The students should be able to formulate and solve structural reliability problems and to assess the partial safety factors included in the probabilistic design of ship structures.

Student responsibilities:

Grading and evaluation of student work over the course of instruction and at a final exam:

Colloquium (or numerical exam) 40%, oral exam 30%, project 30%

Methods of monitoring quality that ensure acquisition of exit competences:

esting through homework

Upon successful completion of the course, students will be able to (learning outcomes):

After successful completion of the course students will be able to: - independently determine probabilistic models of load and strength variables to be used in structural reliability studies. - calculate ship structural reliability with respect to the ultimate strength criterion. - independently analyse rules of classification societies developed based on reliability methods;

Lectures

1. Introduction: Traditional and probabilistic approach to structural safety
Modelling uncertainty and variability: What is uncertainty? Types of uncertainty. Different interpretations of probability. Descriptive statistics of samples. Histograms and analytical probability distribution functions.

2. Modelling uncertainty and variability: Estimation and model building from data. Methods of fit and tests of fit.

3. Multiple random variables, univariate and multivariate distributions. Functions of random variables. First- and second-order approximations of moments.

4. Probabilistic modelling waves and wave induced load effects. Short-term wave random wave process and short-term model for wave induced responses. Long-term model for wave induced responses.

5. Probabilistic modelling waves and wave induced load effects. Long-term wave random wave process and long-term model for wave induced responses.

6. Uncertainty in models of wave induced load effects: Uncertainty in short-term and long-term models.
Probabilistic modelling of still water induced load effects. Stochastic load combination.

7. Probabilistic modelling of the strength of ship structures.
Probabilistic modelling of plate strength: Review design methods, effect of material properties, initial imperfection.

8. Probabilistic modelling of the ultimate longitudinal strength of the ship hull girder. Review of methods and probabilistic models. Longitudinal strength of damaged ship structures. Model uncertainty. Effect of the uncertainty in material properties, geometry and residual stresses.

9. Principles of Structural Reliability. Basic formulation of structural component reliability. Second-moment reliability method: Cornell Reliability Index. Problem of lack of invariance.

10. First-order reliability methods (FORM). Transformation to the standard normal space: Rosenblatt, Nataf and Hermite transformations.

11. Reliability sensitivity measures; the second-order reliability method (SORM). Time-variant reliability analysis

12. Monte Carlo, importance sampling, and directional simulation methods for structural reliability evaluation.

13. Time-variant reliability analysis.

14. Systems reliability methods: Bounds on the reliability of series systems; Approximate methods for non-series systems.

15. Probabilistic design. Codified design formats. Partial factor design and LRFD code formats. Assessment of partial safety factors for the longitudinal strength of ships.

Exercises

1. Introduction to Excel for the purpose of the course

2. Basic probabilistic functions in shipbuilding and their use in Excel

3. Basic probabilistic functions in shipbuilding and their use in Excel

4. Use of software MARS

5. Calculation of the ultimate strength using the software MARS

6. Uncertainty of bending moments on still water- practical examples

7. Evaluation of adopted knowledge

8. Long-term distribution of wave-induced bending moment-practical example I

9. Long-term distribution of wave-induced bending moment-practical example II

10. Application of Cornell safety index on illustrative example

11. Application of Cornell safety index in calculation of the ultimate strength

12. Practical use of FORM in Excel I

13. Practical use of FORM in Excel II

14. Use of FORM in engineering practice

15. Evaluation of adopted knowledge

Compulsory literature:

J. Ferry Borges and M. Castanheta, Structural Safety, Laboratório Nacional de Engenharia Civil, 2nd Edition, 1971

Thoft-Christensen, P., Baker, M. J., Structural Reliability Theory and its Applications, Berlin, Germany: Springer-Verlag, 1982

Melchers, R. E., Structural Reliability, Analysis and Prediction. 2nd Edition John Wiley & Sons; 1999.

Guedes Soares, C. (Ed.) Probabilistic Methods for Structural Design. Kluwer Academic Publishers; Dordrecht: 1997.

Recommended literature: