ARCH BRIDGES

Arch bridges have been around for thousands of years. The Romans perfected the semi-circular arch bridge.

The Pons Fabricius was built in 62 BC.- still standing.

The Alcantara in Spain is also around 2000 years old.

Pont du Gard, Languedoc-Roussillon, France

The Pont Du Gard is an aqueduct in France- used to carry water to a city.

So how do you construct an arch?

You start by building a wooden form ( semi-circular for the Roman arch), and lay the stones on top

Once the last stone – the Keystone is laid- the arch is complete and the wooden form (the centering) can be removed.

All the weight of the stones, and the live load ( the people cars etc.) presses down on the arch, compressing the stones.

Stone is great for compression. But notice that as the line of this compressive force travels down through the arch, this force tends to spread the ends of the arch apart. There’s a vertical and horizontal component to the force. The vertical component does straight down into the ground- and as long the ground isn’t sand or mud- the ground will support this vertical force.

The horizontal force is another matter.

We got a little ahead of ourselves here—before we discuss a tied arch, let’s go over ABUTMENTS.

The Romans didn’t have high strength steel to tie their arches together- they used stone, scrap rock, dirt etc. to form abutments.

The stones on either side of the arch are heavy enough to contain the horizontal push.

Let’s take another look at the Pons (Latin for bridge) Fabricius.

The 2 arches meet in the middle but there’s no heavy mass of stones to act as abutment. Plus what is there is pierced by another small arch, so the needed weight is even less. By the way one reason for this small arch is so that when the river rises and submerges that small island and pushes against the bridge, that little arch opening will allow the river to flow through, thereby lessening the force against the bridge.
So back to the abutment– where is the mass of stones Where the arch lands on the banks, you can see the heavy wall on one side and looks like a whole building, on the other.- these function as abutments. But where the 2 arches meet — it’s the island that serves as the abutment. All that rock and dirt are plenty heavy to counter-act the horizontal force of the arches.

The aqueduct in Segovia Spain was supplying water to the town- from a water source 10 miles away- up until the mid 19th century.

Here’s what it might have looked like 2000 years ago .

There’s so much here. First look a the semi-circular wooden frame with the stone blocks set on top. The force goes through the stones and is resisted by the stone columns on either side. Now look at the 2 hollow stone runs on top of the arches. That’s where the water runs from the source all the way to the city.
Now check out the cranes. The boom is made of 2 heavy wooden columns that join at the tip, and there’s a pair of pulleys with a mechanical advantage of 3 lifting the stone. Slaves were plentiful in those days, and you can see a couple of guys walking in the “squirrel cage” that’s connected to shaft where the line is wrapped. So for that windlass- say the radius of the “cage” is 6feet and the radius of the shaft/axle is 1 foot, we get a mechanical advantage of 6. Now we multiply that MA of 6 by the MA of 3 of the pulleys to get a combined MA of 18. There is of course a large amount of friction here- so the real MA might be half of that, but this was state of the art 2000 years ago.

This is a reconstruction of the type of crane used in Europe in the 13th century. You can see how the lifting line goes over 3 pulleys before it wraps around the shaft which is connected to the shaft inside the ” cage”. Look familiar?- this is just like the Roman crane. BUT the angle of the boom is fixed at about 45 degrees. The Roman crane has lots of lines that can adjust the angle of the boom, making it much easier to position the load.

Now on to tied arches.

This is the Fremont bridge. When they installed it in 1973, they built the 2 side spans and floated in the main span.

there was no need for abutments since the horizontal force (thrust) was contained by the deck ( the tie). They built the main span farther up river and then loaded it onto 2 barges and floated it under the existing 2 side spans. I spoke to a guy who was there in 1973 when they “installed” the bridge. They attached lifting screws from the side spans above and then to the 4 corners of the span.
When they started the lift, the barges popped up as soon as the weight cleared the barges.

Since the bridge is not moving, we can say it’s in equilibrium, so we can use the equilibrium equations.

1-The sum of the forces in the vertical direction must all add up to zero and

2- the sum of the forces in the horizontal direction must also add up to zero.