Spherical (dome) houses: designs, layout features. Horses, Mangup, Crimea - my way Calculation of the dome online
This article is a translation of a foreign article about the construction of a dome frame for a greenhouse with your own hands. The unnecessary stuff has been removed, only the technical part is left. Using this information, you can apply these calculations to build a domed greenhouse or home with your own hands.
When it comes to gardening in cold climates, a greenhouse is always a must. It extends the growing season and gives the plants much more heat. When choosing a greenhouse design, the interesting option “Dome House” was chosen.
Factors in favor of using a spherical shape are:
- Interesting, lightweight design;
- Stable against wind and snow loads;
- Optimal light absorption;
- Largest area;
- Intriguing appearance.
How to build a spherical structure
Our example will show how to build a spherical structure.
Materials to use
- Raw lumber (spruce) is used, painted before assembly.
- Screws.
- Coating. Greenhouse clear plastic is used, but the dome can also be covered with shrink wrap, polycarbonate or Solawrap™ foil.
- Automatic window openers and hinges for doors and windows have been added to the design.
To calculate the elements of the dome greenhouse was used. The density of structural elements can be 2B, 3B, 4B. A smaller dome may have a lower density. For the 18' design, a density of 3B was selected. If more than 18', then it should be 4V. Keep in mind that the width of the dome will be half the height.
There is some problem with the 3B dome. The fact is that the red spacers at the bottom, as shown in the diagram, are 2.777% larger than all the other red spacers. Most calculations found on the Internet do not take this small adjustment into account and end up with an uneven base. Of course, you can level the base, but it is much easier to adjust the length of the 10 red posts, all the intermediate pentagons.
Why was 3B chosen, although this is a more complex option? There was space on the site for an 18-dome. Since, a size of 2B will make the triangles too large and too small with 4B. If you want to avoid the problem of 3B dome alignment and have space to spare, choose a larger size design with a 4B density! After drawing up the plan, you need to print it in color for guidance on the construction site.
Construction tools
- Measuring tape;
- Square;
- Pencil;
- Protective glasses;
- Drill;
- A circular saw;
- Level.
Preparation of structural racks
The key to successful construction of a geodome is the accuracy of the calculation of the racks (all further calculations are carried out in the metric system). Here's an example:
The figure shows:
- Alphabetical index of racks;
- Number of racks of this type;
- Numerical designation of the size of the vertices to which the edges adjoin;
- The value of the flat angle to the plane of the outer edge;
- The value of the dihedral angle between the outer edge plane and the cutting plane;
Three-dimensional representation of the rack end in 3D
Ready-made geodesic dome struts
A 0.3 m high retaining wall has been built. Some make supporting walls up to 3 meters high.
Let's start assembling the greenhouse. The process is similar to a Lego game on a larger scale. The posts are attached and held in place with screws as shown in the picture below. We recommend pre-drilling all holes, this will prevent the wood from splitting.
The upper part of the greenhouse is assembled on the ground and installed as a single unit. It is a bit difficult and requires the help of several people.
How to cover a dome
Coating is difficult due to the shape. It also calculates the size of edges well, which is especially important for better greenhouse coverage.
Doors and windows
The door is mounted directly in the pentagon, as shown in the picture, it has two vertical posts, like jambs, and is considered a good solution. This does not interrupt the shape of the dome and works well in winter and rainy conditions. Snow and water just slide off.
The greenhouse has 2 windows with automatic opening. However, if a cooling system is not used, then two windows will not be enough. The door and windows are built from the same studs and covered with plastic.
This is what the finished domed greenhouse looks like:
I assign a lifting arrow and calculate the radius of the dome sphere (Fig. 6). Dome lifting arrowf:
Sphere radius: 
Central angle of a sphere 
defined:
Length of the dome arc in the vertical plane:
Half the length of the arc should be divided by an integer number of tiers of covering panels and the radius of the upper central ring should be selected. I take the length of the shield along the arc of a circle 
in this case, the radius of the central ring according to Fig. 6.:
- compacted after calculating the radial ribs. I determine the number of shields in one tier based on the width of the shield along the support ring 
Number of shields in one tier:
we accept 
Rice. 6. Scheme of the rib - annular dome.
The dome is assembled from three types of trapezoidal panels manufactured at the factory. The design elements of the dome are:
Radial ribs;
Intermediate rings;
Support ring;
Shield width: 
Collection of loads on the dome.
Vertical direction loads are determined by the formula:
Directed downwards;
Directed upward;
Where 
- standard value of the average component of the wind load in height: 
According to intropolation for type B terrain, the coefficient taking into account the change in wind pressure with height has a value of K = 0.770.
