Course detail

# Reliabilty Theory of Building Materials

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 create finite element method model of concrete beam failure in software Atena. Student randomize the model in Sara studio.

Prerequisites

Knowledge from Elasticity, Structural mechanic, Probability and Statistics calculus.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

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 an individual task to create a finite element model of failure of concrete beam in Atena software and randomization of the model.

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) creation and randomization of finite element method model of concrete beam failure.
Students are examined through individual oral questioning.

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 states and philosophy of design by standards; Reliability standards: theoretical failure probability, reliability index.
3.Numerical simulation method Monte Carlo in applications.
4.Computation model, model uncertainty, grosses errors.
5.Numerical simulation methods Latin Hypercube Sampling, Importace Sampling in applications, FORM, SORM approximation methods.
6.Linear elastic fracture mechanic - used of statistics and sensitivity analysis; verification and calibration of standards; design procedures.
7.Modeling of failure process in concrete structures; Fictive crack model, Fictive crack model and rotate crack model.
8.Reliability of the elements made of quasi-brittle materials, computations in ATENA code.

Aims

Stochastic model, reliability condition, numerical simulation methods, limit states, linear elastic fracture mechanics.

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-C-SI (N) Master's

branch M , 2. year of study, winter semester, 4 credits, compulsory-optional

• Programme N-P-E-SI (N) Master's

branch M , 2. year of study, winter semester, 4 credits, compulsory-optional

• Programme N-K-C-SI (N) Master's

branch M , 2. year of study, winter semester, 4 credits, compulsory-optional

#### Type of course unit

Lecture

13 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 states and philosophy of design by standards; Reliability standards: theoretical failure probability, reliability index.
3.Numerical simulation method Monte Carlo in applications.
4.Computation model, model uncertainty, grosses errors.
5.Numerical simulation methods Latin Hypercube Sampling, Importace Sampling in applications, FORM, SORM approximation methods.
6.Linear elastic fracture mechanic - used of statistics and sensitivity analysis; verification and calibration of standards; design procedures.
7.Modeling of failure process in concrete structures; Fictive crack model, Fictive crack model and rotate crack model.
8.Reliability of the elements made of quasi-brittle materials, computations in ATENA code.

Exercise

13 hours, compulsory

Teacher / Lecturer

Syllabus

1. Recapitulation of probability and statistics using simple examples.
2. Examples on usage of Cornell reliability index.
3. Simple example to learn Monte Carlo simulation method using Excel.
4. Calculations of failure probability via Latin Hypercube Sampling in Excel.
5. More complex examples on simulation methods using Excel.
6. Linear elastic fracture mechanics, simple calculations.
7. Finite element method software Atena, creation of computational model.
8. Randomization of Atena model through Sara studio.

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