Course detail

# Theory of Structures Reliability

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.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Student is able to directly or via some approximation method (especially Cornell reliabilioty index) evaluate failure probability. Student is also capable of using simulation methods Monte Carlo and Latin Hypercube Sampling. Student can use these methods to estimate failure probability of simpler problems from civil engineering. Student understands reliability background of design codes (Eurocode). Student elaborates semestral work and presents its results in front of the class.

Prerequisites

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

Co-requisites

experience in Microsoft office software Excel

Recommended optional programme components

Extension of semestral work by more advanced reliability function, eg. using Ansys, Atena of self-created software. For this purpose, special meeting are organized.

Not applicable.

Planned learning activities and teaching methods

During lectures, standard model of theory explanation using the blackboard and projector is used. In the training course, students themselves solves tasks on a paper or with a help of computer. In the second part of training, there is a semestral project which is at the end of the course presented to the rest of the students.

Assesment methods and criteria linked to learning outcomes

Conditions to get credit are (i) active presence in training course (two absences are allowed) and (ii) submission of semestral report describing failure estimation of individually selected random phenomenon.
For examination, students are required to (i) present the semestral work in front of the class and also (ii) pass the test, which is composed of both theoretical questions and practical tasks.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

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.
l2.Introduction of Risk engineering.
13.Reliability software - summary and conclusion.

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.

Specification of controlled education, way of implementation and compensation for absences

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

Classification of course in study plans

• Programme N-P-E-SI (N) Master's

branch K , 1. year of study, summer semester, 5 credits, compulsory

• Programme N-K-C-SI (N) Master's

branch K , 1. year of study, summer semester, 5 credits, compulsory

• Programme N-P-C-SI (N) Master's

branch K , 1. year of study, summer semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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.
l2.Introduction of Risk engineering.
13.Reliability software - summary and conclusion.

Exercise

26 hours, compulsory

Teacher / Lecturer

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.