A suspension bridge works by sending the vertial loads through heavy steel cables. These cables then transfer the load to the vertical towers, which carry the load into the ground and anchorages. These bridges can acheive longer lengths than any other type, though they are very costly to produce.
Arch bridges work by compression, moving the load through the arch to the foundations (one on each side).
Tied arch bridges are a combination of arch and suspension bridges. The deck is suspended by vertical hangers, forcing compression on the arch. The deck acts as a tie, restricting the horizontal movement of the arch.
A bridge needs some way to move the vertical load in order to stay stable, because "[if] the cable [is] completely horizontal, the forces must also be purely horizontal and there's no vertical component that could hold the mass up!" (source) An arch is a great way to transfer these vertical forces. The reason parabolic arches are used instead of semicircular arches is because parabolic shapes are stronger. Take a look at this model made with wooden blocks: (source)
As you can see, with a load applied this model collapses. Now, take a look at this parabolic model:
As shown, the parabolic shape is more structuarly stable than the circular one.
This is my model! I chose to build a suspension bridge, as it was the most interesting in my eyes. It's sitting off to the side. (Don't worry, you can touch it.) I've brought some weights as well, feel free to place those on the bridge.
Most of it is made of Sintra:
Sintra is a lightweight, flexible and easy-to-cut PVC plastic. There is some off to the side, if you would like to touch it. My dad had a few large pieces lying around, so it was an obvious choice. The connecting cables are made of a small steel wire, fastened by copper ferrules. The building process was pretty straightforward, simple, and didn't take very long. Most if it is held together with hot glue, so don't be too rough with it.