Date (Hours Number) |
Topics |
07/01/2015 (6 h) |
- Course presentation.
- General considerations, organization of lessons, exercises and method of examination.
- Introductory overview on the topics.
- Description of the Italian bridges heritage.
- Classification of the bridges on different bases (obstacle passed, road served, material, static scheme).
- Actions assessment on the bridges.
- Standard actions: permanent loads, transit vehicles, wind load, load products from the obstacle passed (hydrodynamic forces, land forces, accidental knocks), fatigue.
- Actions related to time: degradation of materials in time, shrinkage and creep of concrete, steel relaxation.
- Seismic action.
|
08/01/2015 (6 h) |
- Classification of the Italian legislation approaches (DM 14/01/2008 and Circular 617 of 02/02/2009).
- Analytical methods provided and evaluation of structural safety for the bridges.
- Concept of useful life and return period.
- Evaluation of actions.
- Introduction to Bridge Managment through through the evaluation of the LCC.
- Definition of the types of life cycle (physical, economic, functional, etc.).
- Economic concepts (actual cost, discounted cost, discount factor).
- Phases that characterize the management and analysis of a bridge.
- Considerations on bridge managment.
- Importance of the study of the LCC for roads infrastructures.
- Hypothesis, and optimization of the solution.
- Sources of uncertainty and need for a probabilistic approach.
|
09/01/2015 (6 h) |
- Basic concepts of probability.
- Logical statements, basic rules, the concept of independence, variables mutually exclusive and collectively exhaustive.
- Total probability theorem and Bayes' theorem.
- Distribution of probability and their statistics.
- Discrete and continuous distributions, Probability Mass Function (PMF), Probability Density Function (PDF), Cumulative Mass Function (CMF), Cumulative Density Function (CDF), Complementary Cumulative Density Function (CCDF).
- Fundamental probability distributions: Geometric, Poisson, Exponential, Normal, Log-Normal./li>
- Statistics of probability distributions: median, mode, average, expected value, standard deviation.
- Exercises: probability distributions.
|
12/01/2015 (6 h) |
- Linear regression.
- Probabilistic model of linear regression, standard error of the regression, regression in the bi-logarithmic plan.
- Various examples.
- Probabilistic and Seismic Hazard Analysis (PSHA)
- Introduction to the concepts of hazard and seismic risk.
- Measurements of seismic intensity.
- Hazard curves and derivation of the uniform hazard spectrum.
- Closed form expression of hazard curve (exponential) and the use of Italian code data.
- Exercises: regression and hazard curve determination.
|
13/01/2015 (6 h) |
- Structural vulnerability.
- Definition of fragility curve.
- Procedures for make fragility curves using non-linear dynamic analysis: CLOUD and IDA.
- Linear regression in the bi-logarithmic plan to calculate the fragility curves from data obtained from CLOUD analysis.
- Calculation of risk.
- Rigorous methodology through the PEER formula
- Closed form approach (SAC-FEMA 2000).
- Exercises: vulnerability and risk assessment.
|
14/01/2015 (6 h) |
- Structural reliability.
- Introduction to structural safety.
- Definition of limite state function, failure probability and reliability index.
- Reliability assessment of structural elements.
- Methods for structural reliability assessment. Definition of FORM, SORM and FOSM.
- Structural reliability in the Italian code: LRFD.
- Sources of uncertainties and alternative simulation-based methods. Importance sampling technique.
- Concepts of systemic reliability.
- Properties of simple systems: series or parallel systems.
- Composite systems: cutset, pathset.
- Concept of weakest-link system.
- Exercises: structural reliability assessment.
|
15/01/2015 (6 h) |
- Bridge managment: maintenance costs.
- Description of maintenance costs, calculation of costs in closed form from the value of the mean annual cost.
- Calculation of maintenance costs based on a database of maintenance performed.
- Bridge managment: the life cycle cost.
- Calculation of life cycle cost profile given a certain maintenance profile.
- Life cycle cost for a set of infrastructures, starting from different construction time and with an assigned maintenance profiles.
- Exercises: LCC assessment.
|
16/01/2015 (6 h) |
- Bridge managment: maintenance programming.
- Type of maintenance.
- Reliability index and performance index.
- Degradation laws of materials.
- Calculation of the number of maintenances required (during the lifetime) in order to maintain an established reliability index.
- Maintenance programming during the lifetime.
- Exercises: elaboration of maintenence programs.
|
19/01/2015 (6 h) |
- General recap.
- Bridges as critical infrastructure of the road network, life cycle costs and maintenance strategies.
- Structural reliability, structural safety assessment, fragility curves.
- Hazard curves and risk assessment.
- Exercise: complete management over time of a system of road infrastructures.
- Problem definition and objectives.
- Identification of a population of infrastructures.
- State of the structures assessment, evaluation of life cycle cost and time schedule of maintenance.
|
20/01/2015 (6 h) |
Final exam. |