Course detail

# Strength of Materials II

Assessment of solids with cracks, fundamentals of Linear Elastic Fracture Mechanics. Fatigue: basic material characteristics, basic methods of fatigue analysis. General theory of elasticity - stress, strain and displacement of an element of continuum. System of equations of linear theory of elasticity, general Hooke's law. Closed form solutions of elementary problems: thick wall cylinder, rotating disc, axisymmetrical plate, axisymmetric membrane shell, bending theory of cylindrical shell. Introduction to numerical analysis of elastic bodies using finite element method. Oveview of experimental methods in solid mechanics, electric resistance strain gauges.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Learning outcomes of the course unit

Students will be able to analyze common problems of general strength and elasticity, to choose an appropriate method of problem solution via either analytical solution or preparation of input data for a numerical solution or proposal of an experimental method. They will be able to distinguish and assess basic types of failures of engineering structures.

Prerequisites

Mathematics: linear algebra, matrix notation, functions of one and more variables, differential and integral calculus, ordinary and partial differential equations. Ability of application of mathematical software (Maple) is required as well.
Basic knowledge of statics (especially equations of statical equilibrium and free body diagrams) and mechanics of materials (stress and strain tensors, elasticity theory of bars, failure criteria for ductile and brittle materials).

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

The course-unit credit is granted under conditions of active participation in seminars and passing seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final evaluation of the course.
Final exam: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. It consists of a written theoretical test evaluated with max. 30 points and solution of two computational problems (50 pts max.). The problems concern typical profile areas of the subject. The lecturer will specify exact demands like types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim of the course is to enlarge the students' knowledge on possibilities of assessment of safety of engineering structures. Students should become capable to solve stresses and deformations in various model bodies analytically and obtain basic information on possibilities of stress evaluation by means of both numerical methods (FEM) and experimental approaches. Also knowledge on failure criteria is enhanced, especially under conditions of cyclic loading and existence of cracks in the body.

This subject is included into study plan of the 3rd year of general bachelor's study as a compulsory-optional one. It is recommended as a prerequisite of branches M-ADI, M-ENI, M-FLI, M-IMB, M-MET or M-VSR.

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

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DOWLING, N. E. Mechanical behavior of materials: Engineering methods for deformation, fracture, and fatigue. 3rd Ed. Upper Saddle River: Prentice Hall, 2007. ISBN 0-13-186312-6.
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.
ONDRÁČEK, E.; VRBKA, J.; JANÍČEK, P. a BURŠA, J. Mechanika těles: Pružnost a pevnost II. 4. přeprac. vyd. Brno: Akademické nakladatelství CERM, 2006. ISBN 80-214-3260-8.
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.

Not applicable.

eLearning

Classification of course in study plans

• Programme B3A-P Bachelor's

branch B-MET , 3. year of study, winter semester, compulsory

• Programme B3S-P Bachelor's

branch B-STI , 3. year of study, winter semester, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction. Assumptions of the analytical stress-strain analyses. Fundamentals of Linear Elastic Fracture Mechanics.
2. Behaviour of a body with a crack - residual life prediction under cyclic loading.
3. Behaviour of solids under cyclic loading, material characteristics for low-cycle and high-cycle fatigue.
4. Actual approaches and procedures of fatigue strength assessment for bar-like bodies.
5. General theory of elasticity - basic quantities and system of equations.
6. Basic types of model bodies and their analytical solution, generalized Hooke's law.
7. Thick-walled cylindrical vessels - stress-strain analysis.
8. Rotating discs - stress-strain analysis.
9. Axisymmetric plates - stress-strain analysis.
10. Axisymmetric membrane shells - stress-strain analysis.
11. Bending theory of cylindrical shells - stress-strain analysis.
12. Application of Finite Element Method in stress-strain analyses.
13. Experimental methods of evaluation of stresses and other mechanical quantities, electric resistance strain gauges.

Exercise

14 hours, compulsory

Teacher / Lecturer

Syllabus

1. Evaluation of stresses and deformations in bars under combined loads
4. Criterion of unstable crack propagation, LEFM, estimation of the residual life.
6. Fatigue failure under non-symmetrical stress cycle.
8. Thick-walled cylindrical vessels - stress-strain analysis.
11. Axisymmetric membrane shells - stress-strain analysis.
12. Bending theory of cylindrical shells - stress-strain analysis.
13. Course-unit credit.

Computer-assisted exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

3.Stress state in a point of a body, principal stresses, failure criteria under multiaxial stress states.
5. Limit state of fatigue fracture, endurance strength.
9. Rotating discs - stress-strain analysis.
10. Axisymmetric plates - stress-strain analysis.

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