Where 
- for the III district; 
(clause 6)
- the “-” sign is taken into account by the direction of the wind load on the coating.
Horizontal loads on the top of the tank (0.4N) take into account:
Loads causing compression of the dome support ring in the form of active wind and vacuum pressure are determined by the formula:
Where 
. The K coefficient is at its best
Loads causing stretching of the support ring;
wind slope and excess pressure according to the formula:
The vertical concentrated load at the intersection of the radial rib with the ring is determined by the formula:
For the 1st ring, with 
Upward:
Downward:
For the 2nd ring, with 
Downward:
Upward:
Calculation of the radial edge of the dome.
The most stressed will be the radial rib between the support and second rings. The design diagram of the radial rib is shown in Figure 7.
Let's find the angles of inclination of the tangent with the X axis at the levels of the support ring ( 
) And 
2nd ring according to the formula:
;
Rice. 7. Calculation diagrams of the radial rib of the dome for loads:
a – horizontal; b – vertical; c – local.
;
.
.
Let's calculate 
at the level of the first ring at 
.
For a supporting radial edge, the average angle of inclination of the tangents is:
;
the same for the edge between the second and first rings:
.
A certain vertical load on the supporting radial rib is:
;
.
Longitudinal compressive forces in the support rib:
;
;
, Where 
The total longitudinal compressive force in the supporting rib is determined by the formula:
Let's find the greatest value of the bending moment in the supporting radial rib from the distributed load (Figure 8):
Left ground reaction:
Rice. 8. Scheme of loading the support rib with a distributed load.
Let's find the position of the section with the highest bending moment using the formula:
Where 
.
Maximum bending moment value:
I construct radial ribs from two rolled channels (Figure 9), from steel grade VSt3ps6-1 ( 
). The rib works in compression with bending, i.e. for eccentric compression.
Rice. 9. Section of a radial rib. Channel No. 30.
I believe that the flooring is welded to the radial and transverse ribs of the shields, thereby ensuring the stability of the ribs. Therefore, I will rely only on strength for the radial rib. I use channel number 30 () and check the radial rib for strength using the formula: 
;
I check the accepted cross-section of the radial rib for a different combination of loads ( 
And 
), causing stretching.
Longitudinal tensile forces in the rib:
;
.
Distributed loads:
;
Since the intensity of the distributed load directed upward is less than the intensity directed downward, the tensile strength test of the rib should not be carried out.
Let me clarify the radius of the central ring 
from the condition of fixing in it the radial ribs of the shields from two channels No. 30 ( 
). Considering that the width of two channel flanges 
; intermediate rib thickness 
; gap 5mm; the width of the rib support will be 
., then the radius of the central ring: 
.
The length of the shield of the upper tier of the dome will be:
.
The radial ribs of the shield radii experience lower loads: 
etc. Therefore, it is possible to leave the cross-section of the radial ribs constant from two channels No. 30.
The geodesic dome is calculated according to a given radius (base surface area), in order to obtain:
- Estimated sizes of ribs and their number
- Number and type of connectors required
- Angle values between edges
- Required height, total building area
- Dome surface area
Dome base area calculated according to a given radius S=π *R 2 . It should be taken into account that the actual area will be somewhat smaller, due to the fact that the radius of the dome is usually calculated along the outer surface of the hemisphere (along the “vertices”), and the walls of the dome also have a certain thickness.
Geodesic dome height is determined by a given diameter, and for an even splitting frequency it can be 1/2, 1/4 of the diameter (at a high frequency it can be 1/6, 1/8). For odd - 3/8, 5/8 of diameter (etc.).
| 4V, 1/4 sphere | 4V, 1/2 sphere |
Surface area of a geodesic dome calculated using the well-known formula for calculating the area of a sphere S=4π *R 2 . For a dome equal to 1/2 of a sphere, the formula will look like S=2π *R 2 . In a more complex case, when we are talking about the area of a segment or sphere, the calculation formula is S=2π *RH, where H is the height of the segment.
Calculation of structural elements of a geodesic domeThis can be done using ready-made tables that specify:- The number of dome ribs of the same length is ribs A, B, C, D, E, F, G, H, I. A dome with a frequency of 1V has one rib - A. A dome with a frequency of 2V has two ribs - A, B. A dome with a frequency of frequency 3V three edges - A, B, C. Etc.
- The number and type of connectors used are 4-terminal, 5-terminal, 6-terminal.
