The Cellar - Jan 7th, 2020 : Mathematical Bridge

I wonder if it would take me from the question to the answer, the problem to the solution.
Let’s see, #2 pencil, calculator, bridge... OK, I’m ready for the exam.

Built in 1749 and designed by architect William Etheridge who also designed a similar but much bigger Old Walton Bridge over
the Thames. The stone abutments are high enough that the wood will never see flood waters. Etheridge stole the design from
his former boss James King who in 1737 as master carpenter at Westminster Bridge proposed the same design for that bridge.
Winter ice screwed up the prep work so they decided to let him build his design only so ships could pass under while they
built the stone work above.

http://cellar.org/img/math-bridge1.jpg

How do it do? Glad you asked...

Quote:

The Mathematical Bridge is constructed out of interlocking pieces of timber. Each rib of the superstructure are set at tangents to the circle describing the underside of the arch of the bridge. In the arch itself, each member is under compression with little or no lateral force that could cause bending. Where the main members cross, the wood joint transmits the compressive stress from one member to the next, with a bolt serving to hold the joint together laterally, rather than itself carrying any stress. There are also radial members which both support the top rail and lock all the overlapping tangents into a rigid truss. The load bearing deck is supported by horizontal cross-beams attached to the bottom of the radials, close to the junction of two tangents. When a load is applied the vertical forces get distributed along the tangents as compression opposite to the compressive forces from the tangents, thus balancing each other.

Ya got that?

http://cellar.org/img/math-bridge2.jpg

In defense of Etheridge stealing the design from King, some claim King stole it from Leonardo da Vinci.
The design has been used around the world, here’s another one in Morso Denmark.

http://cellar.org/img/math-bridge3.jpg

link