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Strength of Shapes

Exploring Structural Engineering Fundamentals

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Shapes in Bridges

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Shapes in Buildings

Suggested text: Structural engineers use the same types of shapes in buildings. Many building frames are simply repeating squares, as shown in the top left. The bottom left image shows how a square is reinforced by adding a diagonal cross brace in this scaffolding, which divides the square into two triangles. The image on the right shows an Antarctic goedesic under construction. Geodesic domes are like soccer balls and can be viewed as a group of pentagons and hexagons. But, if we break each of those shapes down, we can see that they are fundamentally composed of triangles.

Image sources:

Top left: http://www.osmre.gov/IMAGES/southbldg4.jpg

Bottom left: http://www.presidio.gov/about/Pages/historic-preservation.aspx

Right: http://antarcticsun.usap.gov/AntarcticSun/features/images/dome_demo_jan%207_fisheye.jpg

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Shapes in Other Things!

Suggested text: Even when we get outside the realm of civil or architectural engineering, we can see how engineers rely on the known strength of shapes. A motorcycle frame uses many triangles to support the wheels and seats. Cranes, designed by mechanical engineers, use triangles and squares in their frames. Even satellites use these basic geometries.

So what have we noticed as a common theme? (Hopefully, students answer that all of these structures use triangles.)

Image sources:

Top left: http://www.robertreeveslaw.com/blog/wp-content/uploads/2011/09/Roller-Coaster-Accident.jpg

Top right: http://www.executivegov.com/wp-content/uploads/2011/12/Crane.jpg

Bottom left: 2006 Rich Niewiroski Jr., Wikimedia Commons http://commons.wikimedia.org/wiki/File:2006HondaCBR600RR-002.jpg

Bottom right: http://www.asc-csa.gc.ca/images/recherche/images/5cba4ffa-7be8-4333-b514-93b76fab4cf6.jpg

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Relative Strength of Shapes

On your paper, sketch what you think will happen to these shapes if we apply the force shown in GREEN (assume the sides are rigid)

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Relative Strength of Shapes

The TRIANGLE is the only shape that won’t collapse!

WHY?

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Relative Strength of Shapes

The other shapes collapse because the angles between the structural members change.

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Triangles

The TRIANGLE cannot collapse because the angles are fixed based on the opposite side length.

A

C

B

a

b

c

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Relative Strength of Shapes

All other shapes can be deformed because the angles are not fixed. Draw these shapes in a way that will keep them from collapsing.

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Relative Strength of Shapes

Make TRIANGLES!

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3D Shapes

The same thing applies in 3D

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3D Trusses

The same thing applies in 3D

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Strength of Shapes

Exploring Structural Engineering Fundamentals