Strength of Materials II (FSI-5PP-A)

Academic year 2022/2023
Supervisor: prof. Ing. Jiří Burša, Ph.D.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: English
Aims of the course unit:

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.
Learning outcomes and competences:
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).
Course contents:

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.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Guided consultation  13 × 2 hrs. optionally                  
    Exercise  7 × 2 hrs. compulsory                  
    Computer-assisted exercise  6 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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


Crack growth at static and cyclic loading


Summary + examination
    Guided consultation

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
    Exercise

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

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
Literature - fundamental:
1. 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. 
2. UGURAL, A. C. Plates and Shells: Theory and Analysis. 4th Ed. Boca Raton: CRC Press, 2018. ISBN 978-1-138-03245-3.
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.
4. 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.
5. 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.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
CŽV full-time study CZV Bases of Mechanical Engineering -- Cr,Ex 5 Compulsory-optional 1 1 W
B-STI-A full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 1 3 W
B-STI-Z visiting student --- no specialisation -- Cr,Ex 5 Elective 1 1 W
B-MET-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 1 3 W