Dear researchers;
I want to model a 3D multi-storey building and submit it to earthquake, and then I want to solve the equation of motion of the building under the earthquake load. How can I do that ? can I solve the equation in state space representation ?
Ward regards
You can solve dynamic equation for harmonic excitation using the famous Duhamel Integration. However, it involves lengthy calculations which are tedious and impractical to solve manually. There are plenty of numerical solutions to solve random excitation of structures. You need to master two basic theory before embarking into dynamic solution: (i) base excitation, and (ii) numerical evaluation of dynamic response. If you are looking at nonlinear response (which is usually the case in seismic time history analysis), the equations become more complex.
Dear Patrick, thank you for the replay
Let us assume a 3 storey building, I want to study the response of this building considering displacement in X, Y and rotation, how the motion equation will be ?
Mx'' + Cx' + Kx = Xg"
How the M, K, C matrix will be build ?
And How to solve this using state space resolution ?
Best regards, And Happy New year.
Hi Mahdi. I am using the comercial software Ansys or Comsol for obtain forces in building. Next you need put in the equation. Mx"+Cx'+Kx=Xg.
For obtain M C and K. In the matrix K I use the book how: clough. Or Finit element Books. For the M i use Matrix of consistent.
Good luck in your study.
Dear Ahmed Ebid thank you I'm using A.K Chopra book but I was looking for more details.
Dear Carlos, can you please give the titles of those books you are using ?
Warm regards
The dynamic analysis of a building in X, Y and RZ directions is the simplification of a 3D Analysis (6 Degrees of freedom). The asumptions behind this simplificated pseudo tridimensional analysis are that movements in other directions are negligible. Chopra explains it very well. I recomend to study the modal decomposition to transform the MDOF dynamic analysis in many single DOF dynamic analysis. For seismic response you have to study the step by step numerical methods for solving differential equations. Influence vector is important for seismic analysis. Hope you can review this items in Chopra and also the pages 7 until 14 of the attached notes. May be this Matlab scripts can help you. Kind regards!
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