Why would we be interested in arbitrarily requiring a zero deflection at B?
Suppose we consider a cantilever beam with a roller support at B. This beam is statically indeterminate.
To solve this beam, we will need the equilibrium equations plus one additional equation. The additional equation is obtained by considering the beam deflection at B. Since there is a roller support at B, we know that vB = 0. Using this fact, we can solve for the reaction force applied by the roller at B, as shown in this example. Once we've determined the reaction force at B, we can solve for the other reactions using the equilibrium equations.
Finished