Course detail

Strength of Materials I

FSI-4PP-KAcad. year: 2017/2018

Basic concepts and problems of strength analysis. Basic mechanical properties of material. General theorems of linear elasticity. Definition, classification and assumptions of rod as the simplest model body. Rod under simple stress - tension / compression, torsion, and bending. Strain at a body point. Boundary states of elasticity and brittle strength. Safety conditions. Rods under combined stresses. Supporting stability of rods.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. Ing. Zdeněk Florian, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

Basic knowledge of stress and strain related to simple cases of rod under stress and the idea of the boundaries of applicability of these classical approaches. Conditions of fundamental boundary states and determination of safety in case of general strain with the aim to reliably set the dimensions of bodies or machine parts.

Prerequisites

Basic knowledge of statics and mathematics.
Statics - conditions of static equilibrium and equivalence, the release of the body, the assessment of static certainty, resulting internal effects.
Mathematics - vectors and matrices, differentials and integrals, solutions to differential equations. Knowledge of the software Maple.

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 the condition of active participation in seminars and passing the 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 course evaluation.
Final examination: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and supplied by a theoretical question, proof, etc. The lecturer will specify exact demands like the number and 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 objective of the course Strength Analysis I is to equip the students with methodology for determination of strain and stress in bodies and risk assessment of basic boundary states. Practical experience with computations of the simplest bodies will be further supplemented with basic knowledge necessary for the strength design of real machine parts.

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

Attendance at seminars is required. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by attending a seminar with another group in the same week, or by elaboration of substitute tasks.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Gere J.M., Timošenko S.P.: Mechanics of Materials, , 0
Hoschl C.: Pružnost a pevnost ve strojnictví, , 0
Issler L., Ruoss H., Hafele P.H.: Festigkeitslehre - Grundlagen, , 0

Recommended reading

Gere J.M., Timošenko S.P.: Mechanics of Materials, , 0
Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti Ii, , 0
Janíček P., Ondráček E., Vrbka J.: Pružnost a pevnost I, , 0

Classification of course in study plans

  • Programme B3S-K Bachelor's

    branch B-STG , 2 year of study, winter semester, compulsory
    branch B-SSZ , 2 year of study, winter semester, compulsory
    branch B-AIŘ , 2 year of study, winter semester, compulsory
    branch B-KSB , 2 year of study, winter semester, compulsory

Type of course unit

 

Guided consultation

26 hod., optionally

Teacher / Lecturer

doc. Ing. Tomáš Profant, Ph.D.

Syllabus

Lecture:
1. Definition of the course content. Basic concepts - deformation, stress, strain, boundary conditions, and safety. Mechanical properties of materials and their computational models.
2. Behaviour of linear elastic body. Definition of the linear solids and structures. Basic theorems of linear solids and structures – theorem of reciprocity of work, deformation work of force and force systém, Castigliano's theorem. Saint Venant principle.
3. Rod in strength analysis - definition, classification. Geometric characteristics of the cross section. Quadratic moments of cross sections, transformation to displaced and turned axes. The main and the main central square moments.
4. Simple tension and compression. Strain, stress, strain energy. Effects of deflections on stress and strain. Safety check.
5. Statically uncertain rod placement. Rod systems, systems of rods and non-rod bodies. External and internal static uncertainty.
6. Simple bending. Strain, stress, strain energy. Effects of deflections on stress and strain. Shear stress caused by shear force. Safety check.
7. Statically uncertain cases of rod placement. Shear stress in thin-walled profiles, shear centre.
8. Weakly and strongly curved rods, broken rods (frames).
9. Simple torsion. Stress, strain, strain energy. Effects of deflections on stress and strain. Safety check. Statically uncertain rod placement.
10. Stress at a body point, the main stress. Views of stress in the Mohr plane. Special cases of stress, plane stress.
11. Conditions of boundary states of elasticity and brittle strength during monotonous loading. Safety, reduced stress. Behaviour of bodies under cyclic loading, basic fatigue characteristics of the material.
12. Rods under combined stress. A list of problems to be solved by analytical, numerical and experimental methods.
13. Supporting stability of rods. Effects of deflections on critical force. Boundary states of real material rod under compression. Safety.