Due to triangles ability to withstand tremendous pressure, this shape is often found in architecture to provide stability. Geometry and architecture are linked fundamentally, and by understanding the form of the triangle, architects provide the support they need to a developing structure. A-frame homes, truss bridges, and geodesic domes rely on triangles to create a durable structure. The smallest polygon is the strongest polygon, and the number of structures relying on the strength of the triangle prove that.
As an amateur architect, you can create vast structures using triangles. Triangles are one amazing shape! You can test the strength of a triangle today by building your own truss bridge! Equilateral triangle, and from the middle of each side, one were to place an interior frame board, spanning from each center of the exterior sides to the next, so that now, the triangle has is segmented into four triangles.
Mechanical engineers design cranes, which use triangles and squares in their frames. Even satellites use these familiar and basic regular geometries. Slide 5 On your paper, sketch each of these regular polygons: square, diamond and triangle.
If we push straight down on a shape, putting the whole shape into compression, what happens to the shape? Draw, using a different pen or pencil or dashed line, how the shape would look if you pushed on it. Assume that the sides of the shape are rigid and won't change length or bend. Slide 6 Take a look at this! If you push down on top of the square, it will no longer be a square, but instead takes the shape of a rhombus, which is a type of parallelogram.
This is called "racking. But what about the triangle? The triangle maintains its shape! Slide 7 The reason that the square and diamond collapse is because the angle between the structural members can change without having the length of the members change or bend.
Remember back to geometry when we talked about how polygons are defined? In this case, both quadrilaterals simply require the sum of the interior angles to equal degrees, but each angle can change. Slide 8 Triangles are unique in that sense. The angle between two sides of the triangle is based on the length of the opposite side of the triangle. Do you remember this from geometry? The angle "a" is fixed, based on the relative length of side "A. Slide 9 As we showed, other regular polygons can be deformed without changing the length of the sides.
A square loses its shape as its right angles collapse, and a pentagon and hexagon can be deformed. But the shapes stay "closed" because the sum of the interior angles is kept constant. So what can we do to the other shapes, the squares, pentagons and hexagons, to keep them from collapsing? Draw these shapes on your paper and add what would be necessary. Slide 10 Did you break the shapes into triangles?
Since we know a triangle cannot collapse, and we know that these regular polygons can always be reduced to triangles that's how we figure out the sum of the interior angles, remember? Slide 11 The same concept applies in three dimensions. As shown, a cube can collapse by "racking," just like the square we saw collapse in two dimensions. So what would we do to make a strong 3D structure? Slide 12 We make 3D triangles!
Specifically, we can make rectangular or triangular pyramids! This is why structural engineers rely on triangles, both in 2D and in 3D, to make strong structures! A 3D structure made of individual structural triangles like this is called a "truss," and is used throughout engineering for a strong light-weight structure! Now that we have reviewed the basics of how structural engineers rely on structural shapes, I expect that you will start to notice in your day-to-day life the way in which things are built.
Look around you, at the buildings, and cranes, and bridges, and houses, and cars, and furniture, and you will see that so much of structural engineering is based upon these fundamental and simple shapes. Next, in the activity, you will experience designing, building and testing structural trusses.
So keep in mind the discussions we've had about the different shapes and how they can be used to make strong structures. For example to enable workers to lay brick, install trim or paint. The weight pushes this arch into a stable, tightly squeezed shape. Three Elephant on Triangle Unlike the rectangle, the sides of the triangle did not bend under the tremendous weight.
This is why the triangle is still standing. Six Elephant on Rectangle The weight caused the top side to bend too much, so it failed! Six Elephant on Arch The arch likes to be pushed and squeezed, but not this much! When an arch is pushed too hard, the sides spread apart and collapse. Six Elephant on Triangle The triangle is still standing because the pulling force in the bottom side is balancing the pushing forces in the upper sides.
Nine Elephant on Rectangle The weight caused the top side to bend too much, so it failed! Nine Elephant on Arch The arch likes to be pushed and squeezed, but not this much! Nine Elephant on Triangle Even triangles have their limits! All this weight made the third side stretch so much that it snapped in half. Push Rectangle What happens when you push the side of a rectangle?
The rectangle is a wobbly, unstable shape.
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