- Factors for converting the lengths of the dome ribs to the radius of the dome. For example, if you want to build a dome with a frequency of 2V, a height of 1/2 and a radius of 3.5 meters, you need to multiply the radius value (3.5) by a factor of 0.61803 to determine the length of edge A, and multiply by a factor of 0.54653 to determine the length of edge B. We get: A = 2.163 m, B = 1.912 m.
1V dome
| Ribs | Odds | Quantity |
| A | 1.05146 | 25 |
| 5-pin connector | 6 | |
| 4-pin connector | 5 | |
2V dome
| Ribs | Odds | Quantity for 1/2 |
| A | 0,61803 | 35 |
| B | 0,54653 | 30 |
| 4-pin connector | 10 | |
| 5-pin connector | 6 | |
| 6-pin connector | 10 | |
3V dome
| Ribs | Odds | Quantity for 3/8 | Quantity for 5/8 |
| A | 0,34862 | 30 | 30 |
| B | 0,40355 | 40 | 55 |
| C | 0,41241 | 50 | 80 |
| 4-pin connector | 15 | 15 | |
| 5-pin connector | 6 | 6 | |
| 6-pin connector | 25 | 40 | |
4V dome
| Ribs | Odds | Quantity for 1/2 |
| A | 0,25318 | 30 |
| B | 0,29524 | 30 |
| C | 0,29453 | 60 |
| D | 0,31287 | 70 |
| E | 0,32492 | 30 |
| F | 0,29859 | 30 |
| 4-pin connector | 20 | |
| 5-pin connector | 6 | |
| 6-pin connector | 65 | |
5V dome
| Ribs | Odds | Quantity for 5/8 |
| A | 0,19814743 | 30 |
| B | 0,23179025 | 30 |
| C | 0,22568578 | 60 |
| D | 0,24724291 | 60 |
| E | 0,25516701 | 70 |
| F | 0,24508578 | 90 |
| G | 0,26159810 | 40 |
| H | 0,23159760 | 30 |
| I | 0,24534642 | 20 |
| 4-pin connector | 25 | |
| 5-pin connector | 6 | |
| 6-pin connector | 120 | |
The geodesic dome is calculated according to a given radius (base surface area), in order to obtain:
- Estimated sizes of ribs and their number
- Number and type of connectors required
- Angle values between edges
- Required height, total building area
- Dome surface area
Dome base area calculated according to a given radius - S=π *R 2 . It should be taken into account that the actual area will be somewhat smaller, due to the fact that the radius of the dome is usually calculated along the outer surface of the hemisphere (along the “vertices”), and the walls of the dome also have a certain thickness.
Geodesic dome height is determined by a given diameter, and for an even frequency the division can be 1/2, 1/4 of the diameter (at a high frequency it can be 1/6, 1/8). For odd - 3/8, 5/8 of diameter (etc.).
 |
 |
| 4V, 1/4 sphere | 4V, 1/2 sphere |
Surface area of a geodesic dome calculated using the well-known formula for calculating the area of a sphere - S=4π *R 2 . For a dome equal to 1/2 of a sphere, the formula will look like - S=2π *R 2 . In a more complex case, when we are talking about the area of a segment or sphere, the calculation formula is S=2π *RH, where H is the height of the segment.
Calculation of structural elements of a geodesic dome can be done using ready-made tables that specify:- The number of dome ribs of the same length is ribs A, B, C, D, E, F, G, H, I. A dome with a frequency of 1V has one rib - A. A dome with a frequency of 2V has two ribs - A, B. A dome with a frequency of frequency 3V three edges - A, B, C. Etc.
- The number and type of connectors used are 4-terminal, 5-terminal, 6-terminal.
- Factors for converting the lengths of the dome ribs to the radius of the dome. For example, if you want to build a dome with a frequency of 2V, a height of 1/2 and a radius of 3.5 meters, you need to multiply the radius value (3.5) by a factor of 0.61803 to determine the length of edge A, and multiply by a factor of 0.54653 to determine the length of edge B. We get: A = 2.163 m, B = 1.912 m.
