Conditions of Compatibility:
Compatibility lies within satisfying the geometrical continuity of the structure, as well as, ensuring that the extra constraints placed on it satisfy the new displacement conditions.
For example, in the case of the propped cantilever, if we remove the roller support at B, the end is free for deflect. Within a given loading this vertical displacement can be calculated Strength of Materials course. Therefore, when we have placed the rigid roller support at B this downward deflection is prevented, and as an output a vertical reaction VB appears there. By conditions of compatibility the magnitude of VB should be such that it should neutralize the deflection of cantilever end B due to loads and be able to bring it back to its original level, as if there were no deflection. This also gives us a clue to determine the value of the redundant reaction VB. Knowing VB the remaining three reactions at A, namely VA, HA and MA could be acquired by using the three equilibrium equations.
Here we want to emphasize that for statically indeterminate structures there will be an infinite number of combinations of redundant forces which will satisfy equilibrium conditions. Thus, among them there will be only one set of values that will concurrently satisfy the requirements of both equilibrium and compatibility.