Strength of Materials

The course 132PRE can be graded only after the course 132SM02 has been successfully completed.

The course 132PRE can be graded only after the course 101MA02 has been successfully completed.

The course 132SME3 can be graded only after the course 132PRE has been successfully completed.

Garant předmětu:

Petr Kabele

Lecturer:

Petr Kabele, Lenka Melzerová, Karel Pohl

Tutor:

Lenka Melzerová, Karel Pohl

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.

Requirements:

101MA2, 132SM2

Syllabus of lectures:

1. Assumptions of the theory of elasticity. Geometric, static and material equations.

2. Basic types of loading effects on beams. Member under uniaxial tension/compression. Beam bending 1. Simple bending in the plane. Stress distribution on the cross section. Bending moment as a resultant of normal stress.

3. Bending of a beam 2. Planar cross-section hypothesis. Normal stresses in the cross-section in oblique bending and the combination of normal force and bending moments. Section core. Differential equations of deflection line and boundary conditions.

4. Differential equations of deflection line and boundary conditions. Calculation of deflections and internal forces by solving this equation. Shear stress in bending.

5. Test I.

6. Shear strain. Free torsion of massive and thin-walled members with open and closed cross-sections.

7. Elastic-plastic analysis. Inelastic behaviour of materials. Elastic-plastic and plastic state of cross-section of beams under bending.

8. Elastic-plastic analysis. Limit plastic analysis of beams.

9. Test II.

10. 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.

11. Review.

12. Exam.

13. Reserve.

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, oblique bending.

4. Combination of normal force and bending moments.

5. Deflection line of a beam.

6. Shear stress under bending.

7. Free torsion of massive members.

8. Free torsion of thin-walled members.

9. Elastic-plastic and plastic state of the cross-section of beams under bending.

10. Limit plastic analysis of the beam.

11. Stability - basic Euler cases.

12. Review.

13. 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.

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 & 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
Mon	roomTH:C-204 10:00–12:50 (lecture parallel1) Thákurova 7 (budova FSv) C204
Tue
Wed
Thu	roomTH:B-379 08:00–09:50 (lecture parallel1 parallel nr.103) Thákurova 7 (budova FSv) B379roomTH:B-378 12:00–13:50 (lecture parallel1 parallel nr.102) Thákurova 7 (budova FSv) B378 roomTH:B-378 08:00–09:50 (lecture parallel1 parallel nr.101) Thákurova 7 (budova FSv) B378
Fri

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Management a ekonomika ve stavebnictví (compulsory course)
• Management a ekonomika ve stavebnictví (compulsory course)