Strength of Materials I (FSI-4PP-A)

Academic year 2020/2021

Supervisor:	doc. Ing. Zdeněk Florian, CSc.
Supervising institute:	ÚMTMB	all courses guaranted by this institute
Teaching language:	English
Aims of the course unit:
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 limit 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.
Learning outcomes and competences:
Basic knowledge of stress and strain related to simple cases of loaded bars and beams and the idea of the boundaries of applicability of these classical approaches. Criteria of fundamental limit states and determination of safety and dimensions of designed bodies or machine parts.
Prerequisites:
Basic knowledge of statics and mathematics. Statics - conditions of static equilibrium and equivalence, free-body diagrams, assessment of static determinacy, shear force and bending moment diagrams. Mathematics - vectors and matrices, differential and integral calculus, solutions to differential equations. Knowledge of the software Maple.
Course contents:
Basic concepts and problems of strength analysis. Basic mechanical properties of material. Concepts of stress and strain. General theorems of linear elasticity. Definition and classification of bar and beam as the simplest model of a body. Bar under simple loading - tension / compression, torsion; bending of beams. Basic limit states of ductile and brittle materials under static loading. Safety conditions. Beams and bars under combined loading. Stability of compressed bars.
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:
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.
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 × 4 hrs.	optionally
Exercise	6 × 2 hrs.	compulsory
Computer-assisted exercise	7 × 2 hrs.	compulsory
Course curriculum:
Lecture	1. Introduction to the course. 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 system, Castigliano's theorem. Saint Venant’s principle. 3. Straight members in strength analysis - definition, classification. Geometric characteristics of the cross section. Planar moments of inertia and their transformations. Principal and central principal moments of inertia. 4. Simple tension and compression. Strain, stress, strain energy. Influence of imperfections on stress and strain. Safety of straight bar. 5. Statically indeterminate bars. Bar systems, combined systems of bars and general bodies. External and internal static indeterminacy. 6. Simple bending. Strain, stress, strain energy. Influence of imperfections on stress and strain. Shear stress caused by shear force. Safety of beams. 7. Statically indeterminate bars. Shear stress in thin-walled profiles, shear centre. 8. Weakly and strongly curved bars, frames. 9. Simple torsion. Stress, strain, strain energy. Influence of imperfections on stress and strain. Safety of bars in torsion. Statically indeterminate cases. 10. State of stress in a point of continuum, stress tensor, principal stresses. Representation of stress state in the Mohr’s plane. Special cases of stress state, plane stress. 11. Failure theories for ductile and brittle materials under static monotonic loading. Safety, equivalent stress. Behavior of material under cyclic loading, basic fatigue characteristics of material. 12. Bars and beams under combined loading. An overview of problems to be solved by analytical, numerical and experimental methods. 13. Stability of compressed bars. Influence of imperfections on critical force. Possible modes of failure of real bar under compression. Safety of compressed bars.

Exercise	1. Internal resultant forces and moments in a straight bar - differential approach. 2. Internal resultant forces and moments in a curved bar. 3. Tension/compression of bar, stress, strain and deformation. Statically determinate problems. 4. Tension/compression of bar systems, pin-jointed structures. 5. Bending. Stress, strain and deformation in statically indeterminate beams. 6. Torsion. Statically determinate and indeterminate tasks.

Computer-assisted exercise	1. Internal resultant forces and moments in a frame in 2-D and 3-D. 2. Inertia moments of the cross section. Mohr’s diagram. 3. Tension/compression of bar, stress, strain and deformation. Statically indeterminate problems. 4. Bending. Stress, strain and deformation in statically determinate beams. 5. Curved bars and frames. Use of symmetry and anti-symmetry. 6. Combined loading. 7. Stability of compressed bars. Safety of real bar under compression.

Literature - fundamental:
1. Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, third SI edition, Chapman & Hall, London, Glasgow, New York, 1995
2. Pestel, E., Wittenburg, J.: Technische Mechanik, Band 2: Festigkeitslehre, B I, Wissenschaftsverlag, Mannheim, Leipzig, Wien, Zűrich, 1992
3. Hoschl, C.: Pružnost a pevnost ve strojírenství, SNTL, Praha, 1971