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 and cylindrical body, axisymmetrical plate, axisymmetric membrane shell, bending theory of cylindrical shell.

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

Conditions for granting the course-unit credit: Attendance, active participation in seminars and submission of given tasks, including their presentation.

Examination: Examination is split into two parts. The content of the first mandatory part is the theoretical written test, where the maximum of 80 points can be reached. The content of the second part, which is optional, is an oral examination, where it can be reached from -20 to +20 points. Specific form of the examination, types of the tasks or questions and other details will be communicated during the semester by the lecturer and through e-learing.

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. 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 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

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.
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.
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.

Recommended literature

Not applicable.

Elearning

Classification of course in study plans

• Programme B-VTE-P Bachelor's 3 year of study, winter semester, compulsory
• Programme B-MET-P Bachelor's 3 year of study, winter semester, compulsory-optional

• Programme B-ZSI-P Bachelor's

specialization STI , 3 year of study, winter semester, compulsory-optional

• Programme LLE Lifelong learning

branch CZV , 1 year of study, winter semester, compulsory-optional

#### Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

Syllabus

General strength of materials - basic quantities and system of relationships between them.

Generalized Hooke’s law

Thick-walled cylindrical body

Rotating disks and cylindrical bodies

Circular and annular plates

Axisymmetric membrane shell

Cylindrical momentum shell

Composed bodies, comparison of analytical and numerical (FEM) solutions

Fatigue strength of beams – concept of nominal stresses

Fatigue strength of beams – concept of local stresses and strains, limited life

Brittle fracture, basics of linear elastic fracture mechanics

Summary + examination

Exercise

14 hod., compulsory

Teacher / Lecturer

Syllabus

Stress and strain states and generalized Hooke’s law

Hooke’s law at assessment of strain gauge measurements

Thick-walled cylindrical body

Rotating disks and cylindrical bodies

Circular and annular plates

Axisymmetric membrane shell

Cylindrical momentum shell

Fatigue strength of beams – concept of nominal stresses

Fatigue strength of beams – concept of nominal stresses

Limit state of brittle fracture

Linear elastic fracture mechanics

Presentation of assignments

Presentation of assignments

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

Syllabus

Stress and strain states and generalized Hooke’s law

Hooke’s law at assessment of strain gauge measurements

Thick-walled cylindrical body

Rotating disks and cylindrical bodies

Circular and annular plates

Axisymmetric membrane shell

Cylindrical momentum shell

Fatigue strength of beams – concept of nominal stresses

Fatigue strength of beams – concept of nominal stresses

Limit state of brittle fracture

Linear elastic fracture mechanics

Presentation of assignments

Presentation of assignments

Guided consultation

26 hod., optionally

Teacher / Lecturer

Syllabus

Stress and strain states and generalized Hooke’s law

Hooke’s law at assessment of strain gauge measurements

Thick-walled cylindrical body

Rotating disks and cylindrical bodies

Circular and annular plates

Axisymmetric membrane shell

Cylindrical momentum shell

Fatigue strength of beams – concept of nominal stresses

Fatigue strength of beams – concept of nominal stresses

Limit state of brittle fracture

Linear elastic fracture mechanics

Presentation of assignments

Presentation of assignments

Elearning