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Course info
KME / PP2
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Course description
Department/Unit / Abbreviation
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KME
/
PP2
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mechanics of Materials 2
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
|
Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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|
|
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Automatic acceptance of credit before examination
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No
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Summer semester
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38 / -
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0 / -
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2 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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KME/DPP or KME/PP1
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Courses depending on this Course
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KME/SZMPT
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim of the course is to acquaint students with following problems:
Fundamentals of mathematical theory of elasticity. Finite element method. Axially symmetrical problems (spinning disks, thick-walled cylindrical vessels) - stress and strain, technical applications. Slender curved and cranked beams and frames - stiffness and strength analysis. Structural stability, fundamentals. Fundamentals of stiffness and strength analysis of components from anisotropic materials. Fundamentals of linear and non-linear fracture mechanics. Material fatigue. Construction of computational models for the solution of problems using finite element method.
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Requirements on student
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Requirements for credit:
Elaboration and submission of semester work having relevant quality.
Requirements for exam:
Active knowledge of lectured subject matter and its application in the solution of specific problems.
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Content
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Lectures:
1. Three-dimensional state of stress: principal planes, principal stresses, generalized Hooke's Law.
2. Fundamentals of mathematical theory of elasticity: Derivation of differential equations of equilibrium. Geometrical relations. Physical relations. Boundary conditions.
3. Slender curved and cranked beams: statically determinate and indeterminate. Analysis of forces, stresses, dimensions finding and deflection calculation.
4. Closed planar frames: general and symmetrical frame, influence of cross-piece. Shells: basic terms, membrane conditions. State of stress of thin-walled rotational shell.
5. Spinning disks: theory of spinning disks - disk of constant and variable thickness. Stress and strain analysis.
6. Thick-walled cylindrical vessels: Stress and strain analysis. Ring to shaft press-fitting.
7. Circular plates: Derivation of the basic equation of circular plates. Calculation of plate deformation and stresses.
8. Structural stability: critical force, analysis of Euler's theory, elastic and inelastic buckling analysis.
9. Membrane analogy 1: Stress function, torque, Stokes theorem.
10. Membrane analogy 2: Slim rectangle of torsion, quadratic torsion moment, loose twist of thin-walled open and closed profiles.
11. Fundamentals of fracture mechanics: linear fracture mechanics, Griffith concept, Irvin-Orowan concept of brittle fracture. Stress intensity factor, fracture toughness.
12. Material fatigue: fatigue fracture, cyclic loading, Wöhler's diagram. High-cycle fatigue, fatigue strength (fatigue notch factor, influence of size and surface quality, possibilities of increasing fatigue strength). Fatigue strength of real component.
13. Reserve.
Exercises:
1. Conditions for credit awarding. Review of subject matter from PP1.
2. Three-dimensional state of stress.
3. Theoretical basis for laboratory measurement.
4. Laboratory measurement.
5. Planar curved and cranked beams.
6. Closed frames. Rotational thin-walled shells.
7. Spinning disks. Semester work.
8. Thick-walled cylindrical vessels.
9. Ring to shaft press-fitting, releasing revolutions.
10. Circular plates.
11. Free twisting of open profiles.
12. Free twist of closed profiles.
13. Material fatigue. Credit awarding.
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Activities
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Fields of study
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Guarantors and lecturers
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-
Guarantors:
Prof. Ing. Vladislav Laš, CSc. (100%),
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Lecturer:
Ing. Vítězslav Adámek, Ph.D. (100%),
Prof. Ing. Vladislav Laš, CSc. (100%),
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Tutorial lecturer:
Ing. Vítězslav Adámek, Ph.D. (100%),
Ing. Martin Zajíček, Ph.D. (100%),
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Literature
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Basic:
Hájek, Emanuel; Reif, Pavel; Valenta, František. Pružnost a pevnost I. Praha : SNTL, 1988.
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Basic:
Michalec, Jiří. Pružnost a pevnost II. Vyd. 2. Praha : Vydavatelství ČVUT, 2001. ISBN 80-01-02375-3.
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Extending:
Kolektiv. Pružnost a pevnost II. Praha : Vydavatelství ČVUT, 1980.
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Recommended:
Gdoutos, E. E. Fracture mechanics : an introduction. Dordrecht : Kluwer, 1993. ISBN 0-7923-1932-X.
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Recommended:
Jenkins, C. H.; Khanna, Sanjeev K. Mechanics of materials : a modern integration of mechanics and materials in structural design. Amsterdam : Elsevier Academic Press, 2005. ISBN 0-12-383852-5.
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Recommended:
Hearn, E. J. Mechanics of materials 1 : an introduction to the mechanics of elastic and plastic deformation of solids and structural materials. 3rd ed. Oxford : Butterworth-Heinemann, 1997. ISBN 978-0-08-052399-6.
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Recommended:
Hearn, E. J. Mechanics of Materials 2: The Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials. Third Edition. Oxford : Butterworth-Heinemann, 1997. ISBN 978-0750632669.
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Recommended:
Němec, Jaroslav; Dvořák, Jan; Höschl, Cyril. Pružnost a pevnost ve strojírenství. Praha : SNTL, 1989.
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Recommended:
Kuba, František. Teorie pružnosti a vybrané aplikace. 2. vyd. Praha : SNTL, 1982.
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Recommended:
Plánička, František. Základy lomové mechaniky při statickém zatížení. 1. vyd. Plzeň : ZČU, 1991.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for an examination (30-60)
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50
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Graduate study programme term essay (40-50)
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30
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Contact hours
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65
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Total
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145
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
mít znalosti z oblasti diferenciálního a integrálního počtu |
mít znalosti z oblasti matematické analýzy |
mít znalosti z oblasti lineární algebry |
mít znalosti z oblasti lineární pružnosti |
mít znalosti o řešení napjatosti a deformace jednoduchých součástí namáhaných tahem , ohybem, krutem a jejich kombinacemi |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
umět řešit diferenciální rovnice 1. řádu metodou separace proměnných |
umět vypočítat základní typy integrálů |
umět řešit soustavu lineárních algebraických rovnic |
umět řešit úlohy lineární pružnosti |
umět řešit úlohy napjatosti a deformace jednoduchých součástí namáhaných tahem , ohybem, krutem a jejich kombinacemi |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
popsat a klasifikovat chování pružného tělesa |
sestavit matice tuhosti vybraných prvků pro řešení úloh pomocí metody |
sestavit na základě okrajových podmínek rovnice rovnováhy rotujících kotoučů, silnostěnných válcových nádob |
sestavit rovnice pro řešení úloh stability |
Skills - skills resulting from the course: |
řešit analyticky napětí a deformaci křivého nebo lomeného prutu a uzavřeného rámu |
řešit analyticky stav napjatosti a deformace silnostěnných válcových nádob a rotujících kotoučů |
řešit analyticky úlohy stability prutů |
řešit numericky s využitím software rovinné úlohy pružnosti a pevnosti |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Laboratory work |
Competences - the following training methods are used to achieve the required competences: |
Individual study |
Textual studies |
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