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 as a basis for spatial bearing structures of spans of buildings, floors, beams, trusses, bridges, etc. 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 so as to obtain a triangle, we will see that we will not succeed in changing the shape of the resulting triangle.
rigid construction three boards
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.
This property of the triangle is used in many constructions (bridges, tower cranes, pylons of electric transmission lines).
triangle tower crane
power lines of triangles
 
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, be sure to nail a plank (board), sometimes two strips, so that triangles are obtained. This gives strength to the gate, otherwise it will soon warp.
 
From practical examples of the application of 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 body has such strength 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 edges tetraed 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