P-Delta vs Large displacement

[shostovari]

Hi,

I am trying to use Robot for P-Delta analysis. I did a verification study comparing the results for a simple cantilever column with SAP2000. I get the same displacement and moment for linear static analysis and P-delta analysis.

However, the P-Delta including the large displacements differs a lot. Also I get smaller displacement and moment using P-Delta and large displacement comparing with only P-Delta analysis, which is odd!

I will attach my results and results from a verification study done by SAP2000.

I would appreciate if you could let me know what Robot means by P-Delta and large displacement.

Thank you,

Shadi Ostovari

[Krzysztof_Wasik]

Hi @shostovari 

Usually when I present differences between linear, p-delta and large displacement I use this very simple example of column.

Linear statics internal forces distribution as we expect (loads and column stiffness are defined to get 100 cm of horizontal displacement at the top of calculated column)

P-Delta - reaction MY depends on horizontal displacement Additional bending moment from vertical loads calculated (about 1 kN*m  more) . Shear force Fy = FY load component, axial Fx force = FZ load component. Fx and Fy constant along column length. 

Large displacement - no big differences in moments and displacements, comparing to P-delta but axial force Fx and shear force Fy are not constant along column height.

This is the main difference between P-delta and large displacement method.

In large deformation analysis internal forces are calculated in deformed structure configuration.

Loads, defined in global system of coordinates have to be balanced by internal forces in deformed column configuration. at the top and at the bottom of the column

At the top

Local Fx and Fy  have to be projected on global system of coordinates to balance loads so local Fx is smaler than FZ load, while local Fy is slightly higher FY load (loaded column axis is not vertical).

At the bottom

Local Fy and Fx, are equal to applied FY and FZ loads because near support, column is not deformed (loaded column axis is "almost"  vertical).

[shostovari]

Hi Krzysztof,

Thank you very much for your reply. If you look at my attached file (in my original question), for a different ratio between vertical and horizontal load applied on the cantilever column, I get smaller displacement and moment in Pdelta+large displacement comparing with Pdelta only. I agree with you that the bending moment for P-Delta and P-Delta+large deformation should be equal at base but my analysis does not show this. It shows a smaller value for Pdelta+large deofrmation.

Even in your example you can see smaller moment. However, your example does not show the difference as it should. It is because, I guess (looking at your selected Fz=1 and Fx=2), your vertical load is much smaller than critical buckling load. So we can not observe the problem that I noticed in my model.

I have used an axial load, Fz=4KN. This load is 70% of the critical buckling load for my selected column (10 m high). I used horizontal load as Fh=0.045 KN.

What do you think?

Best regards,

Shadi

[Krzysztof_Wasik]

Hi @shostovari 

Define some intermediate nodes along your column

For 10 intermediate nodes results for large displacement are quite close to P-delta

[shostovari]

Thank you so much. I will add notes 🙂

Is it possible to get input file of your first post please?

Best regards,

Shadi

[Krzysztof_Wasik]

hi @shostovari 

Attached you will find my example

[Krzysztof_Wasik · Accepted solution]

Hi @shostovari 

Missed file

[HoshangMustafa]

Shear force Fy = FY load component, axial Fx force = FZ load component. Fx and Fy constant along column length. 

I think you mean Shear force Fz instead of Fy

[Krzysztof_Wasik]

HI @HoshangMustafa 

Thank you for your correction. It was of course my mistake in effect description