Equations for the slope and the deflection of the beam have been derived; however, these equations include constants of integration C1 and C2. These constants must be evaluated for the particular beam and loading.
Boundary conditions will be used to evaluate the constants C1 and C2. Boundary conditions are simply points on the beam where either the beam slope or the beam deflection is known.
For example, a roller support such as this implies that the beam is prevented from deflecting either up or down at the roller location. This is a boundary condition. It is known with absolute certainty that the beam deflection v must be zero at the roller location.
Each boundary condition will dictate either a slope or a deflection at a specified location x on the beam. The known slope or deflection and its corresponding location x will be substituted into the applicable equation derived for the beam, yielding an equation with only the constants of integration as the unknowns. The number of boundary conditions required for the solution must equal the number of unknowns.