Strength of Materials
Code  Completion  Credits  Range  Language 

132PRE  Z,ZK  6  3P+2C  Czech 
 Vztahy:
 The course 132PRE can be graded only after the course 132SME2 has been successfully completed.
 The course 132PRE can be graded only after the course 101MA2E has been successfully completed.
 The course 132SME3 can be graded only after the course 132PRE has been successfully completed.
 Garant předmětu:
 Petr Kabele
 Lecturer:
 Lenka Melzerová
 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 crosssection hypothesis. Normal stresses in the crosssection 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 thinwalled members with open and closed crosssections.
7. Elasticplastic analysis. Inelastic behaviour of materials. Elasticplastic and plastic state of crosssection of beams under bending.
8. Elasticplastic 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 thinwalled members.
9. Elasticplastic and plastic state of the crosssection 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
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: 8001027422.
Šejnoha J., Bittnarová J.: Pružnost a pevnost 20. Vydavatelství ČVUT Praha 2003. ISBN: 8001027090.
Bittnarová a kol.: Pružnost a pevnost. Příklady. Vydavatelství ČVUT Praha 2003. ISBN: 8001027430.
Bittnarová a kol.: Pružnost a pevnost 20. Příklady. Vydavatelství ČVUT Praha 2004. ISBN: 8001030822.
Megson T. H. G.: Structural and Stress Analysis. Jordan Hill, UNITED KINGDOM: Elsevier Science & Technology 2005. ISBN: 9780080455341.
 Note:
 Further information:
 https://mech.fsv.cvut.cz/homeworks/student
 Timetable for winter semester 2024/2025:

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 Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable 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)