The work of a bridge is to support itself and its load against the pull of gravity (stress). Stress on a material usually results in strain or a change in the material's shape. There are two types of stress: compression and tension. In a bridge stress is also caused by the pull of gravity; the amount of stress is determined by the weight of the bridge plus its load.
A member bearing weight is under compression. Hard stone, like granite, can withstand an enormous compressive force before changing shape. A member being pulled is under tension. Granite, under tension, will break apart under a small amount of strain. In fact, a long beam of unsupported stone will crack under its own weight. Compared to the massive amounts of dead weight carried by each pier, the weight of moving objects on a bridge is insignificant. If a diagonal is placed across a rectangular frame, the shape becomes rigid and forms two triangles. Triangles are the simplest figure whose shape can't be altered without changing the length of one or more of its sides.