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

Academic year 2023/2024
Supervisor: doc. Ing. František Šebek, Ph.D.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: English
Aims of the course unit:

The aim of the subject is to extend the knowledge on the possibilities of safety assessment of engineering structures. The student should manage the analytical solutions of deformations and stresses in various bodies. The knowledge on limit states is also extended, especially under the 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. Its choice (or choice of its English version) is recommended in the case that the student intends to choose the programme N-ADI-P, N-MET-P, N-KSI-P, N-ETI-P, N-IMB-P or N-VSR-P.
Learning outcomes and competences:

Students will be able to categorize common types of tasks of strength of materials and is able to choose an appropriate methodology of problem solution in the given circumstances via the corresponding analytical solution, preparation of input data for a numerical calculation or design of an experimental technique. Student will be able to distinguish and assess the basic limit state of structures.
Prerequisites:

The necessary knowledge from mathematics are linear algebra, matrix calculus, functions of one and more variables, differential and integral calculus and ordinary and partial differential equation. Next the knowledge of programming in MATLAB software is required. The necessary knowledge from solid mechanics in the scope of corresponding to the subject Statics (especially the construction of equations of statical equilibrium and free body diagrams) and Strength of materials I (stress and strain tensors, beam theory, limit states of ductile and brittle materials).
Course contents:

General strength of materials - stress, strain and displacements of an element of continuum in spatial task. System of equations of strength of materials and generalized Hooke's law. Possibilities of analytical solution of strength of materials on elementary types of bodies: thick-walled cylindrical body, rotating disks and cylindrical bodies, circular and annular plates, axisymmetric membrane shell and cylindrical momentum shell. Basics of linear elastic fracture mechanics, assessment of body with crack. Fatigue of material - main concepts of fatigue assessment.
Teaching methods and criteria:

The subject is taught by means of lectures, which have a character of explanation of the basic principles and theory of the given discipline. Seminars are focused on practical coping with topics presented in lectures. Lectures and seminars are complemented by consultations.
Assesment methods and criteria linked to learning outcomes:

Conditions for granting the course-unit credit: Attendance, active participation in the 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 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, questions and other details will be communicated during the semester by the lecturer and through the E-learning.
Controlled participation in lessons:

Attendance on the seminars is mandatory. A continuous control of the presence of students is conducted, including the control of activity and basic knowledge. Unexcused absence is grounds for not granting the couse-unit credit.
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, system of relationships among them and generalized Hooke’s law
Brittle fracture
Thick-walled cylindrical body
Rotating disks and cylindrical bodies
Circular and annular plates
Axisymmetric membrane shell
Cylindrical momentum shell
Basics of linear elastic fracture mechanics
Crack growth at static and cyclic loading
Fatigue strength of beams – concept of nominal stresses
Fatigue strength of beams – concept of local stresses and strains
Composed bodies
    Guided consultation

Dividing into groups and assigning the tasks
Individual consultations
Presentations of assigned tasks
    Exercise

Stress and strain states and generalized Hooke’s law
Hooke’s law at assessment of strain gauge measurements
Brittle fracture (combined loading)
Thick-walled cylindrical body
Rotating disks and cylindrical bodies
Circular and annular plates
Axisymmetric membrane shell
Cylindrical momentum shell
Linear elastic fracture mechanics
Fatigue strength of beams – symmetric stress cycle
Fatigue strength of beams – asymmetric stress cycle
Fatigue strength of beams – combined and non-proportional loading
    Computer-assisted exercise

Stress and strain states and generalized Hooke’s law
Hooke’s law at assessment of strain gauge measurements
Brittle fracture (combined loading)
Thick-walled cylindrical body
Rotating disks and cylindrical bodies
Circular and annular plates
Axisymmetric membrane shell
Cylindrical momentum shell
Linear elastic fracture mechanics
Fatigue strength of beams – symmetric stress cycle
Fatigue strength of beams – asymmetric stress cycle
Fatigue strength of beams – combined and non-proportional loading
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  
B-MET-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory-optional 1 3 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 Recommended course 1 1 W