The main objective of this subject is the study of statics, kinematics and dynamics of rigid bodies, essential background for subjects related to the theory of machines and mechanisms, elasticity and resistance of materials. This subject is based on fundamental principles of physics and mathematics, and will enlarge the practical vision of the students, providing them with the resources needed to analyse different mechanical problems.



Moreover, in this subject the students will get an opportunity to realize how useful the knowledge they already have is, and the application it has in the engineering field. The concepts developed in this subject will be based on vector calculus and matrix algebra, and these will be used on mechanical systems.



The skills developed in this subject are the base of other third year subjects of the Mechanical Engineering Bachelor's Degree: Elasticity and Resistance of Materials, Kinematics and Dynamics of Machines, Design of Machines, Structures and Industrial Constructions and Mechanical Technology. These skills are also the base of Mechanical Engineering that any engineer of the branch of Industrial Engineering (Bachelor's Degree in Electricity and Bachelor's Degree in Industrial Electronics and Automation included) should master.

* Specific skills:



- Get to know, understand, and apply the concepts and basic principles of resistance of materials and of mechanisms and machines. These concepts and principles will be essential in the study of advanced methods and theories of mechanical engineering.



- Apply the strategies of the scientific methodology: analyse any problematic situation in a qualitative and quantitative way and set up a hypothesis and solution by applying the methods used in applied mechanics.



- Express correctly the theoretical knowledge, solution methods, and the results obtained for problems dealing with the equilibrium and movement analysis of mechanical systems, using the specific terminology and vocabulary.



* Transversal skills:



- Ability to work efficiently in team, proposing and debating different ideas and taking decisions along with the other team members.



- Have a responsible attitude, be organized in the work and willingness for the learning process.



* Learning results:

After studying this subject, the students must have acquired the following abilities related to the mechanical analysis and calculus:



- To model a mechanical system composed of rigid elements and simple mechanical elements.



- To evaluate how the different loads are transmitted to the supports in simple isostatic structures.



- To analyse the kinematics of simple mechanical systems, obtaining the velocities and accelerations of points and elements, expressed in fixed and mobile reference systems.



- To obtain the gravity centres and inertia properties of rigid bodies and planar surfaces.



- To analyse the dynamics of simple planar and spatial mechanical systems.



- To evaluate the variation of internal forces in simple beams under point or distributed forces.



- To evaluate the stress in simple elements.



- To transmit all the previous results in a clear and comprehensive way to a specialized audience.

- Lesson 1: Force systems

Basic knowledge of calculus with vectors. Definitions and properties of the momentum generated by a force acting about an axis and a point. Concept and properties of a pair of forces. Equivalence and reduction of force systems.



- Lesson 2: Centroids

Concept and properties of gravity centre and static moment. Centroids of elemental figures. Theorems of Pappus-Guldin.



- Lesson 3: Static equilibrium

Study of structural systems, fundamental axiom of the static equilibrium of a rigid body. Concepts of links and mechanical action. Calculus of the forces and reactions that appear in the different elements of a mechanical system. Analysis of isostatic structures and methods solve lattices.



- Lesson 4: Friction

Study of the simplified hypothesis of Coulomb to analyse the friction in a sliding movement, friction coefficient and friction angle. Industrial applications of the friction.



- Lesson 5: Funicular bodies

Equilibrium study of funicular bodies, cables working under the effect of point and distributed forces. Study of catenaries.



- Lesson 6: Kinematics of the rigid body

Velocity and acceleration concepts applied to a particle. Analysis of the simple movements of translation and rotation of a solid body. Meaning of the angular velocity vector and angular acceleration vector. Law of vector derivatives in mobile frames. Velocity and acceleration fields. Study of the relative movement of a point and a body with respect a mobile system.



- Lesson 7: Kinematics of planar movement

Particularities of planar motions. Concepts of instant centre of rotation and how its position changes in time. Concepts of moving centrode and fixed centrode. Geometry of the planar movement, graphical calculus of velocities. Study of accelerations in a pure rolling movement. Instantaneous acceleration centre.



- Lesson 8: Inertia propierties of solid bodies

Inertia moments with respect to axis, planes and points. Inertia products. Steiner theorems. Inertia tensor and the main inertia direction of a body.



