# Reliability and Risk Analysis of Structures

## Course Description:

Probabilistic models of random variables (Loads, resistances, geometry etc.). Estimation of failure probability and design point. Models of systems and processes (series and parallel systems). Linear and nonlinear limit-state functions. Dependent and independent random variables. Load combinations. Probabilistic assessment of safety factors. Probabilistic natural hazard models. Fragility and exposure. Risk, fragility curves and decision analysis.

### Prerequisite Knowledge

Πιθανότητες, μηχανική, στατική, υλικά.

### Course Units

# Title Description Hours
1 Probabilistic models Modeling of loads and resistances. Load combinations. Series and parallel systems 2Χ3=6
2 Limit-state function. Probability of failure. Second-order methods. Dependent and independent random variables. Linear and nonlinear limit-state functions. Monte Carlo simulation methods 2Χ3=6
4 Structure and infrastructure risk Total probability theorem. Risk Assessment. Methodologies with and without an interface variable (requirements of sufficiency and efficiency). Probabilistic models of natural hazards. Assessment of hazard at one or multiple sites. Fragility curves and surfaces for one component or a class of components. Assessment of losses based on global or local data. Decision analysis. User risk preference. 5Χ3=15
5 Applications Applications and solution of example cases. Building or bridge, reservoir, offshore structure. 2Χ3=6

### Learning Objectives

Upon the successful completion of the course, the students will be able to:

1. Rationally take into account the uncertainties when designing civil engineering projects, including structural, hydraulic and geotechnical infrastructure.
2. Estimate the probability of failure of a complex civil engineering project
3. Design a structure or any other complex system with an acceptable probability of failure
4. Assess structure and infrastructure risk under natural and man-made hazards
5. Make decisions under uncertain information

### Teaching Methods

 Teaching methods In-class lectures. Solution of simple examples and case studies in class. Discussion of case studies in class. PowerPoint presentations and board notes. Computer work using Excel and computational software. Yes: Mathematical computations software and Excel. Yes Three homeworks and one project

### Student Assessment

• Final written exam: 70%
• Assignments (projects, reports): 30%

### Textbooks - Bibliography

1. Thoft-Christensen, P. and M.J. Baker: Structural Reliability Theory and Its Applications. Springer Verlag, 1982.
2. Ditlevsen, O. & H.O. Madsen: Structural Reliability Methods. Wiley, 1996.
3. Madsen, H.O., S. Krenk & N.C. Lind: Methods of Structural Safety. Prentice-Hall, 1986.
4. M.G. Stewart and R.E. Melchers, Probabilistic risk assessment of engineering system. Chapman & Hall, London 1997.

## Lecture Time - Place:

• Tuesday, 09:45 – 12:30,
Rooms:
• Ζ. Κτ. 1 Πολ., Αιθ. 11

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