Course detail

Elasticity and Plasticity (1)

FAST-D27Acad. year: 2020/2021

The topics of the course are designed to follow subject "Fundamentals of Structural Mechanics". Fundamental concepts of strength of material are introduced first: Stress and strain definitions, Hooke´s law, Saint- Venaint´s principle, basic diferential equations.
Then different types of elementary loading are studied: Tension and compression, shear – riveted and bolted joints, bending of beams – normal and shearing stresses, shear centre, torsion, buckling of bars and combined loadings – bending in two planes, excentric tension (compression), core of the cross section. The methods for determination of deflections of beams are also explained: Method of integration of differential equations, Mohr‘s method. Stress state in a point of a body – uniaxial, biaxial and triaxial state of stress, principle stresses for biaxial state of stress, principal stress trajectories and energetic approaches are also included. The course is closed by explanation of basic strength theories of mechanical failure of materials.

Language of instruction

Czech

Number of ECTS credits

4

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Reactions, internal forces, centroid and second order moments of cross-sections

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1.Basic principles, conceptions and assumptions of the theory of elasticity and plasticity (the material strength). Material laws, working diagrams. The relation between internal forces and the stresses.
2. Simple tension – stress and strain state. More general cases of the tension (compression). Statically indeterminate cases. The influence of the initial stress and the temperature field.
3. Simple shear, the connections strained by shearing. Simple bending. Normal stress produced by bending. Design and check of bent girders.
4. Shearing stress in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders. The influence of the shear on the deflection of the beam.
5. Complex cases of the load of the beam. Spatial and biaxial bending.
6. Tension (compression) and uniaxial bending.
7. Eccentric tension and compression. The calculation of the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load.
8. Free warping of a massive and thin-walled (opened and closed) cross-section beams.
9. The differential equation of the deformation line. The integration of the thrust line diff. equation. The method of initial parameters, Mohr’s method.
10. Buckling strengths and the stability of the compressed bars. Euler’s solution. Critical force and critical stress. The influence of the boundary conditions. The strength approach to stability. A bar loaded by a bending and buckling load. The check of the buckling bars.
11. The stress and strain state in a point of the body. The principal stress at the plane stress problem.
12. Energetical approaches. Ritz method.
13. Basic strength theories of mechanical failure of materials.

Work placements

Not applicable.

Aims

Stress, strain, deformations and dimensioning of structures

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bažant, Z. P., Cedolin, L.: Stability of Structures. Oxford University Press 1991
Beer, F.P., Johnston, R.Jr.: Mechanics of Materials. McGraw-Hill Book Company 1981
Servít, R., Doležalová, E., Crha, M.: Teorie pružnosti a plasticity I.. SNTL/ALFA Praha 1981
Šmiřák, S.: Pružnost a plasticita I.. skriptum PC DIR 1995
Timoshenko, S.: History of Strenght of Materials. Dover Pubns 1983

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1.Basic principles, conceptions and assumptions of the theory of elasticity and plasticity (the material strength). Material laws, working diagrams. The relation between internal forces and the stresses. 2. Simple tension – stress and strain state. More general cases of the tension (compression). Statically indeterminate cases. The influence of the initial stress and the temperature field. 3. Simple shear, the connections strained by shearing. Simple bending. Normal stress produced by bending. Design and check of bent girders. 4. Shearing stress in a bent beam. The centre of the shear. Shearing stress in the thin-walled girders. The influence of the shear on the deflection of the beam. 5. Complex cases of the load of the beam. Spatial and biaxial bending. 6. Tension (compression) and uniaxial bending. 7. Eccentric tension and compression. The calculation of the position of the neutral axis, the core of the section. Design of the girders in a case of the complex load. 8. Free warping of a massive and thin-walled (opened and closed) cross-section beams. 9. The differential equation of the deformation line. The integration of the thrust line diff. equation. The method of initial parameters, Mohr’s method. 10. Buckling strengths and the stability of the compressed bars. Euler’s solution. Critical force and critical stress. The influence of the boundary conditions. The strength approach to stability. A bar loaded by a bending and buckling load. The check of the buckling bars. 11. The stress and strain state in a point of the body. The principal stress at the plane stress problem. 12. Energetical approaches. Ritz method. 13. Basic strength theories of mechanical failure of materials.

Exercise

26 hours, compulsory

Teacher / Lecturer