Well before answering the actual question, I want to state that Doubly Reinforced Beams have Compression Reinforcement in addition to Tension Reinforcement and this compression reinforcement may be on either side of the beam (Top or Bottom face) depending upon the type of beam i.e. Simply supported or Cantilever respectively.
Doubly reinforced beams are provided because of the following reasons
1- Doubly reinforced beams are provided in order to increase the moment carrying capacity of the section. We also know that we can increase the moment carrying capacity of beams by increasing its depth but it is not always possible to increase the depth of beam because of Architectural and Aesthetic restrictions. Moreover increasing the depth of the beam will result in the more self-weight (Dead Load).
2- Minimum compression reinforcement is provided to hold the Shear Reinforcement (stirrups) in position and for increasing the ductility of the beam.
For an explanation of point 2
Suppose that if you haven’t provided the top reinforcement, then how you will hold the stirrups on the top part of the beam. In that case stirrups will shake during concreting and even may touch the formwork on one side, which will result in the zero required cover to the reinforcement on that side. See the picture for this, in which stirrup has been marked by a red coloured arrow.
3- A most important reason for providing the doubly reinforced beams is to ensure safety against reversal of stresses in the structure due to Wind Forces, Seismic Forces and temperature stresses.
