Why are triangles such a strong shape to build with?
In: Engineering
if you have another shape like say a square you can squish it without changing the lengths of the sides, only by pivoting the corners. but a triangle is fixed, you cant deform it without changing the length of its sides. most materials are strongest under compression or tension with the weak points being the corners of the shape bending. if the corners cant bend without the sides changing length then you get all the strength of the material whilst minimising its weaknesses.
Basically its the fewest internal angles that a shape with straight lines can have, and you cant move any of the points without also either compressing or stretching one of the lines.
Two main reasons: Joints tend to be the weak part of structures, and it is much easier to bend beams or boards than to compress or stretch them.
Think about a square made of metal beams. You could turn it into a rhombus shape without bending, stretching, or compressing any of those beams. The stress is on those joints and all the leverage of the beams is working against them.
In contrast a triangle made of metal beams cannot be made to change shape without breaking a joint, bending a beam, or stretching or compressing a beam. This plays to the strength of the materials and mechanisms in the structure. The joints don’t need to defend against rotational force with leverage, and the beams don’t need to resist bending but instead compression and stretching.
If you push down at the top of a triangle, the edges cannot be pushed to the side. Because they’re at acute angles (less than 90 degrees), the edge would have to swing upward before it could swing outward.
If you push down on top of a square, the edges can just collapse to the side. Add even more sides and it can just collapse into itself.
Imagine that you have rectangular pieces of cardboard and you make a triangle by attaching them using pins. If you apply force to any of the joints you’ll notice that the triangle stays a triangle.
However, if you make a rectangle in the same way, and apply a force, you’ll see that it won’t stay a rectangle and instead it will flatten. Notice that if you add another piece of cardboard along a diagonal of the rectangle it will resist deforming.
A triangle is stronger because its geometry prevents its members from moving relative to each other which means it maintains its shape.
In a structure composed of triangles every pressure will turn into compressive (pushing) or tension (pulling) pressure.
Push on a triangle and you might apply bending force to the steel beam you’re pushing on, but everything that beam is connected to will experience compression or tension because triangles can’t change shape without making one of the sides either shorter or longer.
It is assumed for your purpose that the sides are perfect tensors and compressors so their lengths cannot change. I this makes them stay as they are and not break.
In reality the materials are not perfect which is a why we have engineering.
Because the resulting shape allows the structural members to carry loads in tension and compression rather than bending. This almost always results in stronger/stiffer/lighter structures.
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