# Results of Response Spectrum

I am doing a case study comparing the fundamental period of a 20-story reinforced concrete building with dual system in both directions and compared the results from SAP 2000 and Midas Gen. The reference building is from the book of SK Ghosh Seismic Design using Structural Dynamics. here is the link of the book http://secure.skghoshassociates.com/product/show_book.php?isbn=9781580017485.

The example problem in the book is solve by the author manually and the modal analysis was done using SAP 2000 and I wanted to verify the accuracy of the result by comparing them with midas gen and staadpro, Midas Gen result is very close with the book's output within 1 to 2 % difference however, staadpro output is way off, Here is the tabulated result,

SAP 2000 3D MODEL                                     MIDAS GEN 3D MODEL                            STAADPRO 3D MODEL

MODE  PERIOD   MASS PARTICIPATION   PERIOD   MASS PARTICIPATION     PERIOD     MASS PARTICIPATION
1              2.485                71.2%                        2.418                     72.19%                  2.738                        22.62%
2              0.659                14.8%                        0.658                     14.19%                  2.386                        36.85%
3              0.300                6.1%                          0.307                       5.98%                   2.034                       14.22%
4              0.178                3.1%                          0.184                       3.16%                   0.779                          3.98%
I have tried analyzing the staadpro model with and without P-delta but still way off. Both SAP 2000 and Midas Gen were using P-delta analysis with Response Spectrum analysis.

• In Section 1.18.2.1.3 of the Technical reference manual, there is an example shown for considering the PDELTA effect during dynamic analysis. It says that if you provide the commands in that sequence, the frequency will be calculated using the [K+Kg] matrix.

Also, I don't have that book that you are referring to. Can you attach the pages of the book describing that example, and the STAAD model?

• SKLose,

The P-delta KG analysis is the one I used in the staadpro analysis and I'm well aware of this analysis. I already posted this before that Etabs, Sap and Midas Gen have been using P-delta with Response spectrum analysis for quite a long time. This has to be implemented because ASCE 7-05 section 12.9.6 has specific requirement that modal response spectrum has to be analyzed together with P-delta. I also remember you did ask me how are those program doing it since the output from RSA are all positive values after the modal combination like CQC, SRSS etc are done.

It can be done as explained in the book of Wilson which is also the technical reference used for Etabs,Sap and Midas Gen by incorporating global geometric stiffness KG into the global lateral stiffness K (K +KG) which is now also implemented by staadpro using P-delta KG analysis. The difference with the implementation between Staadpro and Etabs or Midas Gen for that matter is that the last two has an added parameter called P-delta  load combination in which that particular combination is used to calculate the initial p-delta analysis in order to derive the geometric stiffness to be incorporated into the succeeding analysis. By doing this the P-delta analysis is actually being linearized and superposition method can then be applied. That is why in Etabs or Midas gen combinations can be done after the analysis because you do not need primary load cases (repeat load) anymore for the combination simple load combination will do. This has been shown by raycxx of Bentley support in one of his posts here where  he used load combination for P-delta KG. This is just not properly documented in Staadpro.

• Is there any method in Staad by which one can know whether the net support reaction generated due to Response Spectrum analysis is positive or negative i.e. upward or downward?

• thanks for the clear explanation Kris