Toothpick　Bridge　Contest

Force and Shape
Arch
　　Thinking about a bridge, I visualize an arch bridge first of all. The beautiful wooden arch bridge called Kintaikyo in my home prefecture, Yamaguchi Prefecture, is engraved in my memory. Most people feel the arch bridge is beautiful, looking like a rainbow.
Snow scene, Kintaikyo
Photo by「Kouji Matumoto」
Related Links

The history of Kintai-kyou bridge (in Japanese, English and Spanish)

Kintai bridge

Historic Yamaguchi Prefecture

Iwakuni on the web


Reverse Catenary

Let's take both ends of the chain in one hand, and try to spread it in a horizontally suitable interval. A curve of the chain made naturally at this time is a catenary curve. So, let's go to the outside, and see the electric wire drawn between the electric poles. A curve of the electric wire is catenary .It is not a parabola though it looks like a parabola. The chain is pulled by gravity to the bottom. Then, each chain is pulled. The chain resists as a force of pulling against gravity.


A Catenary curve can be made easily by the chain.
A Catenary curve becomes an arch when your mouse pointer is positioned on the photograph.


It becomes an arch when the image of a catenary is turned over, top to bottom. All force is then changed to a force of compression in the arch, and it stands as a reverse catenary. Of course, an arch can't be built in the chain. It is good to make it of material that can easily resist the force of compression. Stone bridges commonly use an arch in many places because stone is awfully good at resisting compression.

Oji bridge in Kyoto Prefecture Kameoka City
Photo by 「Hasino Sanpomiti」Studio T.B.S.A.　
It is said that the bridge has the longest span(18.0 m) outside of Kyushu.
Compare this with the concrete arch bridge of the Kyoto Throughway which can be seen in the background, and this bridge is interesting.
Oji bridge is an arc-shaped bridge. The shape of the concrete arch bridge is a reverse catenary.



The arch form adopted in the toothpick bridges

Weak point of arch, Buckling

The arch receives the force of compression. It sometimes bends before it is crushed when compressive force is added to the stick-shaped member. This phenomenon is called “Buckling”. Most of the arch bridges broke after buckling in the toothpick bridge contest.

Countermeasures for buckling of the arch were taken, too.

１）When early distortion is big, buckling easily occurs even with a light load. Making a straight stick and also making it precisely arched will be a good countermeasure.

２）It is a good method to disperse the force as much as possible.







Force and Shape Truss

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