Cantilever bridges are subject to the two basic forces that are in effect for all bridges. These forces are compression and tension. In a cantilever bridge, with the space between the cantilevered portion spanned by a suspended deck, the compression and tension are straightforward.
As you can see in this diagram above, from Merriam-Webster, a load will put weight on the deck. The cantilever arms support the weight of the load. So where is the tension and compression in the beam itself?
Here you can see that when the load adds weight to the bridge, the top supports are subject to tension (<– –>), the pulling force. The cantilever arms and bottom supports are in compression (–> <–), the pushing force.
As with any type of bridge, if the bridge is subject to too much tension, the bridge will snap. Too much compression and the bridge will buckle. As long as the forces are balanced, the bridge will stand and function as it was designed to function.
Let’s look at it a less scientific way. Suppose you are at a swimming pool. There two diving boards, one each on opposite sides of the pool. These are no ordinary diving boards. These are very long and extend out over the water from each side, so that only about 2 feet of the distance is uncovered. The springy ends of the diving board are supported by the weight at the end that is on land. If only the diving boards were longer … They could cover the entire expanse of the water without anything getting in the way of the swimmers beneath the boards. The cantilever bridge is just such a type of bridge. By putting a beam span between the two diving boards, the weight of the beam span will be supported by the diving boards. NOW you have a cantilever bridge!
More: The Forth Railway Bridge More about bridges at PBS