igloo-perfect block shape?

<is there a perfect shape?>

Consider the mathematics of the inverted catenary arch: http://en.wikipedia.org/wiki/Catenary, integrated through 360deg into a structure with a circular base. The traditional brick kiln structure, a number of which survive in Staffordshire, are this shape.

A structure of this shape requires the minimum of materials for its construction compared with that needed to form other shapes that are stable, even a hemisphere.

http://en.wikipedia.org/wiki/Geodesic_dome

In response to absolutely nothing at all, except your "photo": Not kicking very high, mate. My 9 year old is a black belt, and has won 1st place in tournaments, and he consistently kicks over his head. Just a smile for you on Halloween!

Well I have no problem kicking over my head especially with nine years of classical ballet training prior to TKD. You did notice that I am airborne when the kick breaks the board right? I also have no problem breaking a board held horizontally 12" above my head or four 8" x 8" x 1/2" stacked ceramic floor tiles with my fist. But if you look at the particular kick I am using to break the board you can see that it would be difficult for my assistants to hold the board vertically and above my head height. So your nine year old breaks boards held at a height above his head does he? That's very impressive! Unfortunately in our school a nine year old can't be but a junior black belt and not a very good one in the scheme of things. There is only so far you can realistically get in the amount of time you could have studied by age 9. We study from a 9th degree Grand Master and we are part of the World TaeKwonDo federation out of Seul Korea so our black belts are registered world wide within that system. We also spare full contact without any safety equipment. Think the movie "Fight Club" except we don't punch to the face. Sometimes we have people come to us from other schools like TaeKwonDo America, which isn't much more than a day care center. They usually don't stay very long, too hard, get beat up too much, can't cut it. Oh well, something for everyone I guess. Keep encouraging your son, it is very good discipline!

http://www.google.ca/search?hl=en&q=igloo+%2Bconstruction&btnG=Google+Search&meta=

It sounds like you have the bricks on site. If not go ferro cement. I hope this is not too late. Have a good one. Ky.

I feel that you need to make a strong wooden form for the inside, that will support your structure till it is finished. It must be bolted together in such a way that allows you to easily remove it when the structure is finished...

You need to use building steel and nets both inside and outside, which must be an integral part of the structure.

Try a small version first, weigh it and use this as a basis for the weight of the complete structure, double it at least for the foundation strength.

Remember that such structures can "push outward", the problem that medieval builders had with cathedrals....

Check your local building codes first...

Send us photos when finished.

Unfortunately, a single building block cannot form the doubly curved shape that you require.

Think of it like this, if you have a sheet of paper that you divide into a grid (any type of grid: rectangular, hexagonal, penrose . . .) then try to deform this into a doubly curved shape. No doubly curved shapes are possible (we won't count the cone as doubly curved, it has a single but varying curvature)

But with two types of building block, you can. Think footballs (soccer) and how they are made: pentagon + hexagon.

These are the beginnings of the geodesic forms already identified in other replies.

Otherwise, the secret is in the joint which you can thicken as required. Some fabulous shapes have been made with simply bricks (and some cable reinforcement). Google Eladio Dieste.

What about half a bucky ball. Instead of making hexagonal and pentagonal "bricks" you could make two types of triangular "brick". If you made five bricks for the pentagons and six for the hexagons you would need to cut some in two: so what about 10 "bricks" for a pentagon and 12 for a hexagon.

http://architecture.about.com/library/ucdome.htm

Make sense?

I saw a documentary, CBC believe, about igloos. The showed the Inuit placing the blocks in a spiral. It is done so that the newest block always has the previous one to hold it up .

