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Lecturer(s)
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Horák Lukáš, Ing.
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Vaňková Tereza, Ing.
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Heczko Jan, Ing. Ph.D.
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Zajíček Martin, Ing. Ph.D.
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Laš Vladislav, Prof. Ing. CSc.
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Course content
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1) Introduction: classification of the subject, content of the subject. Principal assumptions for the solution of problems in mechanics of materials, methods of solution. External effects on body, external and internal forces, definition of stress and strain. 2) Pure tension - compression. Tensile test, work diagram, deformation energy, strain energy density, Hooke's Law, law of superposition of stresses and displacements, deformation of rod, strength condition. Strain energy for pure tension (compression). Transverse deformation (Poisson's ratio), relative change of volume. Statically indeterminate problems. 3) Geometrical characteristics of cross-sections: first, second and product moments of area, moments of composite areas, moments for parallel axes - (Huygens-Steiner) Parallel axis theorem. Moments for rotated axes. Mohr's circle, principal axes and principal moments. Polar moment of area. 4) Bending of straight beams: definition of pure bending. Identification of internal force effects - normal and shear forces, bending moment - method of sections, Schwedler's theorem. Normal and shear stresses and distribution thereof over cross-section, strength criterion, strain energy. 5) Deflection of beams: double integration method, method of moment areas (Mohr's method). 6) Method of moment areas (Mohr's method) for determining the beam deflection (simply supported beam, cantilever beam, overhanging beam). 7) Deflection of variable cross-section beam. Statically indeterminate cases: compensation method. 8) Torsion: definition of pure torsion. Circular cross-section: derivation of stress and strain formulae, strength condition. Generalization for arbitrary cross-section. Strain energy. 9) Plane stress: definition, relations for stress components in arbitrary plane, Mohr's circle, principal stresses, maximum shear stress. Strains for plane stress - Hooke's Law. 10) Three-dimensional elasticity: definition, principal stresses, Mohr's circle, Hooke's Law, review of uniaxial and plane stresses from the 3D case point of view. Strain energy density for 3D case. 11) Ultimate stresses (Yield criteria): Guest, Von Mises, Mohr. 12) Combined loading. 13) Fundamentals of strain-gauge measurement: electrical resistive strain-gauges, compensation of temperature changes, strain-gauge measurements, principal of measurement bridges. Calculation of stress from measured strains: uniaxial, plane stress for known and unknown principal directions.
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Learning activities and teaching methods
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Lecture
- Preparation for an examination (30-60)
- 50 hours per semester
- Contact hours
- 65 hours per semester
- Undergraduate study programme term essay (20-40)
- 30 hours per semester
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| prerequisite |
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| Knowledge |
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| zná základní metody derivace a integrace |
| zná základy maticového a vektorového počtu |
| zná mechaniku hmotného bodu a tuhého tělesa |
| zná základy matematické analýzy |
| Skills |
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| dovede řešit soustavu lineárních rovnic |
| dovede řešit základní typy integrálů |
| dovede používat maticový a vektorový počet |
| dovede použít základy matematické analýzy |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| student - se orientuje v souvislostech lineární pružnosti a pevnosti |
| umí řešit napjatost a deformace jednoduchých součástí namáhaných tahem, krutem, ohybem a jejich kombinacemi |
| umí řešit úlohy rovinné napjatosti a aplikuje podmínky pevnosti |
| aplikuje znalosti předmětu na základní problémy lineární pružnosti v technické praxi |
| Skills |
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| dovede analyticky řešit napjatost a deformaci prutu namáhaného tahem krutem a ohybem |
| dovede dimenzovat namáhaný prut |
| dovede analyzovat rovinnou a prostorovou napjatost |
| dovede aplikovat podmínky pevnosti |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture supplemented with a discussion |
| Skills |
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| Practicum |
| Textual studies |
| Competences |
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| Textual studies |
| Self-study of literature |
| assessment methods |
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| Knowledge |
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| Written exam |
| Skills |
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| Written exam |
| Competences |
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| Seminar work |
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Recommended literature
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Pružnost a pevnost II : kolektiv. 2. díl. Praha : ČVUT, 1985.
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Gere, J. M. Mechanics of materials. 6th ed. Toronto : Thomson, 2006. ISBN 0-534-41793-0.
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Hájek, Emanuel. Pružnost a pevnost I. Praha : ČVUT, 1984.
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Hájek, Emanuel; Reif, Pavel; Valenta, František. Pružnost a pevnost I. Praha : SNTL, 1988.
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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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Laš, Vladislav; Hlaváč, Zdeněk; Vacek, Vlastimil. Technická mechanika v příkladech. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-849-8.
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Němec, Jaroslav; Dvořák, Jan; Höschl, Cyril. Pružnost a pevnost ve strojírenství. Praha : SNTL, 1989.
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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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