a lot stronger for the next one. 

https://www.youtube.com/watch?v=yzboyLgAfp4&t=7s

Happy 2018

[Dick Fischbeck]

Talk to Peter Roberts of Alfred Station, NY.

https://www.facebook.com/peter.roberts.777

http://masonrydesign.blogspot.com/

[lemondealc]

Juan, I think my domes would be very useful to you as a structural form for your larger builds. Check out my post here:

https://groups.google.com/d/msg/geodesichelp/1EIpXGvAOzA/XC-R-4waAwAJ

Let me know if you'd like a kit sent to you. There would be no cost to you, but I would like to your feedback on the dome's usefulness as a concrete form. 

[Juan Sebastián Bidegain Umpiérrez]

Hi, I dont know your name LOL

I checked your post and that looks pretty cool. how do you go about sizes? I am trying to figure out a way that can be used for any size dome up to 32', the one on the video was my first trial at 4 feet and currently I am making the molds for one that is going to be 11' to see how hard is to put it together.

The way I make my bricks is by making some melamine molds with some calculated angles so when I put them together they naturally form the curvature of the dome. I did notice that when putting the last rows of triangle bricks they dont like to stay up so I can see your dome working as scafolding for when I build it and maybe it can stay in place after as I plan to cover the interior with regular concrete for added strenght so it can stay in as rebar.
I appreciate you getting in touch, I would love to try your dome kit, but as we are so far apart I wonder what the shipping cost would be, How heavy and how bulky is the whole kit when not assembled?

Cheers

Juan

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De: geodes...@googlegroups.com <geodes...@googlegroups.com> en nombre de lemondealc <lemon...@gmail.com>
Enviado: jueves, 11 de enero de 2018 21:57
Para: Geodesic Help Group
Asunto: Re: Making triangular "concrete bricks" for a 3V dome in sketch up

 

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[Bryan]

Hi Juan,

I like the air-crete and brick dome concepts.

I am not sure why you are struggling to design your bricks. To give thickness to any dome, measure your thickness from a vertex towards the origin. This will preserve the angles.
Attached is a 3v 5/9 Kruschke which gives a level base but has two hex bricks as well as the pent.

I am thinking that for a brick dome like this, one needs to allow for the thickness of the mortar between the bricks. Also, 32 feet would be a bit big for 3v...
I noticed on another video of an air-crete dome they used rods anchored to the centre as spacers to get the placement right. For a bigger dome maybe an internal frame as a form to hold the bricks till the mortar dried. Plenty to think about...