- Lesson 9: Dynamics of the rigid body

Elemental magnitudes in dynamics, quantity of movement, kinematic moment and kinematic energy. Fundamental theorems in dynamics. Expressions of the kinematic moment and the kinematic energy in solid bodies. Concept of inertia force and gyroscopic momentum. Application of D'Alembert principle in the dynamic analysis of mechanisms. Energetic theorems.



- Lesson 10: Dynamics of bodies with a fixed axis

Study of bodies with a rotation movement about a fixed axis. Calculus of the reaction forces in the links. Equilibrium of rotors.



- Lesson 11: Dynamics of planar movement

Study of the magnitudes and equations of dynamics for a planar case. Analysis of the different possible cases and how to solve them. Application to mechanical systems that are part of machines and mechanisms.



- Lesson 12: Inertia momentums of a surface

Description of the moments and products of inertia for planar surfaces. Main moments of inertia and main directions of inertia, obtained by applying the circle of Mohr.



- Lesson 13: Internal forces

Concept of internal force in a section of a body. Axial force, shear force and bending moment. Representation of the corresponding diagrams.



- Lesson 14: Normal tensions

Concept of normal tension and unitary deformation in the axis of a body. Relation between the tension and the deformation, Hooke law. Relation between the tensions and the internal forces in a section.

The main theory lectures will be complemented with exercises solving lectures and computer practise.

• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 80
  • Team projects (problem solving, project design)) (%): 20

Tasks: 20% of the final mark:



During the scholar year, students will be asked to develop different tasks (10 approximately).



Written exam: 80% of the final mark:



* Exams period in the first semester:

- First partial exam: from lesson 1 to lesson 7. To pass the exam, students must earn a minimum mark of 5/10. Students who pass the exam will not be tested again on this material in the second partial exam.



* Exams period in the second semester. There are two possible cases:

- Second partial: from lesson 8 to lesson 14. To be eligible for this option, students must have passed the first partial. The final mark of the subject will be the GEOMETRIC mean of the marks obtained in the two partials.

- Final exam: all syllabus. Students who did not pass or appear for the first partial must take this exam.



Additional information:



- Students who apply to the final evaluation will be evaluated with a single exam, the results of which will constitute the 100% of the final mark of the subject. Students who want to be evaluated with the final evaluation system must apply for it within the deadline established in the Norma reguladora de Evaluación del alumnado en las titulaciones de Grado de la UPV/EHU before the 4th week of the second semester.



- In all exams, partial and final, the theory part will account for 40% of the mark of the exam, and the exercises will account for 60%.



- Students who do not attend the second partial or the final exam will get a final mark of No presentado (did not attend).

- Students who have not passed the ordinary evaluation will get the chance of writing a final exam of the whole subject.



- By default, the marks of the tasks will be also taken into account in this evaluation (20% of the final mark), so the mark obtained in final exam will be the 80% of the total mark in the subject.



- If in any case the mark obtained in the final exam is higher than the one obtained after considering the tasks, the final mark in the subject will be the higher mark.



- The evaluation for students who do not attend the exam will be “Not presented”.

Lectures book: Mecánica Aplicada -Erik Macho- 2023 Edition
https://web-argitalpena.adm.ehu.es/listaproductos.asp?IdProducts=UIGPD235483&titulo=Mec%E1nica%20aplicada


Software GIM: http://www.ehu.eus/compmech/software/

Basic bibliography

- F.P. Beer, E.R. Johnston Jr., et al., Vector Mechanics for Engineers, New York: McGraw-Hill, ISBN 0-07-293110-8.



- F.P. Beer, E.R. Johnston Jr., et al., Mechanics for Engineers: Statics and Dynamics, New York: McGraw-Hill, ISBN 0-07-004584-4.



- Rao, A. V., Dynamics of Particles and Rigid Bodies: A Systematic Approach, Cambridge University Press, 2006

In-depth bibliography

Ingeniería mecánica, Estática. Hibbeler. Prentice Hall
Ingeniería mecánica, Dinámica. Hibbeler. Prentice Hall

Estática, Mecánica para ingeniería. Bedford, Fowler. Addison Wesley
Dinámica, Mecánica para ingeniería. Bedford, Fowler. Addison Wesley

Mecánica de materiales. Beer, Johnston, Russell. Mc Graw-Hill
Mecánica de materiales. Hibbeler. Prentice-Hall