Study-unit PROBABILISTIC METHODS FOR EARTHQUAKE ENGINEERING
| Course name | Civil engineering |
|---|---|
| Study-unit Code | A001082 |
| Curriculum | Strutture |
| Lecturer | Massimiliano Gioffre' |
| Lecturers |
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| Hours |
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| CFU | 5 |
| Course Regulation | Coorte 2022 |
| Supplied | 2022/23 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | ICAR/08 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Principles of probability theory. Random variables, stochastic processes and fields. Monte Carlo simulation. Algorithms and programming codes for probabilistic structural analysis. |
| Reference texts | A. Papoulis, S.U. Pillai, Probability random variables, and stochastic processes, McGraw-Hill Inc., 2002. D.E. Newland, An introduction to Random Vibrations, Spectral & Wavelet Analysis, Dover Publication Inc., Mineola, New York, 2005. M. Grigoriu, Stochastic Calculus, Applications in Science and Engineering, Birkhauser, Basel, 2002. |
| Educational objectives | Knowledge of the Monte Carlo simulation for random variables and vectors, stochastic processes and fields. Knowledge of problems connected to implementation of numerical codes for solving random problems in structural engineering. |
| Prerequisites | In order to be able to understand and apply the majority of the techniques described within the Course, the following knowledge is recommended: Maths: derivation and integration techniques for one-dimensional and bi-dimensional functions; differential equations. Physics and Meccanica Razionale: vector calculus; equilibrium equation both for static and dynamic problems. Structural Mechanics and Strength of Materials: equilibrium, compatibility and constitutive equations for the elastic continuum; beam elastic deflection equations. Non-linear mechanics and structural dynamics: plane problems (plane stress and plane strain problems); equilibrium equation for discrete systems (multi degree fo freedom - MDOF); modal analysis and modal superposition technique. Solution of structural systems using the Finite Element Method (FEM). |
| Teaching methods | Face-to-face both theoretical and practical classes. |
| Other information | Attendance to classes: optional but strongly advised. |
| Learning verification modality | Hands-on practice and oral exam. |
| Extended program | Principles of sets theory. Principles of probability theory: experiment, events, probability definitions, complementary and total theorems, conditional probability, total probability theorem, Byes theorem. Random variables: distribution and density functions, moments, second moment characterization, Monte Carlo simulation. Random vectors: joint and marginal distribution and density functions, moments of joint distributions, second moment characterization, Monte Carlo simulation. Stochastic processes and fields: finite dimensions joint distributions, weak and strong stationarity, ergodicity, correlation structures and spectral densities, second moment characterization, time averages, Monte Carlo simulation for generation of spectra-compatible seismic acceleration time histories. Algorithms for numerical static and dynamic analysis of structures. Structural analysis by means of commercial software. |