What Determines the Breaking Point of a Bridge Under Increasing Load?

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Couperin
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This is a very basic concept but I can't seem to explain it properly.

Say you have a simple bridge made from two bricks that are, say, a metre apart, and a piece of wood spanning them. If you put a load on the wooden bridge, a normal force acts upward on the load. If you keep increasing the load, the normal force gets bigger.

At what point can the bridge no longer increase the normal force, i.e. what is it about a heavy object that causes the bridge to snap?
 
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When the plank bends slightly the normal force creates a tension in the material. When this tension reaches a value greater than the forces holding the material together, the material cracks.

In an arch, the load force is turned into compression which is much less destructive on stone, say.