Course code Meha4013

Credit points 3

Total Hours in Course81

Number of hours for lectures8

Number of hours for seminars and practical classes24

Independent study hours49

Date of course confirmation06.04.2021

Responsible UnitInstitute of Mechanics and Design

lect.
## Mārtiņš Dauvarts

Bc. sc. ing.

Mate4019, Mathematics I

The aim of the study course is to master the main basic principles of theoretical mechanics. Force computation in static structures, mechanical movements of material solid body, and research into their conditions. It develops logical thinking and create a knowledge base for the acquisition of technical disciplines.

Knowledge – understanding the difference between force and moment of force, the calculation of forces by the projection method and ability to compile equilibrium equations. Understanding how to determine the moment of force, and count them. Understanding of work and power in mechanics, work computation – 1. And 2. Test.

Skills – ability to look at the condition of various solid objects and structures in an abstract and analytical way, and how it effects on other mechanical systems – practical and independent works.

Competences – ability to use the basic principles of theoretical mechanics in practical work and research, as well as the invention and implementation of technically innovative processes – 3. and 4. Test.

1. 1. Basic concepts of mechanics. (Lecture – 1h)

2. The axioms of static. The algebra of vectors. (Lecture – 1h, practical work – 4h, independent work – 4h)

3. The force. Calculus of the force(vectors). (Lecture – 1h, practical work – 2h, independent work – 4h)

4. Concentrated force systems in plane. 1st test on basic concepts of mechanics, statistical axioms, vector algebra and force. (Lecture – 1h, practical work – 2h, independent work – 4h)

5. Spread force systems in plane. (Lecture – 1h, practical work – 2h, independent work – 4h)

6. Force moments. Calculus of the moments. (Lecture – 1h, practical work – 2h, independent work – 4h)

7. Double force moments. Calculus of double force moments. 2nd test on the system of spread forces in the plane, the moment of force, the double force moments and the double force moment of the calculus. (Lecture – 1h, practical work – 2h, independent work – 4h)

8. Sliding friction. Rolling friction. (Lecture – 1h, practical work – 2h, independent work – 4h)

9. Equilibrum of body systems according to friction. (Practical work – 2h, independent work – 6h)

10. Gravity of the body. Stability. 3rd test on sliding and rolling friction, body system balance, body center of gravity and stability. (Practical work – 2h, independent work – 6h)

11. Strength work. (Practical work – 2h, independent work – 4h)

12. Power. 4th test on strength work and power. (Practical work – 2h, independent work – 4h)

Grade with a mark:

o four tests must be written successfully (at least 4 points)

o successfuly done all independent works.

Independent work – to solve theoretical problems of mechanics, to master in depth the topics covered in lectures and perform independent works:

1st Independent work: Addition of vectors by projection method.

2nd Independent work: Addition of forces of the system of connecting forces.

3rd Independent work: Addition of forces and moments of a distributed force system.

4th Independent work: Determination of friction force.

5th Independent work: Determining the center of gravity of a figure's area.

6th Independent work: Calculation of power according to the work done by force.

The test with a mark is formed as the arithmetic mean of the sum of the assessments of the tests.

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

1. Kabus K. Mechanik und Festigkeitslehre. Aufgaben, 5. Auflage, Carl Hanser Verlag: München Wien, 2003. 276 S.

2. Kabus K. Mechanik und Festigkeitslehre. 5. Auflage, München Wien: Carl Hanser Verlag , 2003. 351 S.

3. Muvdi B.B., Al-Khafaji A.W., McNabb J.W. Statics for engineers. Bradley University, 1996.

4. 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.

Prof .Dr.Ing. Vasile Szolga. Theoretical Mechanics. [tiešsaiste] [skatīts 13.12.2020.]. Pieejams: https://www.pdfdrive.com/theoretical-mechanics-d7357440.html

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