what I have understood is so, if it is wrong please correct me!
In this method we define a virtual leaning frame next by our frame, with almost a zero lateral stiffness, the lateral displacement in the main frame, induces the same lateral displacement in virtual frame, the gravity loads applied on the virtual frame multiplied by this lateral displacement generates an extra lateral force that are transferred to the main frame through rigid truss elements, and finally this extra lateral forces simulate the p-delta effects on the frame....
But this extra lateral force cause a non-real extra base shear force on the frame and it is not the same scenario that occurs in real physical model!
well, in a real model, the p-delta effects will only cause an extra Moment in members, and the member shear forces are not changed!
I have done a Stability analysis for a high story frame, the pushover curve of the frame that is the curve of Roof displacement against the base shear ( which is captured from first story column shears forces) is raising nevertheless the Load Factor of analysis decreases!
I think maybe this extra lateral force that is caused by virtual frame in this method, will change the analysis results such much that causes the frame capacity to be far underestimated....!?
the leaning column is added to account for the P_Delta effects on the lateral system from the gravity columns in the rest of the building. The way people model it is as you described and is as described by many others in the litarture. Now if this column is added and it's sole purpose is to add additional lateral loads into the frame then from simple statics one should understand that the lateral forces in the base will either increase or decrease if the sum of these forces at all the floor locations do not add to 0.0
i will grant you that in real physical systems the gravity columns are not trusses and will be capable of taking some of these lateral forces. however that is not how it is typically modeled.
here is a paper to get you started:
http://elearning.eng.cu.edu.eg/str/imag ... 2002Q4.pdf
I studied it, it was very helpful to clear me about the method, but my problem is that I have not used this method to solely account for the p-delta effects of the leaning columns or the gravity columns in my frame, actually I have no gravity column in my lateral resistant frame! and following some other researcher work, I have used a fictitious leaning column to solely model the frame p-delta effects in opensees.
I also checked a 2-story pushover example developed by yourself that has used the same method to model p-delta effect, about that model, the pushover curve obtained from both methods (force shear of base columns, and sum of lateral external load obtained from load factor multiplied in base shear of lateral load pattern) are the same, about my model, it is not behaving so, I have exactly and accurately used the same method! (by the way I have used force-based nonlinear beam-column elements with fiber sections for both beams and columns).
But finally I have got confused the way this method is implemented! Well, regarding this leaning columns with story gravity loads, it seems at least in a pushover analysis by steadily increasing lateral displacements in story levels, the lateral load generated by it is constantly increased and then it absolutely helps the base shear to increase…!? but you say that finally the sum of these lateral forces in height of the frame adds nothing to 0.0!?
Please if I have a misconception about the implementation of this method, help me!! maybe it is not only my problem, and also I have to justify its usage for my thesis as investigation of frame stabilities ...
I also can send all my OpenSees files to your email...
if in a physical model we would only have an increase in moments due to p-delta effects (with no gravity column in the frame), then maybe the extra lateral force that are applied through leaning columns in this method during a pushover analysis will affects the analysis results...
not to freak you out further BUT if your displacements are Large you should consider Corotational transformation as opposed to PDelta, as PDelta also has it's limits on accuracy when displacements are large! and if your strains are large, corotational may not be accurate enough!
about transformation type, well, carelessly I have used PDelta transformations, but as I am pushing a frame of 20 story height until 2m of roof displacement, I think then it will go under large deformations and strains, and I should have used Corotational transformation type instead of PDelta transformation....