Check out the Eskimo Igloo structural design manual! Or go to: www.primitiveways.com/igloo

hello, from artbyjoe

i want to thank everyone for their replys. some of them are very close. so, i will provide more information to clear up some things that are not in the equation.

my plan is to mold the blocks using extremly light insulating concrete. the target weight is about 15 pounds per square foot. looking and feeling a lot like styrofoam.

i plan to glue and pin the blocks together as i erect it. i will glue it with "Grancrete" which has the properties i have selected to aid me. it does not make cold joints. sets in about 10 to 15 minutes. i will pin it by driving short pieces of rebar from top thru next lower block. this is to hole the blocks until the dome is finished. then i will stick barbs into the blocks to mount my horizontal rebar in place. then wire the vertical rebar to the horizontal. i will do this both inside and outside. then spray the grancrete inside and outside. it is a very expensive cement. 8 times as expensive as portland cement. but its qualities are worth it. it has a consistancy of stiff mortar when sprayed. can be sprayed in very thin coats. no cold joints, so additional coats do not delaminate. it is also water proof. it is also makes 7000 psi concrete. it can be sprayed with a mortar hopper.

so, except for having a redimix truck come up to pour the slab and footer, i should be able to do everything else with my little home mixer, in small batches.

by the numbers i should be able to put in the slab floor and shell for about $4,000 for a 20' diameter dome. so the dome is 3 layers with the insulated concrete in the middle. the slab will also be 3 layers with a regular concrete 3" slab on the bottom. 1 foot of insulated concrete above that , then 1 inch of grancrete for a final surface.

this turns out to one fifth the cost of a "Monolithic Dome". this is because i will not need expensive equipment or contractors.

i am going this approach because i live off grid, in an extreme fire hazard zone, and an extreme earthquake zone, not to mention the occasional hurricane. in 20 years here, so far the biggest hurricane was sustained winds of 85 mph gusting to 120 mph. the biggest earthquake has been 7.6, which caused a visible earth wave of about 2 feet to pass thru. the ground for about 30 miles around rose 4 feet.

again, thank you for your replys. the closest reply to my intent was the one where you said to use hexs and pentas, like a soccer ball. would this actually form almost a true sphere. if not, i will probably continue with using a brick style construction, with the blocks getting smaller with each tier.

joe

Better than this picture from the site I linked above shows.

-------------------------- SNIP ------------------------------------

8. Finally, take the five half hexagons and connect them to the outer edges of the hexagons.

Congratulations! You have built a geodesic dome! This dome is 5/8ths of a sphere (a ball), and is a three-frequency dome. The frequency of a dome is measured by how many edges there are from the center of one pentagon to the center of another pentagon. Increasing the frequency of a geodesic dome increases how spherical (ball-like) the dome is.

-------------------------- SNIP ------------------------------------

Of course you can tailor your design to give you a hemisphere. Good luck. Please let us know how you get on.

The concept of quickly erected cement-domes came up on the inventor programme Dragons Den. Much to my annoyance I can't find a reference for you ( google led me right back to my own mention of this on CR4 !). If you have time you may be able to find more specific detail, and it may be worth your while checking out. In short, a dome is inflated and cement poured. (that's a very crude description, but hopefully conveys the essentials). The idea I saw was proposed as a method of providing rapid-build shelter in disaster zones ( eg Earthquake and similar). I don't recall what became of the idea I saw on TV, but wish you luck in this project.

hi kris,

the dome you are describing are marketed as monolithic domes, at www.monolithic.com. i visited the factory and showroom in texas. it was very nice, and the president, david, talked to me for about an hour. he was kind enough to listen to what i wanted to do (back then). he made several recommendations that made a lot of sense.

as in anyway of doing things, there are a thousand different ways. after i got a quote from them, i then had a target to shoot at, to try to reduce the cost and also to eliminate the polyeurethane foam that is integral to their design. they do it two ways. one from the inside out (the one you described) and the other from the outside in.

anyway you build one, the result is great. since i didn't have the amount of money they wanted to build my dome, i have spent the last year trying to figure out how to do it cheaper, and also, if possible, only with home equipment. i think i have got it figured out now.

thanks again.

joe

Now that is an ultra cool bit of research and linking ! Excellent stuff artbyjoe. You are hereby given some of the Kudus I keep meaning to send STL.

