Course detail

Theory of Structures Reliability

FAST-NDA029Acad. year: 2024/2025

Introduction of reliability theory, reliability background of standards for structural design (Eurocodes), Structural resistance and load action as two independent random variables, limit state and philosophy of design according to standards, theoretical failure probability, reliability conditions, reliability reserve, reliability index, numerical simulation methods of Monte Carlo type, Latin Hypercube Sampling, Importace Sampling, basic methods for failure probability analysis of structures designed by standards for design, basic methods for statistics, sensitivity and probabilistic analysis application to steel structures design. Introduction into risk engineering.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

prof. Ing. Drahomír Novák, DrSc.

Department

Institute of Structural Mechanics (STM)

Entry knowledge

Knowledge from Elasticity and plasticity, Structural mechanics, Probability and statistics.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

Students will get basic knowledge from theory of structural reliability: Stochastic model creation, reliability condition, numerical simulation methods of Monte Carlo type, limit states, risk engineering. Present reliability software will be introduced.
Student will learn basic knowledge from theory of structural reliability: Stochastic model creation, reliability condition, numerical simulation methods of Monte Carlo type, limit states, risk engineering. Present reliability software will be introduced.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme NPC-SIK Master's 1 year of study, summer semester, compulsory

  • Programme CZV1-AKR Lifelong learning

    specialization PNM , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Drahomír Novák, DrSc.

Syllabus

  • 1. Introduction of reliability theory, reliability background of standards for structural design (Eurocodes), structural resistance and load action as two independent random variables, reliability condition, reserve of reliability.
  • 2. Limit state and philosophy of design by standards.
  • 3. Reliability standards: theoretical failure probability, reliability index.
  • 4. Aproximation methods FORM a SORM.
  • 5. Numerical simulation method Monte Carlo in applications.
  • 6. Computation model, model uncertainty, grosses errors.
  • 7. Numerical simulation methods Latine Hypercube Sampling, Importace Sampling in applications.
  • 8. Random process and random fields – Stochastic finite element methods and these applications.
  • 9. Probabilistic optimization, problems of live-time of structures.
  • 10. Weibull theory.
  • 11. Unbalanced levels of the failure probability of the structures designed by standards, option of input variability modelling.
  • 12. Introduction of Risk engineering.
  • 13. Reliability software – summary and conclusion.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Lukáš Novák, Ph.D.

Syllabus

  • 1. Statistical evaluation of random variable.
  • 2. Recapitulation of probability and statistics using simple examples.
  • 3. Examples on usage of Cornell reliability index.
  • 4. Simple example to learn Monte Carlo simulation method using Excel.
  • 5. Calculations of failure probability via Latin Hypercube Sampling in Excel.
  • 6. More complex examples on simulation methods using Excel.
  • 7. Evaluation of previous examples in Freet.
  • 8. Failure probability estimation using FORM method (First Order reliability Method).
  • 9. Calculation of failure probability using Importance Sampling.
  • 10. Introduction to individual semestral project.
  • 11.–13. Work on individual semestral projects.