Technical Mechanics

stacjonarne

I stopnia

obowiązkowy

W 34/E, C 34/+; total: 68 hours, 6 points ECTS

Mathematics 1, 2 / Ability to transform expressions containing power functions, trigonometric functions, exponential functions, and logarithms, ability to solve algebraic and trigonometric equations, knowledge of the concept of a vector, its representation and operations on vectors, knowledge of the basics of matrix calculus, knowledge of the concept of ordinary and partial derivatives, ability to determine the derivative of a function, ability to determine a definite integral, ability to solve simple ordinary differential equations;

Physics 1 / Knowledge of basic concepts of mechanics: force, torque, work, power, potential energy, kinetic energy, velocity, acceleration, knowledge of basic conservation laws, knowledge of the law of universal gravitation, knowledge of Newton's laws of motion, knowledge of SI units of measurement for mechanical quantities.

III semestr /Aeronautics and Astronautics/ all fields of study

dr inż. Rafał KIESZEK

student activity/workload in hours:

1. Participation in lectures / 34

2. Participation in laboratories / 0

3. Participation in classes / 34

4. Participation in seminars / 0

5. Individual study of lecture topics / 25

6. Individual preparation for laboratories / 0

7. Individual preparation for classes / 35

8. Individual preparation for seminars / 0

9. Project implementation / 0

10. Participation in consultations / 20

11. Exam preparation / 30

12. Preparation for assessment / 0

13. Participation in the exam / 2

Total student workload: 180 hours/6 ECTS.

Classes with teachers (1+2+3+4+9+10+13): 90 hours/3 ECTS.

Classes related to scientific activity: 150 hours/5 ECTS

The concepts and principles of statics, reduction of force systems and equilibrium conditions, the laws of friction and how to calculate centroids. Strength of Materials includes basic concepts, issues of tension, compression, bending, torsion and buckling, characteristics of multidimensional stress state, calculations of deflections of beams and trusses. The basic concepts and terms of kinematics, kinematics of a point, complex motion of a point, planar motion and spherical motion of a rigid body. The basic concepts and terms of dynamics, dynamics of a point and a system of material points, dynamics of rotational motion and planar motion of a rigid body. The elements of analytical mechanics include a description of the dynamics model of a real object and definitions of special deformable elements with linear properties. It introduces an extended classification of constraints, definitions of the general equation of dynamics and Lagrange's equation.

Lectures / verbal-visual method, using modern multimedia techniques. Providing content for independent study to consolidate the knowledge specified by the effects W1, W2, W3, W4, W5, W6.

1. Introduction: discussion of the didactic requirements of the subject (2 hrs.)

Mechanics, its role and classification. Modeling in mechanics. Histori-cal outline of mechanics.

2. Concepts and basic principles of mechanics (2 hrs.)

Newton's laws. Axioms in mechanics. Equivalent systems of forces. Degrees of freedom bonds and their reactions. External and internal forces. Reduction of any system of forces to one force and one pair of forces.

3. Equilibrium conditions of any system of forces (2 hrs.)

The aim of statics. Equilibrium conditions of a force system. Spatial arbitrary system of forces. Special cases of a system of forces. Sub-stitute equilibrium conditions. Statically determinable systems. Graph-ical methods in mechanics.

4. Friction in planar systems (1 hr.)

Frictional drag forces. Positive (sliding) friction. Static and kinematic friction. Friction of tendons. Rolling friction, rolling resistance.

5. Centers of gravity and centers of mass (2 hrs.)

The center of parallel forces. The centers of gravity of elementary solids. Centers of gravity - material line, surface, solid. The center of mass. The geometric center.

6. Trusses (2 hrs.)

Types of trusses, simplifying assumptions, solution methods (analyti-cal, graphical).

7. Fundamentals of strength of materials (1 hr.)

Idealization - real object, computational model. External and internal forces in bars. Nomenclature of internal forces and basic load cases. The concept of stress at a point.

8. Tension (compression) of bars (1 hr.)

Basic assumptions and relationships. Tensile (compression) strength condition. de Saint- Venant’s.principle.

9. Stress-strain analysis (1 hr.)

Generalized Hooke's law: Definitions of displacements and defor-mations. Allowable stresses. Young's modulus and Poisson's num-ber. State of stress and strain. Relationship between deformations and stresses - generalized Hooke's law.

10. Twisting of rods (1 hr.)

Basic assumptions. Description of the deformation of a circular bar. Determination of maximum stresses and angle of torsion. Strength and rigidity condition for torsion.

11. Rod bending (2 hrs.)

Classification of issues. Cutting force, bending moment. Relationship between cutting force and bending moment. Diagrams of cutting force and bending moment. Analysis of deformations and stresses in a bending bar. Bending strength condition. Differential equation of the deflection line of the bar.

