Course detail

# Statics

FSI-3STAcad. year: 2020/2021

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 effects in straight rods.

Supervisor

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 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.

Prerequisites

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

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Hibbeler, R. C.: Engineering Mechanics - Statics and Dynamics, 13th ed., 2012

Florian, Z., Ondráček, E., Přikryl, K.: Mechanika těles - statika, 1995

Beer, J. P., Johnston, E. R. Jr.: Vector Mechanics for Engineers, Statics and Dynamics, 9th ed., 2009

Florian, Z., Suchánek, M.: Mechanika těles - úlohy ze statiky, 1997

Muvdi, B. B., Al-Khafaji, A. W., McNabb, J. W.: Statics for engineers, 1997

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:

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.

Language of instruction

Czech

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

Classification of course in study plans

- Programme B-VTE-P Bachelor's, 1. year of study, winter semester, 5 credits, compulsory
- Programme B3A-P Bachelor's
branch B-MET , 2. year of study, winter semester, 5 credits, compulsory

- Programme B3S-P Bachelor's
branch B-STI , 2. year of study, winter semester, 5 credits, compulsory

- Programme B-PDS-P Bachelor's, 2. year of study, winter semester, 5 credits, compulsory
- Programme B-MAI-P Bachelor's, 2. year of study, winter semester, 5 credits, compulsory
- Programme B-FIN-P Bachelor's, 2. year of study, winter semester, 5 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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.

3. Centre of gravity and methods of its evaluation.

4. Equivalent force systems. Static equilibrium of a 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 a constrained body.

8. Basic graphical constructions.

9. Body systems and their static numerical and graphical solutions.

10. Pin-jointed structures, the general and sequential method of solution.

11. Bonds with the passive resistance - their analysis and computational models, basic models of body connections.

12. Bonds with the passive resistance - static equilibrium of bodies and systems in motion.

13. The internal resultant forces and moments in straight bars - an integral and differential approach.

Exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Moment of force and couple 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, resultants of distributed force systems.

Centre of gravity determination.

Constraints of a rigid body, concept of a free-body diagram.

Solution of static equilibrium of a constrained body.

Static equilibrium of movable body, equilibrium position.

Classification of rigid body systems, their degrees of freedom. Free–body diagram of a body system.

Computational and graphical solution 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 hours, compulsory

Teacher / Lecturer

Syllabus

Moment of force and couple 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, resultants of distributed force systems.

Centre of gravity determination.

Constraints of a rigid body, concept of a free-body diagram.

Solution of static equilibrium of a constrained body.

Static equilibrium of movable body, equilibrium position.

Classification of rigid body systems, their degrees of freedom. Free–body diagram of a body system.

Computational and graphical solution 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.

eLearning

**eLearning:** currently opened course