I guess the "incrementally" here means the analysis iteration with P-Delta option. The stiffness matrix will be updated with the step-by-step load increase.
The answer by Dr. Louis F. Geschwindner makes me more confused. Actually, in accordance with CISC S16-94, there isn't a word saying with P-Delta analysis K value can be simply 1.0 anywhere. The code distinguishes beam and column although we can name both "beam-column" in actual structure. For beams K=1.0 (SAP2000 gives a default value K=1.0 for all beams, also there isn't a K required in calculation of Mr in S16-94), end moments will include the 2nd-order effect, which is obtained either by a P-Delta analysis option or by a moment magnification factor (old formula). For columns which are prone to buckling, as per Clause 9.3.3, K will be determined by either Appendix B and C. Appendix B gives the column K values, ranging from 0.65 to 2.0. Appendix C is for K value of columns in a continuous frame with side-sway prevented. In another word, S16-94 removed the K value chart for columns of side-sway permitted frame. This creates a room for confusion.
In real design, I still use the old approach: check the column strength with K values according to the support conditions, which can be definitely larger than 1.0. On the other hand, P-Delta analysis is not usualy my choice to trade off the K value. Quote a few words from a SAP2000 manual: "A well designed building should not have significant P-Delta effects. Analysis with and without the P-Delta effects will yield the magnitude of the P-Delta effects separately. If those lateral displacements differ by more than 5% for the same lateral load, the basic design may be too flexible and a redesign should be considered."
I hope AISC can make the issue clearer.