Course detail

# Selected Chapters of Structural Mechanics 1 (K)

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

The result is a practical knowledge about models and theories utilizable for inelastic deformation and subsequent failure of materials of structures, particularly quasi-brittle silica-based composites. Student will be able to perform nonlinear structural analysis of reinforced concrete structure using appropriate special software including evaluation of failure progress and its consequences. Students will get some additional knowledge on cables.

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

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

Recommended optional programme components

cooperatino on projects lead by teachers

Not applicable.

Planned learning activities and teaching methods

Lectures using slides accompanied by discussions and derivations on black board. Next, work on projects by using advanced software on PC

Assesment methods and criteria linked to learning outcomes

The conditions for getting the credits are: (i) sufficient attendance, (ii) individual project on computer and, (iii) active work in practical lessons. Finally, a written exam focused on theory must be at least 50 % correct.

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

• Programme B-P-E-SI (N) Bachelor's

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

• Programme B-K-C-SI (N) Bachelor's

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

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

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.

Exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Submission of individual problems to be solved on computer.
2. - 10. Work on the tasks with the help of the teacher.
11. Presentation of the results, credits.