12. Shearing (1 hr.)

Fundamentals. Technical shear. Actual stress distribution in a shear bar - Zurawski's formula. Shear strength condition.

13. Buckling of bars (1 hr.)

Basic cases of buckling of bars. Determination of the critical force - Euler's formula. Critical stresses. Slenderness of the rod. Limits of applicability of Euler's formula.

14. Strength hypotheses (2 hrs.)

The essence of the hypothesis of material strain. The concept of re-duced stresses. Huber-Mises-Hencky (HMH) hypothesis. Coulomb hypothesis. Examples of complex strength.

15. Energy methods (1 hr.)

Linear-elastic systems. The concept of deformation energy. Elastic energy for simple load cases. Castigliano's theorem. Statically inde-terminate systems. Menabrei's theorem.

16. Kinematics of a point (1 hr.)

Description of motion using the leading vector, description of motion in rectangular coordinates, description of motion in natural coordi-nates, description of motion in polar coordinates.

17. Kinematics of the rigid body. (1 hr.)

Progressive, rotary, flat, arbitrary motion.

18. Kinematics of motion of a complex point (1 hr.).

Velocity and acceleration of a point in complex motion, Coriolis ac-celeration.

19. Dynamics of a material point (1 hr.)

Differential equation of motion, types of issues in dynamics, princi-ples of dynamics of a material point, potential force field.

20. Dynamics of a system of material points (2 hrs.)

Equation of motion, center of mass theorem, spin (angular momen-tum) of a system of material points, kinetic energy of a system of ma-terial points.

21. Geometry of masses (2 hrs.)

Mass moments of inertia, mass moments of inertia under coordinate system transformation, principal and central mass moments of iner-tia.

22. Dynamics of rigid body (1 hr.)

Progressive, rotational, planar, spherical, arbitrary motion.

23. Mechanical system as a model of the dynamics of a real object (1 hr.)

Basic dynamics relations for a real object

24. Elements of analytical mechanics. (2 hrs.)

Definition of Lagrange's equation.

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Exercises / verbal-practical method, consisting of group and individ-ual task solving to consolidate the knowledge specified by the effects W1, W2, W3, W4, W5, W6 and master the skills U1, U2, U3.

1. Reduction and equilibrium of a planar convergent force system. (2 hr)

Geometric and analytical method for selected cases.

2. Determination and solution of equilibrium equations of planar and spatial arbitrary system of forces. (2 hrs.)

Analytical method for selected cases.

3. Determination of the position of the centers of gravity (2 hrs).

Calculations for complex plane figures by the method of division into elementary surfaces (summation or subtraction) and the position of centers of gravity of elementary plane figures, lines and solids by the method of integration.

4. Determination of reactions and forces in rods of a plane frame. (2 hrs.)

Calculations by analytical method and selected graphical method.

5. Determination of the distribution of internal forces and strength calculations of a tensile (compression) bar of constant and var-iable cross-section. (2 hrs.)

Calculations by analytical method.

6. Determination of the distribution of internal forces, strength and stiffness calculations of a torsion bar. (2 hrs.)

Calculations by the analytical method.

7. Determination of the distribution of shear forces and bending moments in a bent beam. (2 hrs.)

Calculations by analytical method.

8. Strength calculations of a flexural beam. Determination of dan-gerous -sections. (2 hrs.)

Calculations by analytical method.

9. Strength calculations of a shear bar according to the theory of technical shear and using the Zurawski formula. (2 hrs.)

Calculations by analytical method.

10. Determination of the critical force and critical stress in the case of buckling of the bar for different modes of support. (2 hrs.)

Calculations by analytical method.

11. Solving the equations of motion of a material point for different forms of motion. (3 hrs.)

Calculations in rectangular and natural coordinates.

12. Analysis of motion of plane mechanisms. (3 hrs.)

Calculations by the instantaneous center of rotation method and the superposition method.

13. Examples of analysis of the dynamics of a material point (first and second task of dynamics). (2 hrs.)

Selected analytically determinable cases.

14. Determination of the mass moment of inertia of a rigid body. Examples of analysis of the dynamics of a rigid body. (2 hrs.)

Calculations by analytical method.

15. Derivation of the equation of motion for a simple mechanical system. (2 hrs.)

Calculations in which the deformable element is represented by the model: a) Kelvin-Voigt, b) Maxwell, c) Standard I; Na-write the differ-ential equation of motion of a mathematical pendulum with mass m and length l. Solve the task using: a) d'Alambert's principle, b) La-grange's equation .

16. Application of the Ritz method in the technical theory of pris-matic beams. (2 hrs.)

The case of a bale supported by two points.