Joe,

If you want a truly spherical dome, and are most comfortable with conventional brick/block laying techniques, or stone masonry, take a clue from Roman arches. These use beveled blocks that build upward toward the top from two sides, with a keystone at the center. Construction of such arches requires they be brace until the keystone is inserted, then the brace may be removed. Your spherical dome would simply be a Roman arch revolved 360°.

To use blocks nearly cubic with about 1 foot per side, I have worked out approximate values for the radii and angles of the sides. Firstly, the OUT side of the block must have a spherical radius (identical radii in both horizontal and vertical planes) of 20 ft. If you don't mind a mega-faceted structure, or if your outside coating can tolerate varying thickness, you could just leave this flat, but tilted in 1.5° from vertical. The bottom of the block will be flat, but the top must be sloped 3° downward from the OUT side surface to the IN side surface. The IN side surface, like the OUT side, should also have a spherical radius, but the radius should be 19 ft. This gives your block about one foot of length on the bottom and top surfaces. Like the OUTside, you may choose to have a mega-faceted inside wall, but in that case, it should be parallel to the outside wall. If you do use spherical radii for inside and outside, they should be concentric. If you use a radius on one and a flat facet on the other, be sure that the chord or the spherical surface is parallel to the flat facet of the other.

OK, take a breath. Got all that? This stuff ain't easy, you know!

Now, we have determined 4 of the 6 sides. The last two, what I will call the "ends", as if a cube had ends, more like the ends of a brick, because they will be the connecting surfaces, will, like the top and bottom, be slanted inward, but this time the included angle between them is in the horizontal plane, NOT the vertical plane as before. Also this angle must vary, depending on which layer the block is intended for, as the number of blocks required for each lay will diminish as you get near the top. For the first, or ground, layer, 125 blocks of one foot length (actually 1'-1/16" for almost perfect fit, without any mortar between blocks), measured with a tape along outside bottom edge, will be required. On this layer the blocks must have an included angle of about 2.88 degrees, or 1.44 degrees per side off of the centerline.

I did not work out all of the successive layers (30 altogether), but the last one, inserted almost vertically, would need 15 whole and one partial block (or 16 slightly smaller blocks), with an included angle of 22.5°, instead of 2.88 degrees. Therefore, either you must have the capability bevelling one or both of the ends, or your form must be adjustable so that the ends can be cast at different angles for each layer. Otherwise, you will need 30 molds. Also, each layer will have a different number of blocks, making it almost impossible to line up half-block offsets between layers as in the standard bricklaying technique.

Lastly, the center hold can either be brace with a steel hoop, approximately two feet across, or be fitted with a custom shaped window or keystone that is 1 ft thick, and shaped to fit the hole. You may also need to brace the walls as they get near the top, depending on how well your blocks fit together and whether the overhung weight can be supported simply by the pressure exerted by the blocks on each level to keep the dome from collapsing inward.

I hope all of this made sense. Any questions?

OK Joe,

I started building your dome for you, in Solidworks, anyway. It's a little crude, but I think you will get the idea. As I said before the first layer has 126 blocks. Then, rather than go layer by layer, I stacked up several blocks on each other, than arrayed them equallly until the top layer just touched, which was 117 blocks. On this model the in-between layers will show gaps, but in real consctruction you will just put the correct number of blocks in each layer. Somewhere on each layer, the last block must be only a partial block, unless you want to leave gaps between. You could easily do this by varying the mortar thickness, assuming you would use mortar.

Anyway, that's about all I am going to do, so enjoy!

Hi Kris

Not only Alice Springs Mate. If their housing would be created by the CR4 crowd they would be much better off. I once had the idea to supply/establish sand hills to outback communities. 10 feet high. These would be shaped to taste (by trades people) and covered with ferro cement and using the obvious tools. The sand was then removed from the created shape and used for landscaping. Mixed with mulch to start a garden. The slab was put in afterwards. So were windows and doors.

