Materials

Composite materials

Reinforced concrete Concrete is strong in compression because of the stones. but weak in tension because of the brittleness of the cement matrix holding the stones together. It is quite light and very cheap. The steel rods are good in tension because steel is tough, but bad in compression because thin rods buckle (note that steel is relatively heavy and expensive).

So the steel holds the structure together when it might otherwise break under tension, and the concrete gives support when buckling might otherwise occur.

Carbon fibre Carbon fibres are strong in tension, but are very short. By embedding them in a tough matrix  that keeps them in place, any given cross section has plenty of fibres to spread the load.
Fibreglass Glass is strong in tension, but is brittle and breaks if bent. The resin is weak, but it can prevent a cracked fibre from bending in an escalating way if it once reaches the stage of crack propagation (the 'snapping' process). So when the specimen is unbent, the fibres are still intact and able to resist longitudinal stresses again.
Plywood Thin sheets of wood have the grain running in a particular direction, and their structure is like a raft of drinking straws weakly held together. A single sheet can easily be bent with the grain but is much more rigid if it is flexed across the grain. By alternating thin laminas with their grain directions at right angles in adjacent sheets, a board that is stiff in both directions may be obtained.