Forces act mostly on the top and bottom surfaces of a beam bridge.
The force of gravity, acts downwards on objects on the bridge. The reactions in the bridge supports make the beam bend in the middle. This squashes (compresses), the top surface of the beam. At the same time the bottom surface is stretched (in tension).
The load on the bridge causes only forces of compression (squashing) through the bridge.
Downward forces push on the keystone. This pushes sideways, in both directions. The forces are passed round to the foundations of the bridge. All the materials of the bridge are in compression (being squashed). Modern arch bridges are more likely to be built from concrete, than stone. The forces in an arch behave in a similar way, whatever the material.
Note - the diagrams are extremely simplified. They aim just to show if the forces acting on the different parts of the bridge are stretching (tension) or squashing (compression).