Course detail

Selected problems of concrete structures II (K)

FAST-CL59Acad. year: 2019/2020

Non-linear material models of plain and reinforced concrete and their application in some commercial programming systems of FEM (finite element method).
Modelling of concrete members sections behaviour (linear and non-linear analysis) using the FEM analysis, Non-linear analysis of reinforced concrete sections.
Solution of state of stress effected by temperature load.


Institute of Concrete and Masonry Structures (BZK)

Learning outcomes of the course unit

A student gains these knowledge and skills:
• Analysis of linear and non-linear behaviour of concrete structures sections.
• Non-linear static analysis of concrete structures and their parts.


structural mechanics, numerical methods, concrete structures, prestressed concrete


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

WERGNER, R.: Tragverh. von Stahlbetonplatten mit nichtlin. Materialgesetz. TU München, Frankfurt, 1974. (DE)
ZIENKIEWICZ, O, C., TAYLOR, R.L. a ZHU, J.Z.: The finite element method: Its basis and fundamentals. 6th ed.. Amsterdam: Elsevier Butterworth-Heinemann, 2005. ISBN 0-7506-6320-0. (EN)
BATHE, Klaus-Jürgen: Finite element procedures. New Jersey: Prentice Hall, 2006. ISBN 978-0-9790049-0-2. (EN)
GHALI, Amin, FAVRE, Renaud a ELBADRY, Mamdouh: Concrete Structures. Stresses and Deformations: Analysis and Design for Sustainabil. London: Spon Press, 2012. ISBN 978-0-415-58561-3. (EN)
KOLÁŘ, Vladimír et al: Výpočet plošných a prostorových konstrukcí metodou konečných prvků. Praha: SNTL, 1979. (CS)
KOLÁŘ, Vladimír, NĚMEC, Ivan a KANICKÝ, Viktor: FEM: principy a praxe metody konečných prvků. Vyd. 1.. Praha: Computer Press, 1997. ISBN 8072260219. (CS)
KHONKE, P.: ANSYS - User manual. Cannonsburg: SAS IP, 1999. (EN)
ČERVENKA, Vladimír, JENDELE, Libor a ČERVENKA, Jan: ATENA Program Documentation, Part 1 - Theory. Praha: Cervenka Consulting, 2012. [] (EN)
Kolektiv autorů: Scia Engineer 2012 Manuals. Nemetschek Scia, 2012. [] (EN)

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Modelling of cross-section behaviour of concrete members, linear and non-linear analysis. General formulation of the problem as physically non-linear task.
2. Solution of the conditions of equilibrium. Iterative methods. Control of loadd-bearing capacity.
3. Non-linear material models of concrete and reinforced concrete. Cracks, cracks localization, fracture energy, modelling of concrete in tension.
4. Plane state of stress, concrete crushing. Methods of solution of non-linear equations system.
5. Methods of non-linear task solution: layered, integral. Non-linear modelling of flat concrete structures.
6. Non-linear analysis of prestressed concrete sections. Optimisation of reinforcement design into a section.
7. Non-linear material models of concrete and reinforced concrete in some comercial software of FEM systems.
8. Temperature effects on concrete – calculation of temperature stress acting on structures.


Analysis of linear and non-linear behaviour of concrete structures sections.
Non-linear static analysis of concrete structures and their parts.

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.

Type of course unit



26 hours, optionally

Teacher / Lecturer


13 hours, compulsory

Teacher / Lecturer


eLearning: opened course