Strength of Materials I
FSI-4PP-AAcad. 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.
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.
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.
Recommended optional programme components
Recommended or required reading
Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, third SI edition, Chapman & Hall, London, Glasgow, New York, 1995
Janíček P., Ondráček E., Vrbka J., Burša J.: Pružnost a pevnost I,VUT-FSI,Brno,2004
Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti I,2. vyd., VUT-FSI, Brno,1995
Pestel, E., Wittenburg, J.: Technische Mechanik, Band 2: Festigkeitslehre, B I, Wissenschaftsverlag, Mannheim, Leipzig, Wien, Zűrich, 1992
Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, third SI edition, Chapman & Hall, London, Glasgow, New York, 1995 Pestel, E., Wittenburg, J.: Technische Mechanik, Band 2: Festigkeitslehre, B I, Wissenschaftsverlag, Mannheim, Leipzig, Wien, Zűrich, 1992
Hoschl, C.: Pružnost a pevnost ve strojírenství, SNTL, Praha, 1971
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.
Language of instruction
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.
Classification of course in study plans
- Programme B3A-P Bachelor's
branch B-MET , 2. year of study, summer semester, 8 credits, compulsory-optional
- Programme B3S-A Bachelor's
branch B-STI , 2. year of study, summer semester, 7 credits, compulsory
- Programme B3S-P Bachelor's
branch B-STI , 2. year of study, summer semester, 7 credits, compulsory-optional
Type of course unit
52 hours, optionally
Teacher / Lecturer
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.
12 hours, compulsory
Teacher / Lecturer
1. Resulting internal effects in a straight rod - differential approach. (1st week)
2. Resulting internal effects in a curved rod. (3rd week)
3. Tension and pressure of rod, stress, strain and deformation. Statically certain tasks. (5th week)
4. Tension and pressure of rod - systems of bodies. (7th week)
5. Bending. Stress, strain and deformation in statically uncertain rod. (9th week)
6. Torsion. Stress, strain and deformation in statically certain and uncertain tasks. (11th week)
seminars in computer labs
14 hours, compulsory
Teacher / Lecturer
1. Resulting internal effects in a wrapped rod (2-D and 3-D). (2nd week)
2. Quadratic moments of the cross section. Mohr diagram. (4th week)
3. Tension and pressure of rod, stress, strain and deformation. Statically uncertain tasks. (6th week)
4. Bending. Stress, strain and deformation in statically certain rod. (8th week)
5. Curved and wrapped rods. Closed rods (frames). Use of symmetry and antimetry. (10th week)
6. Combined stress. (12th week)
7. Supporting stability of rods. Safety for real material rods under compressive stress. (13th week)