Course detail

Strength of Materials II

FSI-5PPAcad. year: 2007/2008

Strength limits of material - a follow up to the course Strength of Materials I. Brittle fracture criterion MOS. Solids with cracks, elements of Fracture Mechanics. Fatigue: basic material characteristics, basic methods of fatigue analysis. General theory of elasticity - stress, strain and displacement of an element of continuum. Equations of equilibrium, compatibility, constitutive equations and boundary conditions. Closed form solutions of elementary problems: thick walled cylinder, rotating disc, axisymmetrical plate, cylindrical shell with bending, axisymmetrical membrane shell. Introduction to numerical analysis of elastic bodies by the FEM. Experimental methods - overview.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jindřich Petruška, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

Students will be able to select an appropriate method and solve typical problems of general strength and elasticity. They will acquire the knowledge of basic failure theories and can use it for prediction of structural behaviour.

Prerequisites

Mathematics: linear algebra, matrix notation, functions of one and more variables, calculus, ordinary and partial differential equations.
Physics: basic knowledge of solid mechanics as presented in the course of Statics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

The course-unit credit is granted under the condition of:
Active participation in seminars, good results in seminar tests of basic knowledge (three written tests during semester are recommended), solution of additional tasks in case of longer justified absence. Seminar tutor will specify these conditions in the first week of a semester.

Final evaluation is based on the result of examination, which has a combined form: written part (test of elementary knowledge + computational tasks) and oral part (discussion on written part with supplementary questions). It is necessary to have at least 50% of points in the test to pass the introductory part of the exam. The solution of 2-3 computational tasks follows then, the tasks come from typical profile areas of given subject. One of them can be supplied by theoretical question, proof, etc. The result of each task is evaluated from A (excellent) to F(failed). To pass the exam, only one task of all can be evaluated by F(failed), at the most.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim of the course is to provide students with information concerning solution of general problems of strength and elasticity of engineering structures. Analytical, numerical and experimental methods of solution are presented and final assessment of structural limit states is discussed in details.

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

Attendance at seminars is required. One absence can be compensated by attending a seminar with another group in the same week, or by working out an additional assignment. Longer absence is compensated by special tasks assigned by the tutor.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

UGURAL, A. C. Plates and Shells: Theory and Analysis. 4th Ed. Boca Raton: CRC Press, 2018. ISBN 978-1-138-03245-3.
BUDYNAS, R. G. a NISBETT, J. K. Shigleyho konstruování strojních součástí. Brno: Vysoké učení technické v Brně – Nakladatelství VUTIUM, 2023. ISBN 978-80-214-5471-2.
JANÍČEK, P. a PETRUŠKA, J. Pružnost a pevnost II: Úlohy do cvičení. 3. vyd. Brno: Akademické nakladatelství CERM, 2007. ISBN 978-80-214-3441-7.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3904-00 , 3. year of study, winter semester, compulsory

  • Programme B2341-3 Bachelor's

    branch B2339-00 , 3. year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. Ing. Jiří Burša, Ph.D.
doc. Ing. Zdeněk Florian, CSc.

Syllabus

1. Introduction. Postulates of strength and elasticity of material. Failure theories - overview.
2. Theory of brittle failure - Mohr and Maximal Normal Stress Theories.
3. Elastic body with fracture - basics of Linear Elastic Fracture Mechanics.
4. Fatigue failure of materials and structures. Conceptions of fatigue life prediction.
5. General equations of elasticity.
6. Basic types of problems in elasticity and their analytical solution.
7. Thick-walled cylindrical vessels.
8. Rotating discs.
9. Plates in polar coordinates.
10.Bending theory of cylindrical shells.
11.Axisymmetrical membrane shells.
12.Finite Element Method in problems of elasticity.
13.Experimental methods in elasticity.

Exercise

24 hours, compulsory

Teacher / Lecturer

prof. Ing. Pavel Hutař, Ph.D.
Ing. Zdeněk Majer, Ph.D.
Ing. Lucie Malíková, Ph.D.
doc. Ing. Tomáš Profant, Ph.D.

Syllabus

1. Theory of ductile failure.
2. Theory of brittle failure of a body without primary fracture.
3. Limit state of fracture stability.
4. Stable growth of fracture length, prediction of residual life.
5. Fatigue limit.
6. Fatigue under non-symmetrical stress cycle.
7. Fatigue under combined loading, safety in non-proportional loading.
8. Thick-walled cylindrical vessels.
9. Rotating discs.
10.Plates in polar coordinates.
11.Bending theory of cylindrical shells.
12.Axisymmetrical membrane shells.

Computer-assisted exercise

2 hours, compulsory

Teacher / Lecturer

prof. Ing. Jindřich Petruška, CSc.

Syllabus

13.Example of FEM solution of elasticity problem.