Small Displacement Theory

Small displacement theory states that the Deformation/Deflection of a structure are assumed to be small while analyzing the structure. Let’s understand this way, while designing a member generally factor of safety are used, some of them are:
Safety factor for loads.
Partial safety factors for the strength of materials (i.e. steel, concrete etc.)
Then there is serviceability concern, durability concern etc. finally the member designed will be experiencing a load intensity much below its yield capacity. So, the corresponding deflections will also be very less.