Strength of Materials
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 132PRPE | Z,ZK | 6 | 3P+2C | Czech |
- Garant předmětu:
- Petr Kabele
- Lecturer:
- Milan Jirásek, Michal Šejnoha
- Tutor:
- Martin Doškář, Martin Horák, Milan Jirásek, Tomáš Koudelka, Eva Novotná, Zdeněk Prošek, Michal Šejnoha, Michal Šmejkal, Jan Vorel
- Supervisor:
- Department of Mechanics
- Synopsis:
-
Fundamentals of the theory of elasticity: stress and strain of straight beams subjected to bending and free torsion, ultimate plastic capacity of a member in bending, critical loads and buckling lengths of straight compression members. Basic assumptions, quantities, and equations describing the stress and strain state in 3D continuum, plates and walls.
- Requirements:
-
101MA2, 132SM2
- Syllabus of lectures:
-
1. Assumptions of the theory of elasticity. Geometric, static and material equations. Basic types of loading effects on beams. Member under uniaxial tension/compression.
2. Beam bending 1. Simple bending in the plane. Stress distribution on the cross section. Bending moment as a resultant of normal stress. Relationship between bending moment and curvature.
3. Bending of a beam 2. Planar cross-section hypothesis. The distribution of strain on the cross-section. Geometric and static equations. Normal stresses in the cross-section in oblique bending and the combination of normal force and bending moments. Section core.
4. Beam bending 3. Differential equations of deflection line and boundary conditions. Calculation of deflections and internal forces by solving this equation. Effect of temperature changes and displacements/rotations of supports.
5. Shear stress in bending.
6. Test I.
7. Shear strain. Free torsion of massive and thin-walled members with open and closed cross-sections.
8. Elastic-plastic analysis. Inelastic behaviour of materials. Elastic-plastic and plastic state of cross-section of beams under bending. Limit plastic analysis of beams.
9. Stability of a member under compression. Equilibrium and stability. Calculation of the critical load of a member under compression. Proper buckling shapes. Buckling length. Critical stress, slenderness ratio.
10. Plates. Basic assumptions, variables and equations.
11. Test II.
12. Walls, plane stress, stress transformation, principal stress, maximum shear stress. 3D bodies, basic variables and governing equations for the description of stress and strain in 3D.
13. Course summary and review
- Syllabus of tutorials:
-
1. Review: types loading effects and internal forces of beams. Member under uniaxial tension/compression.
2. Member under uniaxial tension/compression: calculation of displacement, strain and stress.
3. Simple bending.
4. Oblique bending.
5. Combination of normal force and bending moments.
6. Core of a cross-section. Deflection line of a beam.
7. Deflection line of a beam.
8. Shear stress under bending.
9. Free torsion.
10. Elastic-plastic and plastic state of the cross-section of beams under bending.
11. Limit plastic analysis of the beam.
12. Stability - basic Euler cases.
13. Review. Reserve.
- Study Objective:
-
Students will be able to solve the stress and strain of straight beams subjected to tension or compression, bending and free torsion, determine the ultimate plastic capacity of a member in bending, and determine the critical loads and buckling lengths of straight compression members. They will learn about the basic assumptions, quantities, and equations describing the stress and strain state in 3D continuum, plates and walls.
- Study materials:
-
Study aids online:
https://mech.fsv.cvut.cz/homeworks/student/
http://mech.fsv.cvut.cz/wiki/index.php/Department_of_Mechanics:_Student%27s_corner
Jíra A. a kol.: Sbírka příkladů pružnosti a pevnosti, FSv ČVUT, 2021 (online)
Šejnoha J., Bittnarová J.: Pružnost a pevnost 10. Vyd. ČVUT Praha 2003. ISBN: 80-01-02742-2.
Šejnoha J., Bittnarová J.: Pružnost a pevnost 20. Vydavatelství ČVUT Praha 2003. ISBN: 80-01-02709-0.
Bittnarová a kol.: Pružnost a pevnost. Příklady. Vydavatelství ČVUT Praha 2003. ISBN: 80-01-02743-0.
Bittnarová a kol.: Pružnost a pevnost 20. Příklady. Vydavatelství ČVUT Praha 2004. ISBN: 80-01-03082-2.
Megson T. H. G.: Structural and Stress Analysis. Jordan Hill, UNITED KINGDOM: Elsevier Science & Technology 2005. ISBN: 978-0-08-045534-1.
- Note:
- Further information:
- https://mech.fsv.cvut.cz/homeworks/student
- Time-table for winter semester 2024/2025:
- Time-table is not available yet
- Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Stavební inženýrství, obor Konstrukce pozemních staveb (compulsory course)
- Stavební inženýrství, obor Konstrukce a dopravní stavby (compulsory course)
- Stavební inženýrství, obor Příprava, realizace a provoz staveb (compulsory course)
- Stavební inženýrství, obor Management a ekonomika ve stavebnictví (compulsory course)
- Civil Engineering (compulsory course)
- Civil Engineering (compulsory course)
- Stavební inženýrství, specializace Pozemní stavby (compulsory course)
- Stavební inženýrství, specializace Vodní hospodářství a vodní stavby (compulsory course)
- Management a ekonomika ve stavebnictví (compulsory course)
The course 132PRPE can be graded only after the course 132SM02 has been successfully completed.
The course 132PRPE can be graded only after the course 101MA02 has been successfully completed.
The course 133BEK1 can be graded only after the course 132PRPE has been successfully completed.
The course 133BZ1 can be graded only after the course 132PRPE has been successfully completed.
The course 134OK1 can be graded only after the course 132PRPE has been successfully completed.
The course 134DK1 can be graded only after the course 132PRPE has been successfully completed.
The course 134DKO can be graded only after the course 132PRPE has been successfully completed.
The course 132SM3 can be graded only after the course 132PRPE has been successfully completed.
The course 134DK01 can be graded only after the course 132PRPE has been successfully completed.