To develop a third equation, the known deflection of the beam at point B will be utilized. The steps involved in this process can be outlined as follows.

• Replace roller B with an unknown force B_y.
• Using the method of superposition, derive an expression for the beam deflection at B in terms of B_y.
• Since the beam deflection at B is known, a geometry of deformation equation can be written for the beam.

These steps will produce an equation in terms of B_y based on the deflection of the beam at B. This type of equation is known as a compatibility equation.