Displacement method vs force method

The statement means that, in the displacement (stiffness) method, the set of unknowns and the primary structure are unique for a given structure, while in the force (flexibility) method they depend on the analyst's choice.

Why the displacement method is unique

1. Unknowns are fixed. The unknowns are the independent joint displacements (rotations and translations) that are free to occur. The degree of kinematic indeterminacy is a single, definite number for a structure, whatever the loading.
2. The restrained structure is fixed. Locking all the joints gives a single restrained structure made of fixed-ended members whose fixed-end moments are available in tables. No choice is involved.
3. No choice of redundants. In the force method one may remove different reactions or release different members (several primary structures are possible), and the work involved changes with the choice; a poor choice can even give an unstable primary structure.
4. Systematic and general. The same member stiffness relations ($4EI/L$, $2EI/L$, $6EI/L^2$, $12EI/L^3$) and the same assembly rule are used for every problem, so the method is easy to program. This is why most computer packages use the displacement method.

Example: fixed-ended beam under a point load

The fixed beam AB (both ends fixed) is statically indeterminate to degree 2: ignoring axial effects there are four reactions ($V_A$, $M_A$, $V_B$, $M_B$) but only two equilibrium equations. In the force method one must choose the redundants (for example $M_A$ and $M_B$, or $V_B$ and $M_B$) and compute several flexibility coefficients.

In the displacement method the same beam has zero kinematic indeterminacy, because the ends cannot rotate or translate. The end moments are directly the fixed-end moments:

$$M_{AB}=-\frac{Pab^2}{L^2},\qquad M_{BA}=+\frac{Pa^2b}{L^2}$$

and no equation has to be solved.

For a two-span continuous beam ABC on simple supports, the force method has one redundant, which the analyst may choose as the middle reaction or the support moment at B. In the displacement method the unknowns are the joint rotations $\theta_A$, $\theta_B$ and $\theta_C$ (or only $\theta_B$ if the modified stiffness $3EI/L$ is used for the spans with hinged far ends). Either way the unknowns are fixed by the geometry of the structure, not chosen by the analyst. The number of unknowns may be larger in either method depending on the structure (a multi-storey frame has many redundants and many joint displacements), but in the displacement method each unknown is a uniquely identified joint displacement.