Course detail

Strength of Materials I

FSI-4PPAcad. year: 2013/2014

Basic concepts and problems of strength analysis. Basic mechanical properties of material. General theorems of linear elasticity. Definition, classification and assumptions of rod as the simplest model body. Rod under simple stress - tension / compression, torsion, and bending. Supporting stability of rods. Strain at a body point. Boundary states of elasticity and brittle strength. Safety conditions. Rods under combined stresses.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

doc. Ing. Zdeněk Florian, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

Basic knowledge of stress and strain related to simple cases of rod under stress and the idea of the boundaries of applicability of these classical approaches. Conditions of fundamental boundary states and determination of safety in case of general strain with the aim to reliably set the dimensions of bodies or machine parts.

Prerequisites

Basic knowledge of statics and mathematics. Statics - conditions of static equilibrium and equivalence, the release of the body, the assessment of static certainty, resulting internal effects. Mathematics - vectors and matrices, differentials and integrals, solutions to differential equations. Knowledge of the software Maple.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Conditions for granting the credits: Active participation in tutorials, gaining at least 15 points in the control tests of in-course knowledge. Point gain from in-course tests (max. 30 points) is part of the final assessment of the course.
Examination: written and oral. Point gain from the examination is maximum 70 points. The content of the examination are questions on theory and solving the typical tasks related to profile areas of the course. Detailed examination conditions shall be specified by the lecturer in the first lecture. The final assessment is given by the sum of points gained in tutorials and examination. To pass the course, the student must gain at least 50 points.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The objective of the course Strength Analysis I is to equip the students with methodology for determination of strain and stress in bodies and risk assessment of basic boundary states. Practical experience with computations of the simplest bodies will be further supplemented with basic knowledge necessary for the strength design of real machine parts.

Specification of controlled education, way of implementation and compensation for absences

Tuition attendance is mandatory. The tutor is responsible for in-course check-ups of students’ attendance, their activities and basic knowledge. Unexcused absence is a reason for not granting the credits. One absence can be compensated by presence in another tutorial group within the same week, or by giving additional tasks. The conditions for granting credits: - Active participation in tutorials, good results in in-course tests of basic knowledge, solving additional tasks in case of excused absence. A detailed form to meet these requirements is given by the tutor in the first week of the semester.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, third SI edition, Chapman & Hall, London, Glasgow, New York, 1995
Pestel, E., Wittenburg, J.: Technische Mechanik, Band 2: Festigkeitslehre, B I, Wissenschaftsverlag, Mannheim, Leipzig, Wien, Zűrich, 1992
Hoschl, C.: Pružnost a pevnost ve strojírenství, SNTL, Praha, 1971

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B3A-P Bachelor's

    branch B-MAI , 2. year of study, summer semester, compulsory
    branch B-MET , 2. year of study, summer semester, compulsory
    branch B-FIN , 2. year of study, summer semester, compulsory-optional

  • Programme B3S-P Bachelor's

    branch B-STI , 2. year of study, summer semester, compulsory-optional
    branch B-KSB , 2. year of study, summer semester, compulsory

Type of course unit

 

Lecture

52 hours, optionally

Teacher / Lecturer

doc. Ing. Vladimír Fuis, Ph.D.
prof. RNDr. Ing. Jan Vrbka, DrSc., dr. h. c.

Syllabus

1. Definition of the course content. Basic concepts - deformation, stress, strain, boundary conditions, and safety. Mechanical properties of materials and their computational models.
2. General properties and general theorems of linear elastic body. Saint Venant principle, the law of conservation of energy, deformation work of force and force system, the principle of superposition of strain and deformation, theorem of reciprocity of work, Castigliano's theorem.
3. Rod in strength analysis - definition, classification. Geometric characteristics of the cross section. Quadratic moments of cross sections, transformation to displaced and turned axes. The main and the main central square moments.
4. Simple tension and compression. Strain, stress, strain energy. Effects of deflections on stress and strain. Safety check.
5. Statically uncertain rod placement. Rod systems, systems of rods and non-rod bodies. External and internal static uncertainty.
6. Simple bending. Strain, stress, strain energy. Effects of deflections on stress and strain. Shear stress caused by shear force. Safety check.
7. Statically uncertain cases of rod placement. Shear stress in thin-walled profiles, shear centre.
8. Weakly and strongly curved rods, broken rods (frames).
9. Simple torsion. Stress, strain, strain energy. Effects of deflections on stress and strain. Safety check. Statically uncertain rod placement.
10. Stress at a body point, the main stress. Views of stress in the Mohr plane. Special cases of stress, plane stress.
11. Conditions of boundary states of elasticity and brittle strength during monotonous loading. Safety, reduced stress. Behaviour of bodies under cyclic loading, basic fatigue characteristics of the material.
12. Rods under combined stress. A list of problems to be solved by analytical, numerical and experimental methods.
13. Supporting stability of rods. Effects of deflections on critical force. Boundary states of real material rod under compression. Safety.

Exercise

12 hours, compulsory

Teacher / Lecturer

doc. Ing. Jana Horníková, Ph.D.
Ing. Martin Houfek, Ph.D.
doc. Ing. Jan Klusák, Ph.D.
Ing. Ondřej Krepl, Ph.D.
Ing. Petr Kubík, Ph.D.
Ing. Jakub Mikula
doc. Ing. Tomáš Návrat, Ph.D.
Ing. Petr Padělek
doc. Ing. Stanislav Polzer, Ph.D.
doc. Ing. Tomáš Profant, Ph.D.
doc. Ing. František Šebek, Ph.D.
prof. RNDr. Ing. Jan Vrbka, DrSc., dr. h. c.

Syllabus

1. Resulting internal effects in a straight rod.
2. Quadratic moments of the cross section. Mohr diagram.
3. Tension and pressure of rod, stress, strain and deformation. Statically uncertain tasks.
4. Bending. Stress, strain and deformation in statically uncertain rod.
5. Combined stress.
6. Supporting stability of rods. Safety for real material rods under compressive stress.

Computer-assisted exercise

14 hours, compulsory

Teacher / Lecturer

doc. Ing. Zdeněk Florian, CSc.

Syllabus

1. Resulting internal effects in a wrapped rod (2-D and 3-D).
2. Resulting internal effects in a curved rod.
3. Tension and pressure of rod, stress, strain and deformation. Statically certain tasks.
4. Tension and pressure of rod, stress, strain and deformation. Systems of bodies.
5. Bending. Stress, strain and deformation in statically certain rod.
6. Curved and wrapped rods. Closed rods (frames). Use of symmetry and antimetry.
7. Torsion. Stress, strain and deformation in statically certain and uncertain tasks.