Basic:

• Hibbler R. C.: Engineering Mechanics Statics: in SI Units. Prenti-ce Hall, 2007.

• Hibbeler R. C.: Engineering mechanics: dynamics. Pearson Edu-cación, 2004.

• Siddiquee A. N., Khan Z. A., Goel P.: Engineering mechanics: problems and solutions. Cambridge University Press, 2018.

• Kleppner D., Kolenkow R.: An introduction to mechanics. Cam-bridge University Press, 2014.

• Beer F. P., Johnston E. R., DeWolf J. T., Mazurek D.: Statics and Mechanics of Materials. McGraw-Hill Education 2010.

• Den Hartog J. P.: Strength of materials. Courier Corporation. 2012

Supplementary:

• Timoshenko S.: Strength of materials. 1930

• Wittbrodt E.: Mechanika ogólna, teoria i zadania. Wydawnictwo Politechniki Gdańskiej, Gdańsk 2010.

• Brzoska Z.: Wytrzymałość materiałów, PWN, Warszawa 1979.

• Koruba Z., Osiecki J. W.: Elementy mechaniki zaawansowanej. Politechnika Świętokrzyska, Kielce 2007.

• Leyko J.: Mechanika ogólna - statyka i kinematyka, tom 1, PWN, 1997.

• Leyko J.: Mechanika ogólna - dynamika, tom 2, PWN, 1997.

• Misiak J.: Mechanika techniczna - statyka i wytrzymałość mate-riałów, tom 1,WNT, 1997.

• Misiak J.: Mechanika techniczna – kinematyka i dynamika, tom 2, WNT, 1997.

• Jakubowicz A., Orłoś Z.: Wytrzymałość materiałów, WNT, War-szawa 1972.

Symbol and number of the course outcome / learning outcome / reference to the programme outcome:

W1 / has knowledge of mathematics, encompassing algebra, elements of matrix calculus, mathematical analysis, including problems of differential and integral calculus of functions of many variables, elements of ordinary and partial differential equations, probability theory and elements of applied mathematics/ K_W01

W2 / has knowledge of physics, encompassing mechanics/ K_W02

W3 / has well-structured and theoretically grounded knowledge of gene-ral mechanics. / K_W06

W4 / has well-structured and theoretically grounded knowledge of the basics of machine design and strength of materials / K_W07

W5 / has well-structured and theoretically grounded knowledge of the structural problems of machines and processes leading to failures of mechanical objects / K_W09

W6 / has advanced knowledge of the selected facts about objects and phenomena and concerning the methods and theories which expla-in the complex interrelationships among them, constituting the basic general knowledge within the disciplines of mechanics and mecha-nical engineering / K_W19

U1 / is able to obtain information from literature, databases and other sources, can integrate acquired information. / K_U01

U2 / Is able to self-educate, including with a view to improving profes-sional competence. / K_U04

U3 / Is able to determine basic parameters in an analytical manner and formulate simple mathematical models to simulate aircraft compo-nents / K_U07

The course is graded based on: an exam.

Classes are graded based on: passing with a grade;

The exam is conducted in writing (during the exam session) and consists of 5 open-ended questions or, alternatively, 20 closed-ended questions covering learning outcomes W1, W2, W3, W4, W5, W6.

The condition for admission to the exam is passing the classroom exercises with a positive grade.

Passing the classroom exercises with a grade is based on the average of the positive grades received for the preparation and performance of classroom exercises and a written test verifying the achieved learning outcomes U2 and U3.

The achievement of outcomes W1, W2, W3, W4, W5, W6 is checked during the exam, answers in auditorium exercises and colloquiums, and when passing these exercises, as well as when checking skills U1, U2, and U3. The grade for achieving these outcomes is awarded jointly for achieving skills U1, U2, and U3.

Achievement of learning outcomes U1, U2, U3 is assessed during oral and written responses in classroom exercises, as well as indirectly in the assessment of exam questions.

Distance learning methods and techniques may be used during lectures and classroom exercises.

During lectures and classroom exercises, basic English terminology related to the subject will be taught.

It is possible to complete lectures and exercises remotely.

The exam result is assessed on a point system (PKT) as the average of the marks for individual exam questions, i.e.

A very good grade is awarded to a student who has received (4.55< PKT ≤ 5.00)

A good plus grade is awarded to a student who has received (4.10 < PKT ≤ 4.55)

A good grade is given to a student who receives (3.65 < PKT ≤ 4.10)

A satisfactory plus grade is given to a student who receives (3.20 < PKT ≤ 3.65)

A satisfactory grade is awarded to students who receive (2.75 < PKT ≤ 3.20)

A failing grade is awarded to students who do not meet the above requirements, i.e. (2.00 ≤ PKT ≤ 2.75)