Nothing came of it. It was simply to cheap. Nothing in it for the middle man. Long live ferro cement. Cutting blocks seems to be a bit like splitting hairs. All the best. Ky.

Hey Ky, nice to see ya ! This thread has some great potential. Cheap or rapid build housing might be very useful. Getting the land and planning permissions are usually the main problems here in the UK, but I bet there are loads of ingenious methods that could be found within CR4. Down the road from me in Dungeness, loads of nice places have been built from corrugated iron sheet and stuff. You aren't allowed to just go do that anymore, but some of those things have lasted for years (despite a somewhat dodgy appearance). All we need to do is keep the profit taking middle-men at bay. That's probably the hardest bit.

Kris

thank you stl.

i realise that many problems in this are problemsn in conceptualization. it took a friend hours to convince me i couldn't use a square pattern tapered to the center. we did lay it out with starting blocks brick shaped 1 foot high, and 2 feet thick, approx. the layout we use though, we did not change the angles. all blocks have the same included angles, both horizontal and vertical. what changed was just the length of the block to maintain the same number of blocks. this gave us the overlaping brick pattern. it did make for quite small blocks. so at regular intervals, when the block length got to one half of original, i doubled the length of the blocks and started the process over. the offsets of corner to flat didn't seem to bad. especialy since i am spraying both inside and outside, the offsets will not show visibly.

the beveled blocks, is exactly what i have in mind right now, with a keystone cap. also, we figured out that we could mold in trough form, and just cut the blocks to length, cutting on the included angles.

the only difference we use from what you describe, is that we used no square corners except on the outside and inside, which are rectangles. the other 4 surfaces have equal bevels. pointing towards the center.

does this make sense? also, on my last post, i descirbed the blocks as weighing 15 pounds per square foot, obviously i ment per cubic foot.

My mind keeps wanting to cheat the design. I am imagining A traditional arch 30' or so wide by a similar height. Now the same intersecting so you have an arch cross. And now a third of same at 45° bisecting the 2 previous. Then a fill for the curved triangles not captured by the 3 arches.

I actually like it so much I might begin some serious sketching as I am in the market for a home.

I saw the link to the dome in the Texas hill country and must say I found it to be quite unappealing to my tastes.

There should be no problem making all the blocks identical:-

This is on a half inch grid: the outside (left) is a 1 foot square and the inside (right) is 10.80 inches square. If you built your bottom circle with these and raised the inner edge by 0.6 of an inch the "real" base of the perfect hemisphere would be "half way up" the bottom tier of bricks.

Note this allows no thickness for glue/mortar. You'd need to make about 250 allowing for cut bricks. The outer diameter is 20 foot (inner 18 foot).

Also note that STL has started to build a dome with a 20 foot radius not diameter.

I've slept on this and re-considered. You do need to change the shape as you move up the tiers unless you go for a geodesic design. So it looks as though you're back to Pentagons and hexagons with a fairly "high frequency" (see post #12) dome. You'll need three brick shapes (pentagon, hexagon and half hexagon) unless you can cut or "bury" half hexagons.

Buckminster Fuller rules I guess.

"the only difference we use from what you describe, is that we used no square corners except on the outside and inside, which are rectangles. the other 4 surfaces have equal bevels. pointing towards the center."

Joe,

I did not use square corners either. I used a 3 degree angle between top and bottom, which would give side corners of 88.5 and 91.5 degrees, basically a tipped over regular trapezoid. As I said, the outside and inside could be flat, if you don't mind a faceted wall, but as long as you are molding the parts anyway, why not use a spherical surface?

You may certainly change the length of the blocks so you get the same number in each layer and overlap at the centers, but what does that get you? I think you will find that you will have a lot more waste by the time you are done, if you have to cut the 1 foot blocks to size. And the top layers will be extremely small.

