Math

I was toying with the idea of a small A-frame cabin-like structure up at the Beta Site. The simplicity appeals to me but the inefficient use of space does not. Obviously, your head room diminishes as you approach the sloped walls. So, what if you wanted, say, eight feet of headroom for a space, say, ten feet wide. How wide would the base of the structure have to be, and how tall would it have to be? Welcome to math.

It’s been a million years since I needed to do trigonometry. Fortunately the internet provides. Threw this into AI, “How wide is the base of a right triangle with a height of eight feet and base angle of 60 degrees“. According to the interwebs, 4.6188 feet for the base of that triangle. Okay, so to get a ten foot wide space that has eight feet of headroom, I’d go 4.6188′ for the left side, add ten feet of space for the middle, and then add 4.6188′ for the right side. Add that up and you get an isoceles triangle with a base of 19.2376′. Lets be grown ups and call it 19.25. Okay, so with an angle of 60* how tall would the triangle be? Back to the interwebs.The answer, it seems, is 16.67 feet.

A bit of a problem there…boards are available at16′ lengths, but they get expensive after that. So, realistically, slightly less than 16′ would be the way to go, yes? That means either the desire for ten foot width, or the desire for an eight foot headroom, will have to be adjusted slightly.

At the moment, I’m contemplating a small A-frame structure that can accommodate a cot, some gear, and a bit of room, so I can have a place to throw out a sleeping bag while I’m working on a larger accommodation and the infrastructure that goes with it…something not too far from this:

Its justa thought for now…another avenue I’m exploring….but it does seem to offer some advantages in terms of ease of construction. More research is called for. And math.

33 thoughts on “Math

    • Cant really price it out until I know exactly what the finished design is going to be. Once I decide on final dimensions, I’ll ‘freeze’ the design and then start doing the accounting.

  1. Quonset hut?
    Straight sides w/ roofing trusses shouldn’t be too hard to build? Could also do salt-style (just a slant). I know you’re cold up there and need pitch for the snow, but… honestly, making roofing trusses is no harder than framing. Then you get 8′ headroom everywhere, and storage above.

    • A slant design might be easier to build and live in. I built a 12×16 shed myself with this design, but only a four inches of slant, and it is still up and watertight after 20 years even with a skylight!

      Most US lumber math works well in 4′ increments so front wall 16′ rear wall 12′ (or 12′ front and 8′ rear) still have the slant for snow melt but only one incline instead of two. Good luck and keep us posted.

    • ^^^^
      THIS

      CZ, you might also consider a weld-up steel frame with 2×6 inset framing. The 2×6 framing because you then use R19 instead of R13 insulation on top of a spray foam closed cell layer.

      Regardless of how you go be sure to use the outer sheathing that is sealed.

      Building and roofing an A-frame is going to be a lot harder than you might think.

    • When I was a kid in the early 50’s, dad got transferred from D.C./Pentagon to Anchorage/Ft. Richardson. Yeah. As a young officer with a pregnant wife and 2 kids the solution to a lack of both civilian housing and officer quarters was a left-over WWII Quonset hut that had been cheaply converted into a rental home taking advantage of the rapidly expanding military presence at Ft. Richardson/ElmendorfAir. (The D.C. bigbrains feared Russian attack because of proximity despite WWII leaving an incapability due to population reduction in Russia.) But Anchorage schools ran on 2 shifts a day. Cheaply converted? I learned it burned down soon after we moved into new officers quarters on post. Oh, and post school classrooms were Quonset huts until replaced with a new real school. But as a family home we lived in it just fine with more space than a mobile home. Conclusion? A Quonset could be superior to an A-frame and very useful for both current needs and easily adapted to suit future needs as they may develope .. . provided you can get one where you want it.

  2. Following. I think the A-frame as an architectural design for a cabin or house is a last century, not a best design, to use any more. It is quaint for those wine and cheese yuppies that have second or third home vacation properties and looks neat-O in pictures and in bragging conversations but that is it. The example photo as a reference shows the footprint and base square footage only then drastically diminishes with the constricting roof pitch to a tiny amount of space for the upper loft, leaving only room up there for a sleeping sarcophagus or gear and junk storage. If constructed robustly enough which is easy nowadays you can have any other type of roof pitch to support a most extreme snow load calculation and not sacrifice losing floor space or second floor loft square footage based upon your blueprint designs. You will be away at your normal job and life so build in that robustness to carry 4 feet of snow sitting on an unheated cabin like dwelling for a period until spring melt or you return for chores or work there. A steel urban security screen door over that door for “bears and burglars” deterrent as well. Plan in the after usage of that as a tool or equip shed etc when your main domicile dwelling is built, an A-frame is not conducive for that unless you want to be a slumlord and rent it out to total stranger living on your property like an air b and b venture. Ha just kidding that would not be cool or wise. Take the time and wargame out designs and best usage researching to maximize materials costs and utility application along with robustness and security features. Good luck it all seems like fun.

