## Frame P-Delta effects by Leaning column

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### Frame P-Delta effects by Leaning column

I think there is an issue with so called "Leaning Column" technique that is commonly used by OpenSees users to model P-Delta effects in 2D frames

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....!?

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....!?

Last edited by sirwan on Sun Apr 13, 2014 12:09 pm, edited 1 time in total.

### Re: Frame P-Delta effects by Leaning column

I suggest you read up on the subject.

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

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

### Re: Frame P-Delta effects by Leaning column

Thanks for your help dear professor fmk and also for the paper

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...

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...

Last edited by sirwan on Sun Apr 13, 2014 12:19 pm, edited 1 time in total.

### Re: Frame P-Delta effects by Leaning column

i said will either increase or decrease (possible in earthquake excitation) IF the sum of these forces is not 0. for your case they will not sume up to 0 and will definitly increase the base shear. (assuming all lateral load that are pushing the model are acting in same dirn as is typical .. though given what some people do with OpenSees not gauranteed!)

### Re: Frame P-Delta effects by Leaning column

again thanks for your reply dear fmk, now I have just one last question regarding the increase of frame base shear in a pushover analysis: if in a real frame, do we have the same phenomena, I mean the lateral displacement of the frame would oppose both an additional shear and moment to the frame or just an additional moment?

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...

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...

### Re: Frame P-Delta effects by Leaning column

you seem to be worried about these 'additional forces' .. the forces ARE REAL (and to answer your question the frame is accounting for them in the analysis) .. STOP thinking about the global equilibrium of forces in the UNDEFORMED configurton, START thinking about global equilibrium in the DEFORMED configuration .. the PDelta gives a more accurate estimate of the actual forces than the linear transformations (which are only accurate for SMALL displacement)

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!

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!

### Re: Frame P-Delta effects by Leaning column

well, actually each time to check my conceptions about the method I have drawn a 2 story moment frame under lateral loads in deformed shape, and then I see to consider the p-delta effects, we only need an extra moment to be opposed on frame and no shear forces should be developed unless we have also a gravity column in our moment frame, but this method also opposes an extra base shear on frame....

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....

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....