I understood your original post to be saying that the base of your cantilever was supported by six individual springs, three translational springs each aligned with the global Cartesian axes and three rotational springs also each aligned with the global axes.[ ] Each of these springs has its own stiffness value, and because of their orthogonal alignments their actions are completely uncoupled.[ ] You now seem to be suggesting you have only a single spring ("the spring at bottom has got 6 dofs"):[ ] if this is the case then I do not adequately understand your problem, so ignore what I said above and ignore what I am about to say below.
If my original understanding still applies, then the global stiffness matrix you create by ignoring all external restraints is 12x12.[ ] Each row and column represents one of the structure's 12 overall degrees of freedom.[ ] Each one of the 12 terms along the matrix's leading diagonal represents the stiffness "experienced by" one of the degrees of freedom if all the other degrees of freedom were rigidly clamped.[ ] Hence the effect of a spring support at that degree of freedom can be modelled merely by adding the numerical value of the spring's stiffness to that term on the leading diagonal.[ ] What you are doing, in effect, is treating each spring as a very simple member (so simple it has a 1x1 member stiffness matrix), then merging that simple member stiffness matrix into the global stiffness matrix.
This is really basic stuff.[ ] So basic it is actually quite hard to describe.
If you have any follow-up queries I will not be able to field them, as I am going away for a fortnight to one of those increasingly rare places that do not have ready internet access.