A typical one-bay, one-story frame comprised of 3 bending elements is shown in Figure1(a). As shown, the frame has 3 degrees of freedom (DOF), two rotations and one lateral displacement. The damage detection procedure will require loads be applied at a subset of DOF and displacement measurements be taken at another subset of DOF. Although mathematically feasible, practical applications prevent concentrated moments be applied to a structure and additionally rotational displacements can be difficult to measure. Therefore, the frame shown in Figure1(a) is not a good model to use in actual damage detection routines. As a solution, rather
than using a single bending element to connect each column span, two elements are used. This modification creates two additional degrees of freedom at the joint between each element, as shown in Figure1(b). As can be seen, now a vertical degree of freedom exists where loads can be applied and displacements can be measured. To reiterate, the additional DOF are not required for the mathematical formulation, but it does create a damage detection procedure that is more suitable to conversion to actual practice as it is less difficult to obtain vertical displacements than it is to obtain rotational displacements.
Figure 1(a, b). One-bay, One-story Frame Comprised of Bending Elements