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The most durable construction

Rod tetrahedron

Which geometric solid known to us has the greatest strength? Which is most resistant to external deformations?

 

The tetrahedron (regular polyhedron) forms a rigid, statically definable construction. A tetrahedron made of rods is often used to create spatial bearing structures of spans of buildings, floors, beams, trusses, bridges, etc. 
rigid construction three boards
The rods have only longitudinal loads.
What lies behind the term stiffness?
Stiffness is the ability of structural elements to resist deformation under external influence.
To understand this term, we simplify the problem, move from bulk models to flat ones.
If we take three metal or wooden planks, fix their ends with pins or studs, obtain a triangle, we will see that we will not change the shape of the resulting triangle.
 
 
rigid structure direction of force
A regular triangle, a triangle with which all sides are equal, has the highest resistance to deformation.
 
ot rigid construction direction of force
Plates assembled in the shape of a square may shift after the application of force. Internal corners are changing.
Thus, the quadrilateral (square) is not a rigid figure. That is, it is subject to deformation.
triangle bridge
The sides of a triangle determine its angles uniquely.
Of all the polygons, only the triangle is a rigid figure.
The triangle's property is used in many constructions (bridges, tower cranes, pylons of electric transmission lines).
triangle tower crane
power lines of triangles
Demonstrate the example of a crane jib.
The construction is a sequential combination of tetrahedrons (red) and quadrangular pyramids (green).
The most durable construction
The most durable construction
 
 
 
rafters of triangles
Rafters of buildings have the form of triangles. This gives them strength and stability.
hard triangle in the gate
When constructing a garden gate, a board (board) must be added, sometimes two planks to make triangles. This gives strength to the gate; otherwise, it will soon warp.
 
From practical examples of applying a rigid triangular structure, we return to exact mathematical bodies — the tetrahedron.
The tetrahedron will be considered as a rib construction.
Each of the four sides of the tetrahedron is a regular triangle. Since the rods forming these regular triangles are not subject to deformation all together, these six rods (edges) of the tetrahedron create an extremely rigid structure.
No other solid has such strong characteristics.
 
We suggest you assemble a tetrahedron model of six separate rods (edges).
For assembly, you will need to print the drawing on two A4 sheets. Download nets edge tetrahedron here.
 
First, you need to glue each of the six edges of the tetrahedron.
Then glue the base of the three ribs and consistently paste another three edges to it.
 
1. tetrahedron details
2. collect rib tetrahedron
 
 
3. collect rib tetrahedron
4. collect rib tetrahedron
 
 
5. collect rib tetrahedron
6.rib tetrahedron
We get the edge model of a tetrahedron.
 
Rotation of a polyhedron
 

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