Earthquake Dynamics and Engineering

Recommended Prerequisites

Mathematic Analysis; Algebra; Theory of Structures; Vectorial Mechanics; Numerical Methods; Finite Elements.

Teaching Methods

Theoretical lectures with detailed explanation of the concepts, principles and fundamental theories, supported by audiovisual media. Resolution of some practical exercises, helping to frame the subjects and put them in tune with the students understanding.

Programming of the practical works distributed to the students in the classes.

Discussion and clarification of doubts concerning the study or the development of the works.

Learning Outcomes

It is intended that the students get familiar with the numerical techniques to approximate the solution of the differential equation of dynamic equilibrium of a discrete or continuum system, consisting on the formulation and solution of a set of algebraic equations representing relations between displacements, velocities and accelerations at a finite number of degrees of freedom. Afterwards, the students should understand and get skills on the use of commercial tools (software) for structural dynamic analysis, with the emphasis in the context of Seismic Engineering.

Work Placement(s)

No

Syllabus

1. SDOF systems
Equation of dynamic equilibrium. Undamped and viscous damped free vibration. Logarithmic decrement. Harmonic actions. Transfer function. Ressonance. Pulses. General action. Fourier and Duhamel integrals. Methods for the solution of the motion equation. Discretization of the Duhamel Integral. Step-by-step integration.
2. Continuous systems
Motion equation for linear elements. Eigenmodes and eigenfrequencies. Orthogonality and normalization. Modal superposition. Rayleigh method.
3. MDOF discrete systems
Mass and stiffness matrices. Eigenmodes and eigenfrequencies. Rayleigh-Ritz and Stodola methods. Modal analysis.
4. Analysis of structures under seismic action
Seismology and seismic analysis of structures. Characterization of the seismic action. Response spectra. Modal superposition method. Rayleigh method. Peak response. Eurocode 8.

Assessment Methods

Continuous
Reports of practical work: 50.0%
Exam: 50.0%

Bibliography

1. Ray W. Clough and Joseph Penzien, “Dynamics of Structures”

2. Bathe, K. J. e Wilson, E. L.- “Numerical Methods in Finite Element Analysis”

3. Paz, Mário-Structural Dynamics

4. Barbat, A. ; Canet, J., “Estructuras sometidas a acciones sismicas-Cálculo por ordenador”,CIMNE,Barcelona,1994