Why are Triangles strong?

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How can a shape be strong?

In: Engineering

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It is the way a force applied to them goes through the structure without bending the elements in the structure.

The shape is rigid because in order to deform you need to stretch and compress the members. The shape is strong because essentially the loads to be carried almost entirely by compression and tension forces.

This is in contrast to any shape with more sides. If you take a square frame, fix the base, and try to push it over – there are tension and compression forces, but the members that make it up are also trying to bend.

The way the section properties work any given shape has much less capacity to resist bending than it does to resist tension/compression, and the stiffness against bending is significantly less than the stiffness against stretching/compressing.

Imagine a square. If you push the top in a lateral direction, the joints at the vertexes can change their angles away from 90 degrees, turning it into a rhombus and making the total height shorter. A structure made of squares can be distorted and eventually collapse this way. This can’t happen with a triangle, all the vertexes are stuck at their preset angle unless the sides (beams) bend or undergo heavy tension/compression. Ideally they’ll be made of a material which is highly resistant to this.

When a triangle grabs you and puts you in their big strong arms you feel safe and warm like in your mothers womb again. That kind of strength is not something you find every day.

When you have steel girders or wooden beams that are welded, nailed, screwed or riveted together, the joins will usually be the weak spots. It’s way easier to change the angle of one of the joins than it is to stretch, shorten or bend one of the beams.

Triangles have the neat property that a triangle can be fully defined by the lengths of its three sides. So as long as you don’t put enough force to bend or stretch one of the beams, you also can’t change the angles of the triangle.

Other shapes don’t have that property. A quadrangle with four equal sides could be a square – but it could also be a rhombus. So no matter how strong the beams are, any square can easily be squished into a rhombus and then totally flattened.