Course detail

Statics

FSI-3STAcad. year: 2015/2016

Introduction to solid mechanics, specification of the course Statics and 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 on the elements of Statics - force, moment of force about a point, moment of force about an axis. Discussion on both concentrated and distributed force systems. 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 quilibrium. 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 effects in straight rods.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Vladimír Fuis, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

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 replacement. Students will be made familiar with computational models of body connections without and with passive resistances. 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 graphics methods and calculate of the resulting internal effects in straight rods.

Prerequisites

Solution of system of equations (linear, nonlinear), vectorial calculus, grounding of matrix calculus, integral calculus. 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 15 ECTS points out of 30 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 70 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 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.

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

Beer, F. P. et al.: Vector Mechanics for Engineers, Statics and Dynamics, 12th ed., 2018 (EN)
Hibbeler, R. C.: Engineering Mechanics - Statics and Dynamics, 15th ed., 2022 (EN)
Potter, M. C. et al.: Schaum's Outline of Engineering Mechanics: Statics, 7th ed. (Schaum's Outlines), 2021 (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B-MET , 2 year of study, winter semester, compulsory
    branch B-MAI , 2 year of study, winter semester, compulsory
    branch B-FIN , 2 year of study, winter semester, compulsory

  • Programme B2341-3 Bachelor's

    branch B-STI , 2 year of study, winter semester, compulsory
    branch B-KSB , 2 year of study, winter semester, compulsory
    branch B-VSY , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.
doc. Ing. Radek Vlach, Ph.D.
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 values.
3. Centre of gravity and methods of its evaluation.
4. Equivalent force systems. Static equilibrium of rigid body.
5. Basic tasks of Statics.
6. Geometry and characteristics of body supports and connections, their computational models.
7. Algorithm of static equilibrium solution of constrained body.
8. Basic graphical constructions.
9. Body systems and their static numerical and graphical solutions.
10. Trusses structures, the general and gradual method of joints.
11. Passive resistances - their analysis and computational models, basic models of body connections.
12. Passive resistances - static equilibrium of bodies and systems in motion.
13. The resulting internal effects in straight rods - an integral and differential approach.

Exercise

12 hod., compulsory

Teacher / Lecturer

Ing. Petr Hájek, Ph.D.
Ing. Zdeněk Majer, Ph.D.
Ing. Jakub Němeček
Ing. Martin Houfek, Ph.D.
Ing. Oldřich Ševeček, Ph.D.
doc. Ing. Radek Vlach, Ph.D.
Ing. Petr Vosynek, Ph.D.
Ing. Martin Slažanský, Ph.D.
Ing. Petr Skalka, Ph.D.
Ing. Michal Peč

Syllabus

1. Moment of force and couple of force about a point and about an axis. (1st week)
2. Replacement of a force system by an equivalent force, resultants of distributed force systems. (3rd week)
3. Constraints of a rigid body, concept of a free-body diagram. (5th week)
4. Static equilibrium of movable body, equilibrium position. (7th week)
5. Computational and graphical solution of equilibrium of rigid body system. (9th week)
6. Static equilibrium of movable body with passive resistances. (11th week)

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Vladimír Fuis, Ph.D.

Syllabus

1. Force and moment resultants of force system. (2nd week)
2. Centre of gravity determination. (4th week)
3. Solution of static equilibrium of constrained body. (6th week)
4. Classification of rigid body systems, their degrees of freedom. Free–body diagram of body system. (8th week)
5. Computational and graphical solution of trusses structures. (10th week)
6. Static equilibrium of movable body system with passive resistances. (12th week)
7. Resulting internal effects in straight rods - an integral and differential approach. (13th week)