A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh damping matrix of the system with 5% damping for both modes.

A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh damping matrix of the system with 5% damping for both modes.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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FEA for Dynamic Problems

Finite element analysis or FEA is a computational tool that evaluates the approximate solution for a particular engineering problem. The tools provided by FEA help to evaluate the solutions of partial differential equations (PDEs) computationally following a numerical approach. Solutions of the PDEs can also be performed by following traditional algebraic approaches, but when the problem gets towards the complex side, it becomes very tedious and almost impossible to arrive at the solutions. In such cases, the FEA fulfills the purpose by evaluating the equations following multiple time steps and iterations. The more the time steps and iterations, the more accurate the solution. The solution plotted by FEA analysis and mathematical approaches varies asymptotically.

Question

A two-storey building structure is shown in Figure 5. The beams are assumed as rigid and the flexural
rigidity of the columns is given in the figure. a) determine vibration frequency and mode shape of the
structure; b) check the orthogonality condition of the derived mode shape; and c) determine the Rayleigh
damping matrix of the system with 5% damping for both modes.
M=10000 kg
El=10,000 kNm
El=10,000 kNm
3m
М-20000 kg
EI=30,000 kNm
EI=30,000 kNm
3.0m
Figure 5

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