Structural members are designed for loads that are expected to occur during the intended life of the structure. But sometimes the structure gets loaded beyond these loads and the structural members could fail. In such circumstances we want that the people living in the building should get sufficient warning before the structure collapse.
So we expect the failure to be ductile failure (Think of loading a plastic ruler until it fails) i.e. there must be sufficient deformation of the structural member before it breaks as opposed to a brittle failure (Think of loading a glass ruler until it fails) where the member suddenly fails.
In a reinforced concrete beam the ductility is because of the steel reinforcement.
The above figure presents the strain diagram for Balanced section, Under reinforced section and over reinforced section.
The steel provided in the beam is such that both concrete and steel reach the limiting values of strain simultaneously.
Under Reinforced Section
The steel provided in the beam is such that steel reach the limiting values of strain prior to concrete. This results in yielding of the steel and the steel could yield till it attains the ultimate strain at which point it breaks. It is important to notice that it is the yielding stain that is considered as failure strain in steel and not the ultimate fracture strain. The steel still has to undergo strain hardening, softening and then fracture.
Over Reinforced Section
The steel provided in the beam is such that concrete reach the limiting values of strain prior to steel. This results in breaking of concrete and since now there is no concrete present to take the compression the beam fails suddenly.
The additional margin that we get in under reinforced section helps in prevention of a sudden failure and provide the necessary warning to the inhabitants of the building.