Course detail

Statics

FSI-3STAcad. year: 2025/2026

Introduction to solid mechanics and Statics, its relation to other courses of solid mechanics. Model and theoretical aspects of engineering mechanics, specification of basic terms and general principles. Introduction to and discussion of the elements of Statics - force, moment of force about a point, moment of force about an axis. Classification of force systems and their resultants. Equivalent force systems. Replacement of a force system by a force and a couple, replacement of a force system by a single force. Conditions for rigid-body equilibrium. Basic tasks of Statics. Centre of gravity and methods of its evaluation. Body supports and connections, their computational models, kinematic pairs. Degrees of freedom of a single body, constraints, concept of a free-body diagram. Statically determinate and indeterminate problems. Algorithm of static equilibrium solution of a body and its application to the analysis and solution of statically determinate systems, mechanisms and trusses. Basic graphical constructions. Passive resistances - their analysis and computational models, dry friction and rolling resistance. Free-body diagrams in actual states of motion. Application to engineering problems including friction forces and rolling resistances. Integral and differential approach to calculation of the resulting internal forces moments in straight rods.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. Ing. Vladimír Fuis, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Entry knowledge

Solution of system of equations (linear, nonlinear), vectorial calculus, basics of matrix calculus, integral calculus. Knowledge of the software Maple.

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:
The exam is divided into two parts. The content of the first part is a cross-sectional written test, from which it is possible to obtain a maximum of 40 ECTS points. Progression to the second part of the exam is conditional on gaining at least 20 ECTS points. If this condition is not met, the exam is graded „F“. The content of the second part is a written solution of typical tasks from the profiling areas of the subject, from which it is possible to obtain a maximum of 40 ECTS points. The specific form of the exam, types, number of examples or questions and details of the evaluation will be announced by the lecturer during the semester.

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 ECTS 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 aim of course "Statics" is to define and introduce basic terms, computational models, theories and algorithms of static problem solutions. Acquired knowledge is necessary to continue in following courses related to mechanics of solids (Dynamics, Strength of Materials). Knowledge of static problems solutions is important for structural design of machine parts.
Students will acquire basic knowledge of mechanics of solids, description and classification of force systems, determination of their characteristics and resultants as well as possibility of their equivalent replacement. Students will be made familiar with computational models of body connections without and with friction. Also provided will be the knowledge of kinematic and static analysis of supported and connected solids and mechanisms, equilibrium solution and concept of free-body diagram. Students will be able to solve static problems using basic graphic methods and calculate the internal resultant forces and moments in straight bars.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Beer, F. P. et al.: Vector Mechanics for Engineers, Statics and Dynamics, 12th ed., 2018 (EN)
Budynas, R. G. a Nisbett, J. K. Shigleyho konstruování strojních součástí. 2. vyd. Editor Martin Hartl, Miloš Vlk, VUTIUM, 2023 (CS)
Florian, Z., Ondráček, E., Přikryl, K.: Mechanika těles - statika, 1995 (CS)
Florian, Z., Suchánek, M.: Mechanika těles - úlohy ze statiky, 1997 (CS)
Hibbeler, R. C.: Engineering Mechanics - Statics and Dynamics, 15th ed., 2022 (EN)
Islam, M. R., Al Faruque, M. A., Zoghi, B. & Kalevela, S. A. Engineering Statics (1st ed.). CRC Press, 2020 https://doi.org/10.1201/9781003098157 (EN)
Potter, M. C. et al.: Schaum's Outline of Engineering Mechanics: Statics, 7th ed. (Schaum's Outlines), 2021 (EN)
Schmerr Jr., L. W. Engineering Statics with MATLAB® (1st ed.), Chapman and Hall/CRC, 2024 https://doi.org/10.1201/9781003372592 (EN)

Type of course unit

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Vladimír Fuis, Ph.D.

Syllabus

1. Definition of mechanics, basic concepts, force, moment of force about a point, moment of force about an axis.
2. Force systems, their classification and characteristic features, gravity, center of gravity.
3. Equivalent force systems.
4. Static equilibrium of a rigid body - characteristics of bonds without passive effect, basic models of body connections.
5. Numerical solutions of the static equilibrium of a bound body.
6. Graphical solutions of the static equilibrium of a bound body.
7. Solving the static equilibrium of systems of bodies – numerically and graphically.
8. Trusses structures.
9. Bonds with a passive effect - analysis and calculation models, basic models of body connections.
10. Solution of the static equilibrium of a bound body with bonds with a passive effect.
11. Solving the static balance of a system of bodies with a passive effect.
12. Bar – definition and basic characteristics, loading and bonds.
13. Internal resultant forces and moments in straight bars - an integral and differential approach.

Exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Vladimír Fuis, Ph.D.

Syllabus

Force, moment of force about a point and about an axis.

Force and moment resultants of force system.

Replacement of a force system by an equivalent force.

Centre of gravity determination.

Static equilibrium of a bound body.

Static equilibrium of movable body.

Computational solutions of equilibrium of rigid body system.

Graphical solutions of equilibrium of rigid body system.

Computational and graphical solution of trusses structures.

Static equilibrium of movable body with passive resistances.

Static equilibrium of movable body system with passive resistances.

Internal resultant forces and moments in straight bars - an integral and differential approach.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Vladimír Fuis, Ph.D.

Syllabus

Force, moment of force about a point and about an axis.

Force and moment resultants of force system.

Replacement of a force system by an equivalent force.

Centre of gravity determination.

Static equilibrium of a bound body.

Static equilibrium of movable body.

Computational solutions of equilibrium of rigid body system.

Graphical solutions of equilibrium of rigid body system.

Computational and graphical solution of trusses structures.

Static equilibrium of movable body with passive resistances.

Static equilibrium of movable body system with passive resistances.

Internal resultant forces and moments in straight bars - an integral and differential approach.

VUT

Faculties

University Institutes

Parts

Statics

Type of course unit