Course detail

Limit States and Reliability

FSI-RMSAcad. year: 2017/2018

The course is concerned wit the following topics:Limit states - classification, limit states in strength analysis. Basic terms of dependability theory with emphasized characteristics of reliability and durability. Most significant conceptions of linear elastic and elasto plastic fracture mechanics. Fatigue of structures, essential characteristics, durability assessment under low- and high-cycle fatigue. Evaluation of the resistance of structures to brittle fracture in the design stage. Assessment of the crack as a defect under monotonic and cyclic stresses.

Learning outcomes of the course unit

Students will master to solve simpler cases of reliability and durability assessment of structures with respect to the danger of fatigue and brittle fracture. They will have a clear idea of the current theoretical and experimental basis of this scientific branch. They will acquire skills to formulate assignment for experts of the branch and interpret their findings.


Basic knowledge of description and characteristics of deformation and fracture of materials under different types of loading and different temperatures. Basic terms of dependability theory concerning especially reliability and durability


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Bílý, M.: Dependability of Mechanical Systems, , Elsevier 1989
Vlk, M.: Mezní stavy a spolehlivost, , VUT FS Brno 1991
Kunz, J.: Základy lomové mechaniky, , ČVUT Praha 2000
Anderson,T.L.: Fracture Mechanics - Fundamentals and Applications, , CRC Press, Boca Raton 1995
Vlk, M.: Dynamická pevnost a životnost, VUT FS Brno 1992
SAE: Fatigue Design Handbook, Society of Automotive Engineers, 1997

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course-unit credit requirements: active participation in the seminars, good results of elaborated laboratory exercises, solving additional tasks in case of longer excusable absence. Seminar tutor will specify these conditions in the first week of semester.
Examination consists of 2 parts: written (knowledge of elementary terms, important regularities and their applications) and oral (discussion over the written part of examination and problems solved in seminars). To pass the examination, neither the written nor the oral part must be evaluated by the failling degree F.

Language of instruction


Work placements

Not applicable.


The objective of the course is to make students familiar with elementary terms and parameters in the field of limit states and dependability theory. Theoretical basis of two most important limit states of steel structures -–limit states of fatigue and brittle fracture will be explained to them as well as topical methodology procedures in deterministic and probabilistic assessment of reliability and durability of structures will be demonstrated.

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

Attendance at seminars is required. One absence can be compensated by attending a seminar with another group in the same week, or by working out substitute tasks. More absences are compensated by additional assignments according to the instructions of the tutor.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 2. year of study, winter semester, 5 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. An introduction to the problems. Limit states, definition of the term, classification of limit states.
2. An introduction to the fracture mechanics, systems of fracture mechanics concepts.
3. Griffith‘s theory. The stress intensity factor concept.
4. The crack opening displacement and J-integral approaches. Two-criteria approach.
5. Two-parameter fracture mechanics. Subcritical crack growth.
6. Crack growth under cyclic loading.
7. Assessment of the known crack-like defect in the real structure.
8. Assessment of the structure for brittle fracture resistance in the design stage
9. Probability assessment of limit states.
10. High- and low-cycle fatigue – influence of stress and strain concentration
11. Fatigue durability in the one-stage loading and simple and combined stresses.
12. Durability in the stochastic loading.
13. Laboratory testing of reliability and durability.

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer


1. FEM-model of the body with crack, crack tip elements.
2. Determination of the stress intensity factor by means of finite element method.
3. Comparison of stress intensity factor from FEM and from the handbooks available.
4. Solving of materials non-linearity tasks in ANSYS.
5. Computation of J-integral.
6. Two-parameter fracture mechanics, Q-factor.
7. Computation of Q-factor for simple testing specimens.
8. Stress field near the crack tip under small scale yielding.
9. Probabilistic assessment in the program system ANSYS.
10. Simulation methods in ANSYS.
11. FORM and SORM methods.
12. Monte Carlo method with direct simulation - programs AntHill and VaP
13. Credit.