Yes, it looks like I goofed on the 20' diameter (not radius, as I used). I misread the question, thinking you had specified a 20 ft. height, which would also be the radius of a dome.

Also, even if you use shorter blocks, if they are to fit together with either no gaps, or with parallel gaps (for mortar) you must change the angle of the surface where the blocks join. If you do not, when you fit the blocks together at their inside corners, you will leave larger and larger gaps on the outside. If that is acceptable, then go ahead.

Good Luck with your project. Keep us posted on this thread how it is going!

Well AbJ, I think these guys have you pretty well covered, but I thought I would add just a note. If you are going to build a form or forms to make your 3D trapezoid, with either a faceted or curved face, you could just as easily make some positioning and locking fixtures to hold the blocks in place while the cement cured.

Adding these features would now give your blocks a top and bottom, left and right, but they would have much stronger joints in the end due to the increased bonding area and be inheritantly more stable during your stacking.

Please keep us informed of your progress, your project is very interesting. Is your process for the lightweight, insulative concrete, available on the web, or is this more of a secret. Any idea on what the straight R-value is?

Thanks for your post.

hello greenshoes,

i also find it very interesting. no it is not a secret how to make it, but i am also not sure if the pocess is patentable. so i would like to hold off a little. there are many lightweight concrete aggregates on the market. examples: polystyrene balls, foaming agents, compressed air, vermiculite, perlite, expanded clay. i just happened to stumble upon one that industry is not using, that i think will work better than all of the others. it is a common, over the counter material. most of what industry is using is for large batches, using heavy equipment, and expensive aggregates. i went looking in the other direction for something that would work without all of that. of course i had to give up all thoughts of structural strengh. the nearest product to what i am making is "autoclaved aireated concrete". i have no idea what the r value will be. i do know that the concrete will be 95 percent air.

The University of Missouri-Rolla, shortly to be re-named Missouri University of Science and Technology, has done extensive research on alternative concrete materials, including using glass and ceramic micro-spheres. Because of the inherent compressive strength of the spheres (as opposed to polystyrene or other air entrapping materials) very little strength is lost in reducing the weight of concrete. Since a large part of the strength of a dome is required just to hold up its own weight, let alone any external loading (snow, wind, maintenance workers and equipment, etc.) this becomes very important. The cost might be somewhat higher than other materials, but the increase in strength should offset the cost by allowing proportionally lower volume of material, perhaps even using material saving voids as standard concrete blocks use.

thank you stl,

i had read about using glass and ceramic spheres. i didn't go that direction because of weight. imagine, or take a guess at what a cubic foot of them weigh. i would bet that a cubic foot of air would weigh a lot less. also, the smaller the spheres, the heavier per cubic foot. the romans were the first to do this. to lighten their concrete, they made small clay jars, capped them with tar and placed them in their constructons as the cement was wet and going up in layers. they also used cat tails as rebar. you can still see this construction showing in their aquaducts where the plastering has flaked off. of course they also didn't use portland cement, they used tuffa and roasted limestone. still standing 2,000 years later. well, enough trivia. well may be not. how about the ultimate trivia question? what is the orgin of the word trivia.

what is the orgin of the word trivia.

Easy, when you know where to look. Merriam-Webster says:

Main Entry: triv·ia

Pronunciation: \ˈtri-vē-ə\

Function: noun plural but singular or plural in construction

Etymology: New Latin, back-formation from Latin trivialis

Date: 1920

AND

Main Entry: triv·i·al

Pronunciation: \ˈtri-vē-əl\

Function: adjective

Etymology: Latin trivialis found everywhere, commonplace, from trivium crossroads, from tri- + via way — more at way

Date: 1589

STL's right. My wife's book on word origins states much the same:

Trivia The derivation of the word trivia comes from the Latin for "crossroads": "tri-" + "via", which means three streets. This is because in ancient times, at an intersection of three streeets in Rome (or some other Italian place), they would have a type of kiosk where ancillary information was listed. You might be interested in it, you might not, hence they were bits of "trivia."

it also had another meaning, which was: where did you learn that? at the trivia. or streetcorner, where everybody hung out, because you could see what was happening up and down the streets.