1V dome
2V dome
 |
| Ribs | Odds | Quantity for 1/2 |
| A | 0,61803 | 35 |
| B | 0,54653 | 30 |
| 4-pin connector | 10 | |
| 5-pin connector |
6 | |
| 6-pin connector |
10 | |
3V dome
 |
| Ribs | Odds | Quantity for 3/8 | Quantity for 5/8 |
| A | 0,34862 | 30 | 30 |
| B | 0,40355 | 40 | 55 |
| C | 0,41241 | 50 | 80 |
| 4-pin connector |
15 | 15 | |
| 5-pin connector |
6 | 6 | |
| 6-pin connector |
25 | 40 | |
4V dome
 |
| Ribs | Odds | Quantity for 1/2 |
| A | 0,25318 | 30 |
| B | 0,29524 | 30 |
| C | 0,29453 | 60 |
| D | 0,31287 | 70 |
| E | 0,32492 | 30 |
| F | 0,29859 | 30 |
| 4-pin connector |
20 | |
| 5-pin connector |
6 | |
| 6-pin connector |
65 | |
5V dome
| Ribs | Odds | Quantity for 5/8 |
| A | 0,19814743 | 30 |
| B | 0,23179025 | 30 |
| C | 0,22568578 | 60 |
| D | 0,24724291 | 60 |
| E | 0,25516701 | 70 |
| F | 0,24508578 | 90 |
| G | 0,26159810 | 40 |
| H | 0,23159760 | 30 |
| I | 0,24534642 | 20 |
| 4-pin connector |
25 | |
| 5-pin connector |
6 | |
| 6-pin connector |
120 | |
A greenhouse at the dacha has long become not only a help in growing vegetables, but also an opportunity to realize one’s creative ambitions. Among all the innovative solutions, the geodesic dome, the brainchild of modern architecture, deserves special attention. The interest in the original design is explained simply - even an inexperienced craftsman can install such a greenhouse on his site - the hemisphere is easily assembled from simple parts, and the productivity of its beds is not inferior to the yields from standard structures.
Geodesic dome - beautiful, practical and simple
The growing popularity of domed greenhouses is due to several factors:
- Installation does not require a solid foundation, since its design is much lighter than conventional shelters of similar size.
- The structure is easy to assemble and disassemble, and if necessary, it is easy to move it to a new location.
- The hemispherical shape is highly durable and stable. The cellular frame better withstands strong winds, easily withstands snowfalls and has good earthquake resistance.
- Compared to traditional forms of shelters, the construction of a dome greenhouse is cheaper, since complex equipment is not required for installation. Simple available materials are used in construction - wooden blocks or plastic tubes for the frame, screws, polycarbonate, agrofibre or greenhouse film for cladding.
- Due to the unique sectional structure, there is no need to install internal supports, and this significantly saves building materials.
- Unlike rectangular greenhouses in a hemisphere, there is no need to orient the beds relative to the cardinal points - the plants are always well lit.
In the geodome it is easy to provide the necessary microclimate for growing several crops of garden crops per year. The soil always warms up well, and to maintain temperature stability, environmentally friendly heat accumulators - water tanks - are used.
In winter, the geodome can withstand even heavy snowfall
How to build a dome greenhouse yourself
It is not difficult to build such a structure on your site. To do this, you will need to calculate the dimensions of the sections, print out the assembly diagram, prepare the frame parts, clear the space for installing the greenhouse, and you can begin installation.
Options for dome greenhouses
Principles of designing a dome frame
At their core, all geodesic domes are polyhedra, the faces of which form a surface that is as close in shape as possible to a sphere. The shape of the edges may be different, but the triangle is considered the most stable and stable. Therefore, in most cases, the main structural element for creating a hemispherical frame is a triangle.
Triangular sections - the basis of a streamlined and stable frame
For the construction of the frame of small domed buildings in summer cottages - greenhouses, gazebos, guest houses - frame-panel technology based on isosceles triangles of different sizes is most often used. The smaller the size of the sections, the more of them will be needed to create a spherical greenhouse. The principle of connecting them together is similar to sewing a soccer ball - the triangles are connected into convex hexagons and pentagons, which are combined into a stable hemisphere.
Advice! If the connection angles of the fragments were not taken into account when calculating the geodome, then installation is best done using connectors with 4, 5 and 6 blades.
Formula for calculating the length of the dome elements
In order not to make mistakes during the assembly process, you need to calculate in advance the length of all the ribs, the correct sequence of their alternation, and the angles at which the elements are connected. To draw up an optimal scheme, it is necessary to use special formulas. The calculation of a geodesic dome is based on specific dimensions:
- radius of the base of the structure;
- height of the greenhouse (expressed as a fraction of the diameter of the sphere, H);
- sectioning frequency (V).
Wooden blocks for installation
The higher the numeric index V (1, 2, 3...), the more types of edges will need to be prepared. Dome 1V is a truncated icosahedron, all edges are the same length. This structure is more like a pyramid with five sides. For the construction of a home greenhouse, domes 2V (two types of ribs, H = radius) and 3V (ribs A, B, C, height of the structure H = 5/8, 7/12, 5/12 diameter) are best suited.
The length of each type of ribs (La, Lв, Lс...) is calculated using the formula L=R*K, where R is the radius of the base of the frame, and K is the coefficient of splitting frequency.
