Hi!

The P-D efect includes geometrical non linearity, wich means, te aplication points of the loads can change during the loading process.

You can calculate the final displacements by subdividing the non linear analysis in many small steps wich are considered to be linear. (Example: If you have a load "P" divide your problem in 5 steps, aplying 0.2P in each one of them)

The loads for each step has to be applied to the deformed structure determined in the previous step. However, there are no formulas avialible for calculating the displacementes of the loads applied on the deformed structure, thus you would have to calculate them for example by applying the Wirtual Work theorem.

This process is not often caried out in manual calculations, however, it is posible.

Another option is calculating the linear displacements in a linear static analysis and multiplicate them by a factor (say 2,5) to consider the P-D effect.

Dear sir check it the like please

https://docs.bentley.com/LiveContent/web/STAAD.Pro%20Help-v11/en/GUID-26F82B63-0DA5-43E1-BC75-ED2B5F594B5C.html

also you can use CSI SAP2000 program to solve it

https://wiki.csiamerica.com/display/tp/P-Delta+effect+for+a+cantilevered+column

Thanks Calvin Kauenhowen,

Currently, I am using Newton-Raphson and incremental loading to calculate the final displacements at "nodes". However, what I am looking for is the displacement result at a random location along the length of every member without diving members into smaller sub-elements since diving increases to run time.

Do you have any way to calculate displacements along the member for PDelta analysis without diving the member?

Thanks,

NLHHiep

Thanks Ali Kifah Kadhum,

What I am doing is to build a numerical function or method to calculate displacements along the length of member with PDelta analysis rather than using commercial software as SAP2000.

Do you have any idea about that?

Thanks,

NLHHiep

Shape functions are functions that yield the displacement at any point along the bar by interpolation from nodal values. These functions are part of the bar element formulation and do not depend on the type of analysis realized, they should be the same for linear and for non-linear (P-D analysis).

Have you compared the nodal values? If nodal values are within a given tolerance then your analysis is correct.

Also you can compare the shape function you used with shape functions used by the software.

You can find more information about shape functions in "Finite Element Design for Stress Design" by Roobert Cook (1995)

Thanks Calvin Kauenhowen. The nodal values are good comparing to SAP2000. I will try to modify shape functions to obtain better results.