Course detail

Strength of Materials I

FSI-4PPAcad. year: 2025/2026

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.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. Ing. Tomáš Návrat, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Entry knowledge

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 Matlab.

Rules for evaluation and completion of the course

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.


Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

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 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.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Gere, J.M., Timoshenko, S.P.: Mechanics of Materials, third SI edition, Chapman & Hall, London, Glasgow, New York, 1995
Hoschl, C.: Pružnost a pevnost ve strojírenství, SNTL, Praha, 1971
Pestel, E., Wittenburg, J.: Technische Mechanik, Band 2: Festigkeitslehre, B I, Wissenschaftsverlag, Mannheim, Leipzig, Wien, Zűrich, 1992
GOODNO, B. J a J. M. GERE. Mechanics of materials. Enhanced ninth edition, SI edition. Boston: Cengage, 2021, ISBN 978-0-357-37785-7.
HIBBELER, R. C a K. B. YAP. Mechanics of materials. Harlow: Pearson, 2018. ISBN 978-1-292-17820-2.
Janíček P., Florian Z.: Úlohy z pružnosti a pevnosti I,2. vyd., VUT-FSI, Brno,1995
Janíček P., Ondráček E., Vrbka J., Burša J.: Pružnost a pevnost I,VUT-FSI,Brno,2004
Muvdi, B.B., & Elhouar, S. (2016). Mechanics of Materials: With Applications in Excel (1st ed.). CRC Press. Dostupné z: https://doi.org/10.1201/9781315374314
Ross, C., Bird, J., & Little, A. (2021). Mechanics of Solids (3rd ed.). Routledge. Dostupné z: https://doi.org/10.1201/9781003128021

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B-ENE-P Bachelor's 2 year of study, winter semester, compulsory
  • Programme B-PDS-P Bachelor's 2 year of study, winter semester, compulsory

  • Programme B-STR-P Bachelor's

    specialization AIŘ , 2 year of study, winter semester, compulsory
    specialization KSB , 2 year of study, winter semester, compulsory
    specialization SSZ , 2 year of study, winter semester, compulsory
    specialization STG , 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

52 hod., optionally

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

Definition of subject contents. Basic terms – deformation, stress, stress state, limit states, safety.
Mechanical properties of material and its computational models. Characteristics of linear elastic body. Definition of linear strength of materials.
Work done by forces, Castigliano's theorem. Saint -Venant's principle. Beam in strength of materials – definition, classification.
Geometrical characteristics of cross-section. Area moments of inertia, transformation with respect to the translated and rotated axes. Principal central area moments of inertia.
Axially loaded bars:
- Deformation, stress state and strain energy.
- Influence of deviations on deformation and stress state, notches and safety check.
- Statically indeterminate beam loaded in tension and compression.
- Truss structures and trusses.
Bars in torsion:
- Deformation, stress state, strain energy and influence of deviations on deformation and stress state.
- Statically indeterminate beam and safety check.
Beams in bending:
- Stress state, deformation, strain energy. Methods of determination of deflection.
- Influence of deviations on stress state and deformation. Shear stress resulting from shear force. Safety check.
- Statically indeterminate beam.
- Shear stress for thin-walled profiles, shear center.
Stability of columns. Influence of deviations on the critical load.
Stability of columns from real material. Eccentric compression.
Stress state in the point of a body, principal stresses.
Representation of stress state using Mohr's circle. Particular cases of stress state, plane stress state.
Criteria for materials of bodies in ductile or brittle state without a priori defects of the crack type at static loading.
Combined loading of beams.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.
Beams loaded by temperature. Non-linearity in bending.
Overview of problems solvable by analytical and numerical methods.
Examples of possibilities of contemporary methods of experimental strength of materials.
Eurocodes - Design of steel structures.

Exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

Internal forces and moments for straight bar.
Internal forces and moments for curved beam and frame.
Area moments of inertia. Mohr's circle.
Loading in tension, stress state and deformation. Statically determinate tasks.
Loading in tension, stress state and deformation. Statically indeterminate tasks.
Loading in torsion. Statically determinate and indeterminate tasks.
Loading in bending. Stress state and deformation for statically determinate beam.
Loading in bending. Stress state and deformation for statically indeterminate beam.
Stability of columns. Safety for compressive loading of bars from real material.
Calculation of trusses considering the stability of columns. Truss structures.
Combined loading.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.

Syllabus

Internal forces and moments for straight bar.
Internal forces and moments for curved beam and frame.
Area moments of inertia. Mohr's circle.
Loading in tension, stress state and deformation. Statically determinate tasks.
Loading in tension, stress state and deformation. Statically indeterminate tasks.
Loading in torsion. Statically determinate and indeterminate tasks.
Loading in bending. Stress state and deformation for statically determinate beam.
Loading in bending. Stress state and deformation for statically indeterminate beam.
Stability of columns. Safety for compressive loading of bars from real material.
Calculation of trusses considering the stability of columns. Truss structures.
Combined loading.
Curved beams and frames. Closed beams (frames). Utilization of symmetry and antimetry.