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Stacked wood beam pyramid frame Answered

can someone point me in the right direction? i need to find either a tutorial, or the math i need to use for my cuts to make what is in the photo. i have been searching a solid 6 hours, through hundreds of "results" pages. have not found ONE link, not even an image of anything that resembles it. i am 98% sure that the problem is me not being able to word it properly. Please help. Thanks

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I decided to try building my own stacked pyramid, out of cut pencils, to see if the result would look anything like what I imagined it would look like. I took some pictures of the result, and I have attached these to this post.

The first three pictures show the easy case. That is, what happens when I start with a square base, consisting of 4 equal length pieces, and then stack another and another, same length, square base, on top of that, with the "walls" rising vertically.

The result is kind of reminiscent of the vertical walls of a log house. Or maybe it could be the walls of a corral for some very small livestock. Like a My-Little-Pony (tm) or similar.

In the remaining pictures, I show the construction of a pyramid style stack.

First I measure the lengths I want. Then cut. Then stack pencil pieces into something resembling a pyramid.

I decided to cut the pencils (which started with length 7.0, and diameter 0.25, inches) into the following lengths:

1.5 (x4)
2.0 (x4)
2.5 (x4)
3.0 (x4)
3.5 (x4)
4.0 (x4)
4.5 (x4)
5.0 (x4)
5.5 (x4)

These dimensions are in inches. Also because there is a balance of pieces of every length, exactly 4 each of the lengths in the set {1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5}, I was able to cut each pencil exactly once, and have zero scrap pieces left over.

I started the stack, by making a square base with the 4 longest pieces (which have length 5.5) .

Then I used the next 4 longest pieces (which have length 5.0) to build another square base on top of the one below.

Then I build the next square base on top of the one below, and so forth, until all 36 pieces (i.e. all 9 groups of 4 equal length pieces) are all used up.

Of course, the smallest length pieces (length 1.5), are stacked last, on the very tippy-top of the stack.

I am not sure if this structure has a name, but I can tell you where I have seen it before.

The logs that make up the walls of a log house,

https://en.wikipedia.org/wiki/Log_house

are stacked in a similar way. Although, those logs are notched near the corners, so that a wall can be built without large, horizontal gaps.

Actually there is a children's toy called, "Lincoln Logs",

https://en.wikipedia.org/wiki/Lincoln_Logs

which exemplifies this principle, of how the logs fit together, better than actual pictures of log houses.

Anyway, the structure in your picture is more simple, in one sense, because it does not have locking corners.

Actually, have you ever seen a tower of Jenga blocks? That is another children's toy.

https://en.wikipedia.org/wiki/Jenga

Actually, it might be a suitable example if you consider the special case of a Jenga tower with exactly two bricks in each layer, and for which each layer looks like a right angle rotation of the layer below it.

Each layer just consists of two logs, parallel to each other.

Also each layer looks like a right angle rotation of the layer below it.

Example: The first layer consists of two logs, parallel, pointing in a north-south direction. The second layer consists of two logs, parallel, pointing in a east-west direction. The third layer is two logs, pointing in north-south direction. The forth layer, has the logs pointing east-west, and so on. The odd numbered layers have their two logs pointing north-south. The even numbered layers have their two logs pointing east-west

It might be instructive to get a box of wooden pencils, or disposable chopsticks, or square sided wooden toothpicks, and build something resembling a log cabin, in exactly this manner.

Of course the structure in your picture has an important difference, and that is the lengths of the two sticks in each layer seem to be getting shorter as the layers increase.

So that after some number of layers, the length of the two sticks has decreased to almost zero, and the overall effect is pyramidal, like the area of each layer has shrunk to a single point at the top, or approximately this.

You mentioned math. Do you want me to estimate the rate at which the layers, in your picture, are shrinking? Another way to express this is simply the difference in length, from one layer to the next.

I don't want to give away the surprise, but I expect it is a constant length difference, from one layer to the next.

I mean, armed with that knowledge, of how long each stick is supposed to be, I think you would be ready to start cutting sticks, or wood pencils, or chopsticks, or whatever material you plan on using for your prototype.

You might not have found something because you are overthinking the problem ;)
A pyramid is nothing more than a square base with four triangle on top ;)
Simply make a scale drawing on paper.
E.G.: If you want a pyramid that 1 meter wide at the base and 1.2 meters high, draw a triangle of 10cm at the base and 12cm in height.
Make a nice 1:10 scale for measurements.
Assuming you follow logic and select suitably sized wood of lets say 5cm high by 4cm wide and whatever lenght the hardware store has:
Draw lines parallel to the base with a distance of 5mm inside the triangle.
Base line for example make the measurements for the back and front of the first stick, second line for the first stick on the sides.
Then work your way up ;)