CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Strength of Materials

Code Completion Credits Range Language
132PRPE Z,ZK 6 3P+2C Czech
Corequisite:
Mathematics 2 (101MA02)
Structural Mechanics 2 (132SM02)
Mathematics 2 (101MA02)
Structural Mechanics 2 (132SM02)
Garant předmětu:
Lecturer:
Milan Jirásek, Petr Kabele, Michal Šejnoha
Tutor:
Martin Doškář, Martin Horák, Dagmar Jandeková, Aleš Jíra, Milan Jirásek, Petr Kabele, Tomáš Koudelka, Martin Lebeda, Eva Novotná, Pavel Padevět, Zdeněk Prošek, Michael Somr, Michal Šejnoha, Michal Šmejkal
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. Three-dimensional solids. Basic variables and equations.

13. Walls, plane stress, stress transformation, principal stress, maximum shear stress.

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:

Studijní aids online:

https://mech.fsv.cvut.cz/homeworks/student/

http://mech.fsv.cvut.cz/wiki/index.php/Department_of_Mechanics:_Student%27s_corner

https://moodle-vyuka.cvut.cz/

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 &amp; Technology 2005. ISBN: 978-0-08-045534-1.

Note:
Further information:
https://mech.fsv.cvut.cz/homeworks/student
Time-table for winter semester 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomTH:C-21510:00–12:50(lecture parallel1)Thákurova 7 (budova FSv)C215 roomTH:B-28011:00–13:50(lecture parallel2)Thákurova 7 (budova FSv)B280roomTH:B-97614:00–15:50(lecture parallel1parallel nr.105)Thákurova 7 (budova FSv)B976roomTH:B-37816:00–17:50(lecture parallel2parallel nr.206)Thákurova 7 (budova FSv)B378 roomTH:B-37814:00–15:50(lecture parallel2parallel nr.205)Thákurova 7 (budova FSv)B378roomTH:B-97816:00–17:50(lecture parallel1parallel nr.104)Thákurova 7 (budova FSv)B978 roomTH:B-37514:00–15:50(lecture parallel2parallel nr.204)Thákurova 7 (budova FSv)B375roomTH:B-97916:00–17:50(lecture parallel1parallel nr.102)Thákurova 7 (budova FSv)B979 roomTH:B-97914:00–15:50(lecture parallel1parallel nr.101)Thákurova 7 (budova FSv)B979 roomTH:B-97814:00–15:50(lecture parallel1parallel nr.103)Thákurova 7 (budova FSv)B978 roomTH:A-33408:00–09:50(lecture parallel2parallel nr.207)Thákurova 7 (budova FSv)A334roomTH:A-33410:00–11:50(lecture parallel2parallel nr.208)Thákurova 7 (budova FSv)A334 roomTH:B-97908:00–09:50(lecture parallel2parallel nr.201)Thákurova 7 (budova FSv)B979roomTH:B-97910:00–11:50(lecture parallel2parallel nr.202)Thákurova 7 (budova FSv)B979 roomTH:B-97810:00–11:50(lecture parallel2parallel nr.203)Thákurova 7 (budova FSv)B978
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-08-30
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet24300805.html