Not to be argumentative but; 'at the trivia' is referring to the location of the kiosk, as previously posted in the vaguely cited statement above.

cr3

Gotta be easier out of timber... Willow is good too. The incredible curves inside Casa Batllo in Barcelona were done with plaster over willow I believe.

(I implore people...don't go to Disneyland...go to Barcelona...The number of Brits can ill afford it yet are stupid enough to spend a small fortune to go to the USA and what do they see?...bloody Disneyland! If they really must go...why not see the grand canyon? The everglades?...who was said you'll never loose money underestimating the public's taste?...whoops sorry...bit of a rant)

Concrete seems singularly inappropriate.

I think a lot of concrete spread thickly over Calais* would be excellent ! A terrific air base could be made.

I was going to say Okefenokee, but I prefer Americans and 'gators would be up in arms.

Oak is between about £10 and £40 ($20 and $80) per cubic foot; Joe is aiming at $4000 dollars for the whole structure. I think he'll be struggling, but he'd stand no chance with a timber frame.

Think thin and light (preferably outside the box...or igloo)..... doesn't have to be oak.

$4000 ! Should be plenty...or does this thing have to meet loads of building regs?

I was assuming it was just a fun structure in the garden?

Maybe a Native American could help with a practical design...?

Del

hi guys (randell and del the cat)

glad you guys are still talking about it. i repeat, i am in an extreme fire zone (forested ridge top at a gap), with hurricanes. yes, i could build light out of wood, but then the first time a fire went thru, i would be just like all of my neighbors, down at the red cross shelter, wondering how to start over again. the $4,000 number is for a 20' diameter concrete dome on a concrete slab. that is for shell only. also this dome is to prove out my concepts. after it is proves out, i am putting up a 60' diameter dome, up on the view spot, with a view for a hundred miles. my estimate to build that shell is $30,000, again with a slab floor. when i talked to a dome builder, he quoted me $181,000 US. $108,000 if i trunkated the dome to only 21 feet in height, by cutting 9 feet off of the bottom of the spherical dome. he charges $32 per surface square foot of dome. i can achieve those low prices by using a new cement called "grancrete". it is very pricey. 4 times the cost of regular cement in the same size sacks. also, because it doesn't have any gravel or rock in it, i have to use twice as much cement er yard, so the price differential is actually 8 times. the difference is that the grancrete doesn't need any heavy equipment to build it. you can literaly spray it on in 1/8 inch layers, and they bond, without cold joints, and are waterproof. also because it is 7,000 psi cement, i can use thinner wall thickness than shotcrete with regular shotcrete cement, which is only about 2,500 psi

sounds ideal for ferrocement boats etc.

FAQ says aggregate can be added.

Is Grancrete™ a liquid, gel, or loose grout?
Grancrete™ is a fine powder material with fibers in the mix. All that is required to use it is water . Aggreates may be added

If you want to go with some type of concrete design and potentially make many domes, doesn't the matter boil down to designing a good form-work ? Some type of easily assembled and re-used thing. Simply bolt the thing together, spray/pour concrete and then wait for it to cure before dis-assembly and the next job. Capital cost might be high, but with multiple usage....

Joe,

I am confused. Are you still planning to build a layed block structure, or is this grancrete to be used with plywood forms and reinforcing wire and rebar, like the "tilt-a-wall" or "tilt-up" construction where you form large pieces horizontally then "tilt" the wall or dome section up into place using a hoist? I don't know if this technique has ever been used for a dome before.

OR, are you planning to build a wire/rebar frame in place over a built in place form and spray the grancrete over this mesh?

Perhaps a little detail on your planned construction technique would help us understand and advise better.

See post #11

http://cr4.globalspec.com/comment/134093/Re-igloo-perfect-block-shape