Triangles are the building blocks of many structures mainly because of their ability to bear large loads without deformation. They are considered the strongest shape because a triangular structure subject to strong forces only collapses due to material fatigue and not to geometric distortion. It is easier to understand why triangles are so strong when compared to a square or rectangular structure. Consider an equilateral triangle, which is the same as to say that all three sides are of the same length. Each side is connected to the others by a pin that allows rotation but prevents them to separate. If a load is applied to any vertex or side, is is evenly distributed by all sides and, because the sides cannot change length, the shape remains stable. When the same happens to another shape, the forces are applied to the connectors and can make the sides pivot, collapsing the shape. As an example, take an equilateral triangle set on its base and apply a load or force f orce to the top vertex. If this force is vertical, it is distributed by both sides and transmitted to the base. But if this force has a torque or is directed to any other direction, one of the sides is forced to rotate. It can only rotate if the other side increases its length and thus remains in the same position. With an equilateral square in the same conditions, a vertical force does not have any effect, but a torque or imbalanced force causes one side to rotate and because it is not constrained by the fixed length and the angle variation in relation to the base is easily compensated by other segments, the shape can tilt and collapse. Because of these geometrical properties, triangles are used to build strong and indeformable structures, with material strength limits, such as bridges and trusses. A truss is a simple set of triangles sharing sides, and connections. The properties of each triangle are kept and form an even stronger structure. Overall, a triangle is the simplest geometrc figure that will not change shape when the lengths of the sides are fixed. In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.
Regarding point one, this diagram shows how a triangulated structure withstands forces.
Actually, The Mathematical Bridge between between two parts of Queens' College, College, Cambridge also demonstrates a triangulated structure. It is made up of a series of timber tangents joined together to make it rigid.
In architecture, this technique is called tangent and radical trussing. By definition, a truss is a structure consisting of triangular unit(s) constructed with straight members whose ends are connected at joints referred to as nodes. A tetrahedron-shaped base in a flying fox is a simple space truss. It contains six members joined at 4 points. More examples in our city: Bamboo sticks constructed in a tetrahedron shape to f ix the tree in position, preventing it from falling over due to the wind.
The most common form of transport in Cambridge – bicycles – also demonstrates this property. The cycle frame is made of two triangles to withstand your weight. This is an example of a simple truss.
Due to its stability, the "triangular" structure is ubiquitous in our city. To achieve stability, the structure must satisfy this mathematical equation: (where m is the total number of members, j is the total number of joints and r is the number of reactions, e.g. r =3 in a 2-D structure.) Demonstration: In order to test how strong a triangular structure is, we are going to do an experiment.
First of all, we need to accordion fold an A4 sheet of paper.
Use two books as supporters and put the paper on top of them. Now, we put a load on it.
Surprisingly, the A4 paper is able to support two books which are far heavier than its own weight. Some buildings are built with more than the minimum number of truss members required. Therefore, they do not not collapse easily even if some members are damaged.
