Course detail

# Selected Chapters of Structural Mechanics 1 (S)

Theories of deformation and failure of materials of civil engineering structures.
Viscoelasticity - creep and relaxation. Basic rheology models and their coupling. Compliance function for concrete.
Plasticity models for both uni- and multi-axial stress state. Mathematical description of plastic deformation. Plasticity criteria.
Stress concentration around notches. Fundamentals of linear elastic fracture mechanics. Griffith's theory of brittle fracture. Energy balance in cracked body, crack stability criterion. Stress state solution in cracked body, modes of crack propagation. Stress intensity factor, fracture toughness. Size effect. Classical nonlinear fracture models, toughening mechanisms. Cohesive crack models and their parameters, fracture energy, tension softening. Damage mechanics. Stochastic aspects of failure of quasi-brittle materials/structures.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Students will master the subject targets; it means the knowledge about models for inelastic deformation and failure of materials in building industry with particular attention to the theories of failure of quasi-brittle materials, e.g. concrete. The knowledge about selected failure models will be then deepened by practice with special software for analysis of concrete and reinforced concrete structures. The students will get familiar with advanced theories capturing selected phenomena occurring in the field of quasi-brittle structures, such as size effect, random distribution of strength, etc.

Prerequisites

fundamentals of structural mechanics, analysis of structures and theory of elasticity and plasticity, fundamentals of finite element method, infinitesimal calculus, matrix algebra, fundamentals of numerical mathematics

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Classification of structural materials according to the manner of their failure. Classification of models for mechanical behaviour of materials.
2. Viscoelasticity. Creep and compliance function. Maxwell and Kelvin model/chain. Compliance function for concrete.
3. Plasticity. Physical motivation. Schmid law. Plasticity models for uniaxial and multiaxial stress state.
4. Fracture mechanics. Fundamentals of linear elastic fracture mechanics.
5. Fracture mechanics. Classical nonlinear models. Nonlinear fracture behaviour of quasi-brittle materials. Formation and development of fracture process zone (FPZ). Toughening mechanism in FPZ.
6. Fracture mechanics. Classical nonlinear models. Parameters of cohesive crack models. Fracture mechanics. Fracture models based on continuum mechanics and discrete models.
7. Damage mechanics. Classification of models of failure of concrete and their hierarchy.
8. Stochastic aspects of failure and deformation of structures 9. Interaction of progressive collapse and spatial randomness in concrete structures.
10. Cable in plane - introdiction, fibre polygon, parabolic canetarian curve.
11. Statics of cable in a plane - a cable loaded by arbitrary vertical load, cable equation.

Aims

Earning knowledge about models and theories utilizable for inelastic deformation and subsequent failure of materials of structures, particularly quasi-brittle silica-based composites. Getting abilities to perform nonlinear structural analysis of reinforced concrete structure using appropriate special software including evaluation of failure progress and its consequences.

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 B-P-C-SI (N) Bachelor's

branch S , 4. year of study, summer semester, 4 credits, compulsory-optional

• Programme B-P-E-SI (N) Bachelor's

branch S , 4. year of study, summer semester, 4 credits, compulsory-optional

• Programme B-K-C-SI (N) Bachelor's

branch S , 4. year of study, summer semester, 4 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise

26 hours, compulsory

Teacher / Lecturer