  3. The perfect is the enemy of the good. Seems like using 16 foot timbers will give you almost what you want. However, the benefit of the Quonset hut mentioned above is its greater utility as a secondary building after you get the main homestead constructed.

  4. If the reason you’re even considering an “A” frame, is to have the snow load slip off, there’s other ways to achieve that, and still keep a traditional structure, and maximizing space…
    Just design your structure as a simple box design and just have a steep single sloped roof…

  5. Have you thought about erecting your A-frame on a 4 foot knee wall? This would greatly improve the inside height and also add room for closets / storage. The problem with A-frames is that the roof extends to ground level and tends to rot because of moisture and snow.

    • This was to be my suggestion. A 4′ knee wall, the A frame on top of that. 16×16 offers plenty of space, works evenly on materials. Use collar ties on the rafters to make a sleeping loft.

  6. Build a 2 to 4 foot high vertical 2×6 wall around the perimeter and the traditional A-Frame on top of the wall. You can extend the eaves slightly if you prefer the traditional look. It will dramatically increase the useable 7-8 ft headroom inside.

  7. Hello Zero
    Have you thought about a conex?
    We have two in our yard they are not very expensive even if new or used once and clean
    If you are interested I can send you some pictures of how we had a carpenter build a roof on them to keep the snow off the metal roof
    George

  8. Check out the YouTube channel called Bushradical. He’s made dozens of small cabins on his channel in remote areas. Once the main place is finished, it could be turned into a workshop or bunkhouse for the post-shtf co-eds.

  9. CZ have you considered a pre-fab geodesic dome? They have good interior room and variable height to meet your needs. They are well insulated and can be used as storage after or kept as a guest “house”.

  10. This is the reason A frames are only used in snowy environments. Traditional house types, and even barns, are a far more efficient use of floor space.

    It’s up to you, but if it were me I wouldn’t go for an A frame at this point – if you wait for summer, you could probably get a small container or shed in there.
    I’m a fan of containers – cheap, solid, and easy to secure.

  11. CZ,

    KISS.

    Stay away from A frames, quonset huts, Conex boxes (except for storage) blah, blah blah.

    The “world” functions on 2×4’s, spaced at 16″ centers and 8′ lengths for the vertical studs. If you wanted to overkill, use 2×6’s, but I digress. The only exception might be 6″ x 6″ squared timbers for the walls (with chinking). IMHO, it’s still easier to use stick built with 6″ insulation bats, but I digress)

    For the roof, buy factory trusses with a steep enough pitch to withstand “X” pounds of snow load. Not a ‘flatlander’s’ snow load BTW. A decent slope to “shed” the snow when it comes spring time. “A” frames look cute, but you don’t get the usable floor space, that you can stand up in and really use against the walls for things like cupboards and looking out the window……..for visibility.

    Any competent lumberyard has a computer program that can figure all of your required materials out for you. Even, Menards can do that (for big snow country add extra trusses) and use real plywood for sheeting BTW, (not OSB), because Menards also sells in lesser snowfall states.

    Use galvanized metal (or metal roofing) to”shed the snow” when it gets warm enough (to collapse your whole building) by first “kicking the walls out”, because your pitch was not steep enough. For that matter, use one of their “pole barn” blueprints, for a template and beef it up with better trusses and 2×6 walls.

    Also, while you are gone for the winter, brace the trusses from the inside with a vertical post or two, in the event the metal doesn’t “shed”. You sleep better knowing, the walls haven’t “kicked” out, ie, the “load” has been transferred vertically, not horizontally.

    This isn’t rocket science. You don’t need to reinvent the wheel or overthink this.

    It’s been done a million times before.

    Cheers,

    Ben

  12. Aesthetics aside it seems to me like an 8×12 Home Depot shed with a loft would be a really easy solution. Set it up as a lite dry cabin with a cot/ bed, stove, etc. Keep some useful, but not high value items there.

    And in a year or three when you finally build your dream bunker, whatever you can use it as a shed.

  13. Looks like you have trees that are over 4″ diameter inside bark at your desired 16.67′ height. Poles, plywood, insulation, steel sheeting, openings and some siding and you have a rustic guest cabin to rent to air bnb pedo bankers from the big city.

  14. Are you planning on retiring up there or is it just a bug out spot for you…That would determine what kind of structure you should be building in my opinion…

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