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Lecturer(s)
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Grznár Martin, Ing. Ph.D.
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Gabriel Jan, Ing. Ph.D.
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Course content
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1. External and internal forces. Mechanical equilibrium. Method of sections. Definition of stress and strain. Normal and shear stress. Axial and shear strain. Three-dimensional stress state. Assumptions, definition and solution approaches of linear elastostatic problem. 2. Transformation of coordinates, stress tensor, and strain tensor. Principal planes, stresses and strains. Maximum shear stress. Mohr's diagram for stresses and strains. 3. Hooke's law. Determination of material parameters using experimental tests. Stress-strain response of ductile and brittle materials. Engineering constants (Young's modulus, Poisson's ratio, shear modulus). 4. Strain-energy density. Failure and yield criteria (Tresca, Von Mises, Mohr-Coloumb). 5. Geometrical characteristics of areas (first, second, product and polar moments of inertia). Composite shapes. Parallel axis theorem. Moments for rotated axes. Mohr's circle. Principal axes and moments. 6. Pure tension-compression of rods. Assumptions, internal loads, designing dimensions, analysis of deformation (displacement, elongation). 7. Pure torsion of cylindrical rods. Assumptions, internal loads, designing dimensions, analysis of deformation (rotation). 8. Bending of slender beams. Assumptions (Euler-Bernoulli beam theory), internal loads, Schwedler's theorem, designing dimensions, analysis of deformation (deflection, rotation). 9. Effects of temperature. Statically determinate and indeterminate structures (tension, torsion, bending). 10. Castigliano's theorem. Planar curved beams and frames. 11. Stability (buckling) of straight rods. Euler's and Tetmayer's theories. 12. Thick-walled cylindrical vessels. 13. Thin-walled shells of revolution.
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Learning activities and teaching methods
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- Preparation for an examination (30-60)
- 45 hours per semester
- Contact hours
- 65 hours per semester
- Undergraduate study programme term essay (20-40)
- 25 hours per semester
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| prerequisite |
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| Knowledge |
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| knows fundamental methods of differentiation and integration |
| knows fundamentals of matrix and vector algebra |
| knows mechanics of point masses and rigid bodies |
| knows fundamentals of mathematical analysis |
| Skills |
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| is able to solve set of linear equations |
| is able to find basic derivatives and evaluate basic integrals |
| is able to apply matrix and vector alebra |
| is able to apply fundamentals of mathematical analysis |
| Competences |
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| N/A |
| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| student orients himself in the relationships of linear elastostatics |
| is able to solve stress and strain states of simple bodies loaded in tension, torsion, bending, or combinations thereof |
| can solve problems of uniaxial, plane, and threedimensional stress states and applies failure conditions in dimensions designing |
| applies the knowledge of the course on principal problems of linear elastostatics in real-world problems |
| Skills |
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| is able to analytically solve problems of stresses and strains of rods and beams loaded in tension, torsion, or bending |
| is able to design dimensions of loaded rod or beam |
| is able to analyze uniaxial, plane, and three-dimensional states of stress |
| is able to apply failure conditions |
| Competences |
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| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Skills |
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| Practicum |
| Competences |
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| Self-study of literature |
| Individual study |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Skills |
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| Combined exam |
| Competences |
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| Seminar work |
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Recommended literature
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Gere, J. M. Mechanics of materials. 6th ed. Toronto : Thomson, 2006. ISBN 0-534-41793-0.
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Hearn, E. J. Mechanics of materials : an introduction to the mechanics of elastic and plastic deformation of solids and structural materials. 2. 3rd ed. Oxford : Butterworth-Heinemann, 1997. ISBN 0-7506-3266-6.
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Riley, William F.; Sturges, Leroy D.; Morris, Don H. Mechanics of materials. 6th ed. Hoboken : John Wiley & Sons, 2007. ISBN 978-0-471-70511-6.
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