Elasticity 1

The course is not on the list Without time-table
Code Completion Credits Range Language
14EM1 Z,ZK 5 2P+2C Czech
Department of Materials


The course represents an introduction for several another lectures on continuum mechanics and the strength of materials. The first part contains a detailed theory of stress, small strains and linear elasticity. The second one represents a logical descent from the continuum mechanics to the practical engineering solution of simple problems on tension, bending, shearing and torsion in the cross section of bars and beams.

Syllabus of lectures:


1. Tensors 2. Strain: Lagrangian and Eulerian coordinates, finite strain tensor, small strain tensor, rotation tensor, compatibility equations 3. Stress: internal forces, stress vector, Cauchy's stress tensor, equilibrium equations, principal stresses, octahedral shear stress, Mohr's circles. 4. Basic of elasticity theory: generalized Hook's law, linear equations of mathematical theory of elasticity and boundary conditions, Saint-Venant’s principle, superposition principle, Beltrami-Michell equations, Lame's equations, potential and complementary strain energy of internal and external forces, variational principles of elasticity, Castigliano’s theorems, principle of finite element method, elasticity equations in polar coordinates 5. Mathematical vs. engineering solutions of elasticity problems, plasticity conditions, fatigue fracture, brittle and ductile fracture.

6. Bars and beams: geometric characteristics of the cross section, forces and moments in the cross section, load and supports and fixations, statically determinate and indeterminate problems. 7. Tension and compression: statically indeterminate cases, thin-walled pressure vessel, sudden changes in geometry and in the load. 8. Flexural loading of straight beams - stress: pure bending, transverse loading, load and shear and moment relationship, stresses in symmetrical and thin-walled cross sections under the shear force. 9. Flexural loading of straight beams - deflections: curvature of neutral axis, differential equation of the elastic curve, energy methods. 10. Statically indeterminate straight beams, theorem of three moments. 11. Curved beams: flexural stresses and changes in curvature, thin curved beams, frames. 12. Torsion of circular shaft: shear stress distribution, geometry of deformation.


Tensors, Analysis of stress, Small strain theory, Theory of linear elasticity, Axially loaded bars, Bending of straight bars and beams, Curved beams and frames, Torsion of circular shaft

Syllabus of tutorials:
Study Objective:
Study materials:

Key references:

[1]Gross, D., Hauger W., Schröder, J., Wall W. A., Bonet J.: Engineering Mechanics 2: Mechanics of Materials,

2nd ed., 2018, ISBN 978-3662562710

Recommended references:

[2]Boresi, A. P., Schmidt, R. J..: Advanced mechanics of materials. John Wiley& Sons, 2003,

ISBN 978-0-471- 43881-6

[3]Atkin, R. J., Fox, N.: An Introduction to the Theory of Elasticity, Dover Publications, 2005, 978-0486442419

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2022-08-07
For updated information see http://bilakniha.cvut.cz/en/predmet6231806.html