Odds table
To calculate the required amount of material for cladding, use the formula for calculating the area of a sphere: S=2π *R*H, where R is the radius of the base, and H is the calculated height of the greenhouse. For example, with a radius of the base of a 3V greenhouse of 4 m and a height of 3/8d, the calculation of the area will be as follows:
S=2*3.14*4*(3/8*8) = 75.36 m2
Preparing for frame installation
When building a geodesic dome with your own hands, you need to choose a light and durable material for the frame - wooden blocks, lightweight metal rods or plastic pipes. It is better to impregnate wooden blocks with an antifungal compound before painting. When preparing fragments, it is extremely important to maintain accurate markings - all parts of the same type must be interchangeable.
Advice! Paint ribs of the same length with the same color. For example: ribs A are red, B are blue, C are yellow. To make it easier to work with the color assembly diagram, the markings of the finished ribs should match the markings on the drawing.
The number of fins by type and connectors for mounting each type of dome is calculated according to the diagrams.
Field work and foundation installation
To install a geodesic dome in your country house, you must select an open, unshaded area. Fertile soil can be temporarily removed from the site, and the surface itself can be covered with clay and carefully leveled and compacted. If the soil is unstable, then you will have to pour a small foundation under the base or drive support piles under each corner of the base (the shape of the figure follows the outline of the bottom row of the diagram - a ten-, eight- or dodecagon).
The height of the base depends on how the building is intended to be used - for a light summer greenhouse 15-20 cm is enough, and for a winter greenhouse with warm beds it is better to raise the walls by 50-70 cm. The base is usually made of thick timber or wooden panels. A low temporary structure can be installed directly on bricks or stones laid at the corners of the bottom row of the frame.
Installation of the dome greenhouse base
Assembly and covering of the frame
It is better to assemble the structure from the bottom up, connecting the ribs with connectors or screws in accordance with the diagram. It is more convenient to assemble the top of the dome on the ground, and only then attach it to the frame. It is better to install such a “construction set for adults” with an assistant - it is more convenient to fix the parts. To enter during assembly, a door frame is inserted instead of several dome elements.
Advice! For ventilation, install 2 window frames in the upper part of the dome, made according to the internal dimensions of the triangular element.
The next stage is covering the frame. For these works, a dense transparent material is selected - greenhouse film, polycarbonate or glass. There are several ways to cover a domed greenhouse:
- the finished frame is covered with film on top;
- triangles are cut out of polycarbonate (according to the size of each frame cell) and attached like a mosaic;
- Glass is inserted into the cells of the frame.
After the dome is completely sheathed, you need to check its tightness. If necessary, the joints of the slats and sheathing are additionally sealed.
Greenhouse project with beds
Internal arrangement of a geogreenhouse
The assembly of the geodome with your own hands is completed, it’s time to arrange it inside. Before laying the beds, it is necessary to prepare heating, watering and ventilation systems. Inside the dome on the north side it is necessary to fix a shiny material (foil, metallized film) - this way the plants and water tanks will receive more light and heat.
The temperature in the greenhouse is maintained using homemade heat accumulators - several barrels of water are installed under a reflective shield. The water will heat up during the day, thanks to which the required temperature will be maintained inside at night. The same water can be used for drip irrigation.
Approximate diagram of the internal structure of a geodesic greenhouse
To heat the beds, corrugated pipes can be laid under the soil layer, into which warm air will be supplied.
The pipes are covered with a layer of manure or compost. Warm air circulates through the system under the beds thanks to a fan connected to a solar panel. Additionally, to accumulate heat, several five-liter flasks, also filled with water, can be installed in the center of the greenhouse. In addition to the built-in windows, you can install an automatic ventilation system for scheduled ventilation.
The beds in the domed greenhouse are located around the perimeter.
It is better to make the width of the bed no more than 1.5 m, otherwise it will be difficult to care for the plants. Which garden bed to arrange is a matter of taste. You can build standard ones - up to 40 cm in height, tall or warm, vertical or two-tiered. If the radius of the base is large, a flower bed is usually set up in the center, on which tall or climbing crops are planted.
The beds in two tiers are well lit under a transparent arch
Naturally heated geodesic greenhouses are suitable for growing any crops from early spring to November. With a sufficiently large dome volume and the presence of additional heating and lighting, such greenhouses are suitable for year-round use even in areas with a temperate climate.
As you can see, it’s not difficult to build an original domed greenhouse on your own site. And if we take into account that the costs of its creation and maintenance are somewhat less than for other shelters, then we can safely say that the popularity of such structures will grow every year.