Course code Meha4008

Credit points 3

# Theoretical Mechanics I

Total Hours in Course120

Number of hours for lectures16

Number of hours for seminars and practical classes32

Independent study hours72

Date of course confirmation19.10.2011

Responsible UnitInstitute of Mechanics

### Course developers Mehānikas institūts

## Ēriks Kronbergs

Dr. sc. ing. lect.

## Mārtiņš Dauvarts

Bc. sc. ing.

### Prior knowledge

Fizi2021, Physics I

Mate1029, Mathematics I

Mate1030, Mathematics II

### Course abstract

The aim of the study course is to master the main basic principles of theoretical mechanics. Students learn the concept of force, methods of force calculation in static structures, methods of calculation of kinematic parameters of motion, develop logical thinking and form a knowledge base for the acquisition of technical disciplines.

### Learning outcomes and their assessment

Knowledge - understands what is called strength and what is the moment of strength. Has an understanding of force addition by the projection method and is able to compile equilibrium equations. Has an understanding of how to determine the moment of force and is able to count them. Understands how to determine the conditions of motion in mechanics and is able to calculate (tests).
Skills - is able to view in an abstract and analytical way the equilibrium state of various solid bodies and structures and the effect on other mechanical systems (independent works).

Competence - the ability to use the basic principles of theoretical mechanics in practical and scientific work, as well as in the invention and implementation of technically innovative processes (independent works).

### Course Content(Calendar)

1. Introduction. Basic concepts of mechanics course. (1h L; 2h PstD)
2. Static axiom. Vector algebra. (1h L; 2h PrD; 6h PstD) (Test 1 for 1st, 2nd)
3. Strength. Addition of forces (vectors). (1h L; 2h PrD; 4h PstD)
4. In-plane force systems. (1h L; 2h PrD; 4h PstD) (Test 2 for 3rd, 4th)
5. In-plane distributed force systems (1h L; 2h PrD; 4h PstD)
6. Moment of force. Moment counting. (1h L; 2h PrD; 4h PstD)
7. Moment of force pair. Addition of force pair moments. (1h L; 2h PrD; 4h PstD); (3rd test for 5th, 6th, 7th)
8. Sliding friction. Rolling friction. Equilibrium of the body system with respect to friction. (1h L; 2h PrD; 4h PstD) (Test 4 on the 8th)
9. Body center of gravity. Stability. (1h L; 2h PrD; 4h PstD)
10. Techniques of point movement. Speed. Acceleration. Natural triedrs. (1h L; 2h PrD; 4h PstD)
11. Types of solid body movement. Degrees of freedom of movement. (1h L; 2h PrD; 4h PstD)
12. Rotational movement. Gear ratio. (1h L; 2h PrD; 4h PstD) (Test 5 on 10. 11, 12)
13. Complex movement. Accelerating speeds. (1h L; 2h PrD; 8h PstD)
14. Movement in the complex. Accelerations in complete motion. (1h L; 4h PrD; 8h PstD) (Test 6 on 13, 14)
15. Compound movement. Speeds and accelerations in compound motion. Acceleration of carololis. (1h L, 2h PrD; 8h PstD)

16. Compound movement. Cariolis acceleration in compound motion. (1h L; 2h PrD; 4h PstD)

### Requirements for awarding credit points

The test is formed as follows:
• All (six) tests must be written successfully (at least 4 points);

• All correctly solved independent works are included.

### Description of the organization and tasks of students’ independent work

Independent work - To solve theoretical problems of mechanics, in-depth study of the topics covered in lectures and perform independent work:
1. Independent work: Addition of vectors by projection method.
2. Independent work: Addition of forces of the system of connecting forces.
3. Independent work: Addition of forces and moments of a distributed force system.
4. Independent work: Determination of friction force.
5. Independent work: Determining the center of gravity of a figure's area.
6. Independent work: Movement of a point.
7. Independent work: Rotational movement.
8. Independent work: Speeds and accelerations in complete movement.

9. Independent work: Compound movement.

### Criteria for Evaluating Learning Outcomes

Test with a mark is made of the arithmetic mean of the sum of all tests (tests and practical works).

1. Kabus K. Mechanik und Festigkeitslehre. 5 Auflage, München Wien: Carl Hanser Verlag, 2003. 276 S.
2. Muvdi B.B., Al-Khafaji A.W., McNabb J.W. Statics for Engineers. Bradley University, 1996.

3. Müller W.H., Ferber F. Technische Mechanik für Ingenieure. 4 aktualisierte Auflage. Fachbucherverlag Leipzig: Carl Hanser Verlag, 2011. 538 S.

1. Kepe O.,Vība J. Teorētiskā mehānika. Rīga: Zvaigzne, 1982. 577 lpp.
2. Teorētiskā mehānika piemēros. O. Kepes redakcijā. Rīga: Zvaigzne, 1976. 647 lpp.
3. Teorētiskās mehānikas uzdevumi. O. Kepes un J. Vības red. 1.izd. Rīga: Zvaigzne, 1989. 479 lpp.

4. Hibbeler R.C. Statics and mechanics of materials. Singapore: Prentice Hall, 2004. 792 p.

### Periodicals and other sources

1. Journal of Applied Mathematics and Mechanics. Published by Elsevier Science. ISSN: 0021-8928. Pieejams: http://www.sciencedirect.com/science/journal/00218928
2. European Journal of Mechanics - A/Solids. Published by Elsevier Science. ISSN: 0997-7538. Pieejams: http://www.sciencedirect.com/science/journal/09977538

3. Szolga V. Theoretical Mechanics. [tiešsaiste] [skatīts 13.12.2020.]. Pieejams: https://www.pdfdrive.com/theoretical-mechanics-d7357440.html

### Notes

Compulsory study course for full-time and part-time students of the academic higher education Agricultural Engineering and professional higher education study program “Design and Production of Machinery”. 3rd study year.