Course detail

Mathematical Modelling of Concrete Structures

FAST-5L6Acad. year: 2019/2020

Set up of mathematical models for modelling concrete structures in the phase of design and reconstruction. Modelling of behaviour of concrete elements sections (linear and non-linear analysis). National and international codes and their application on finite elements method (FEM) analysis. Static linear and non-linear analysis of a concrete structure and its parts.
Material models of reinforced and non-reinforced concrete, application in some commercial programme systems FEM.
Solution of state of stress effected by temperature load and volume changes.


Institute of Concrete and Masonry Structures (BZK)

Learning outcomes of the course unit

Not applicable.


structural mechanics, numerical methods, concrete structures


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Bathe, K. J.: Finite element Procedures in Engineering Analysis. Prentience Hall, New York 1982
Wergner, R.: Tragverh. von Stahlbetonplatten mit nichtlin. Materialgesetz. TU München, Frankfurt 1974
Zienkiewicz, O. C.: Method der Finiten Elemente. Hanser Verlag, Bonn 1977
Kanický, V., Kolář, V., Němec, I.: Metoda konečných prvků. Výpočet konstrukcí ....... Computer Press, Praha 1998
Khonke, P.: ANSYS - User manual. SAS IP, Cannonsburg 1999
Kolář, V., Kratochvíl, J., Leitner, F., Ženíšek, A.: Výpočet plošných a prostorových konstrukcí metodou konečných prvků. SNTL, Praha 1979

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. A section of reinforced concrete member subjected to normal force and bending moment action. General formulation of the problem as physically non-linear task.
2. Solution of the conditions of equilibrium.
3. Iterative methods.
4. Control of loadd-bearing capacity.
5. Optimisation of reinforcement design into a section.
6. National and international codes for reinforced concrete modelling. Non-linear modelling of framed concrete structures behaviour - load-bearing capacity, deformation.
7. Models of concrete and reinforcement at axial and plane state of stress.
8. Methods of non-linear task solution: layered, integral.
9. Non-linear modelling of flat concrete structures.
10. Application of some comercial software system for non-linear solution of reinforced concrete design.
11. Temperature stress of concrete members.
12. Temperature stress of concrete members - continuation.
13. Solution of state of stress caused by volume changes of concrete.
14. Solution of state of stress caused by volume changes of concrete - continuation.


Ability to analyse the linear and non-linear behaviour of concrete sections.
To apply a time analysis and the geometric and physical non-linearity in the concrete structure design.

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



13 hours, optionally

Teacher / Lecturer


13 hours, compulsory

Teacher / Lecturer