Brick Arch.

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Brick Arch.
Hello.
By its design, the classic cylindrical vault of a Russian stove can be represented as a set of parallel arches, and the Pompeian vault as a set of arches strung on a common vertical axis of rotation.
Therefore, if we regularly build arches that do not break, we will automatically learn to create stable arches from them.
Let's create a simple arch of two bricks.
There can be as many of them in an arch as you like, often even an even number without a “keystone”, but this does not change the essence.
The ends of the arch rest on the so-called heels, which are usually also made of bricks.
In practice, it is very desirable to trim the heels of the arches with rubbing against the lower bricks, so do not criticize me for the rudeness of the experiment.
So, the peculiarity of the arches suggests the fact that each element, in this case a brick, puts pressure on the neighboring ones in the places where they touch each other.
Each brick of the arch perfectly resists the compression forces from neighboring stones, and such a structure automatically becomes very strong and stable.
And the more external influence on the arched bricks, the stronger the structure.
But the two lower bricks of the arch put pressure on the heels, which tend to move apart to the sides, creating the so-called thrust in the horizontal plane.
The main vectors of forces on the heels are directed in the direction of the normals drawn to the surfaces of the arc of the arch in the places of its support.
In turn, each of these vectors can be decomposed into vertical and horizontal components.
The vertical component of the vector is easily compensated by the foundation support, but the horizontal component must be dealt with somehow.
Naturally, the steeper the arc of the arch, the smaller the horizontal force vector and the less horizontal thrust pressure will be transmitted to the heels of the arch.
In kiln structures, the stability of heel bricks is often ensured simply by the friction forces of the heel on the support.
And this friction force will be greater, the more force the heel presses on the support and the larger the spot of their contact.
It is not surprising that in a kiln environment the most stable arch shape is semicircular, that is, formed by exactly half a circle.
At first glance, in such a design, the main vector is directed vertically downward, and the horizontal part, therefore, is completely absent.
But in practice, during heating or external forces (for example, you have a bed on top), certain forces will act on the arch and a horizontal thrust force in the heels may also arise, although not at all significant.
If the arch of the stove is arched, that is, flatter and formed by a relatively small segment of the circle, then the situation will only get worse.
And now I’ll say something completely not obvious:
an absolutely flat lintel supported on vertical walls will also create a small pushing force on the walls.
Remember, for any shape of the stove arch we must ensure the stability of the heels and then everything will definitely be fine.
The easiest way is to tighten the heels with a metal pin, as is done in the architecture of old buildings with vaulted and domed ceilings.
This metal connection is called a “tie”.
But in our case, it is impossible for the metal to be inside the firebox or cap, otherwise, when heated, it will lose its main property of resisting tensile forces from the thrust of the heels of the brick arch.
For example, these steel puffs can be placed under the bottom of a Russian stove, isolating the metal from open fire with a layer of bottom brick.
Nowadays, it is common practice to replace the wooden stove with a lower cap, place the flood chamber in the same place, and build smoke channels.
It is obvious that with this design of the stove, the puff now automatically ends up on the floor of the house, and the heels of the brick arches, therefore, move vertically away from the puff by almost a meter.
What does this mean in practice?
The thrust force from the arch remains unchanged, but now restraining the efforts of the moving heels, due to the lack of tightening, will be aimed at tipping the wall.
Here, the overturning moment is equal to the product of the force and the shoulder.
What compensation measures can we take for our brick arch if the heels begin to diverge?
For example, instead of tightening the heels from the inside of a brick arch, you can create additional external support, such as a metal band on top of the finished stove.
If you don’t like it, you can backfill the arch with a layer of brick or sand, as is often done when arranging a bench in the classic designs of Russian stoves.
You can make the outer wall thicker.
Or arrange something similar to buttresses.
Or you can create smoke channels on the sides of the arch and distribute the overturning load on their walls.
Have you seen ancient architecture that looks like the Temple of Jupiter?
Thank you for attention!