Mechanics 2

Code:

EC0013

Acronym:

MECA2

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Structural Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEC	218	Syllabus since 2006/2007	2	-	6	60	160

Teaching language

Portuguese and english

Objectives

JUSTIFICATION:
The fundamental concepts of kinematics and dynamics and their generalization to three-dimensional space strongly contribute to a better understanding of the surrounding environment and the phenomena that condition and determine it.

OBJECTIVES:
This curricular unit aims teaching and developing the ability to solve problems related to the kinematics and kinetics of particles, systems of particles and rigid bodies, by introducing theoretical concepts and practical methodologies.

Learning outcomes and competences

COMPETENCES AND LEARNING OUTCOMES:
Knowledge: Define and demonstrate knowledge in areas of basic science. Identify key concepts related to kinematics and dynamics of systems.
Comprehension: Interpret and identify the phenomena associated with movement of systems and the causes that produce nuclear knowledge in engineering. Interpret the phenomena in the light of empirical knowledge.
Application: Develop knowledge in fundamental sciences. Apply the concepts of kinematics and dynamics in the resolution of practical cases.
Analysis: Analyze the relationship between kinematics and systems dynamics. Understand the difference between particle and system of particles and the implications in the response. 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The students are required to have basic knowledge on Mathematics and Physics acquired before entering at FEUP, complemented with the Mathematical Analysis and Algebra courses of the 1st year.

Program

Chapter 1 – KINEMATICS OF A PARTICLE
Description of the motion of a particle; Position, velocity and acceleration vectors; Dimensions and units; Velocities hodograph curve and Motion osculator plane; Graphical representation of kinematics quantities; Classification of the particle’s motion; Uniform rectilinear motion; Uniformly accelerated motion; Angular velocity and angular acceleration; Circular motion; Rotation vector or Angular velocity vector.

Chapter 2 – KINEMATICS OF A SYSTEM OF PARTICLES
Translation motion; Rotation motion; Rotation operator; General motion of a solid; Plane motion of a solid; Theorem of velocities projection; Instantaneous centre of zero velocity; Kinematics of the relative motion; Theorem of the composition of velocities; Theorem of the composition of accelerations or Theorem of Coriolis; Newton’s principle of relativity.

Chapter 3 - GEOMETRY OF MASSES
Centre of geometry, centre of mass and centre of gravity of a two dimensional body; Centroids of areas and lines; First moments of areas and lines; Theorems of Pappus- Guldinus; Second moment, or moment of inertia, of an area and of a mass; Parallel axes theorem or Steiner’s theorem; Polar moment of inertia; Radius of gyration; Products of inertia; Principal axes and principal moments of inertia; Graphical determination of moments and products of inertia: Land’s circle and Mohr’s circle.

Chapter 4 – DYNAMICS OF PARTICLES
Fundamental principles of dynamics; Linear momentum; Rate of change of linear momentum – Linear impulse; Notion of field; Work of a force; Theorem of kinetic energy; Potential energy – Conservative fields; Principle of conservation of mechanical energy; Power and efficiency; Angular momentum; Rate of change of angular momentum; Central forces – Motion under a central force; Newton’s law of gravity; Trajectory of a particle under a central force; Principle of D’Alembert.

Chapter 5 – DYNAMICS OF A SYSTEM OF PARTICLES
General equations of motion; Centre of mass theorem; Linear momentum; Rate of change of linear momentum; Principle of conservation of linear momentum; Impact – Direct central impact and Oblique central impact; System of particles with variable mass; Angular momentum; Rate of change of angular momentum; Principle of conservation of angular momentum; Kinetic energy; Theorem of kinetic energy; Rotation of a solid about a fixed axis; Extension to the principle of D’Alembert.

Chapter 6 – VIBRATION OF DISCRETE SYSTEMS WITH ONE DEGREE OF FREEDOM
Characterization of discrete systems with one degree of freedom (DS1); Formulation of the DS1 equations of motion; Motion of DS1 without damping in free vibration and when subjected to harmonic actions; Motion of DS1 with damping in free vibration and when subjected to harmonic actions.

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
The fundamental concepts of kinematics and dynamics and its generalization to three-dimensional space contribute significantly to a better perception of the surrounding environment and phenomena that condition it.

Mandatory literature

Henriques, A.A.R.; Guedes, J.P.M.; Apontamentos de Mecânica 2, 2002
Beer, Ferdinand P; Mecânica vetorial para engenheiros. ISBN: 85-86804-49-5
Meriam, J. L.; Mecânica - Dinâmica. ISBN: 85-216-1176-5

Complementary Bibliography

Shames, Irving H.; Engineering Mechanics. ISBN: 0-13-356924-1
Timoshenko, S.; Advanced Dynamics
Spiegel, Murray R.; Schaum.s outline of theory and problems of theoretical mechanics with an introduction to Lagrange.s
Pestel, Eduard C.; Dynamics

Teaching methods and learning activities

All subjects of the course are discussed in the theoretical and practical classes. Exposition and explanation of concepts, principles and methods, complemented and illustrated with the resolution of some of the problems proposed at the exercises sheets, are done in the theoretical classes. In the practical classes it is promoted the discussion of the problems proposed at the exercises sheets, being the students asked to solve them individually or in group.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
Students are encouraged to apply the concepts of kinematics and dynamics in the resolution of practical cases, to analyze and relate kinematics and dynamics of systems, to understand the difference between particle and system of particles and the implications for the response.

keywords

Physical sciences > Physics > Classical mechanics > Structural mechanics
Physical sciences > Physics > Classical mechanics > Kinetics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Teste	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Frequência das aulas	49,50
Total:	49,50

Eligibility for exams

Achieving final classification requires compliance with MIEC assessment rules.

Calculation formula of final grade

The final classification is defined based on a distributed evaluation that consists of 2 tests to be done during the semester and that will take place in the theoretical classes, and a final exam. The distributed evaluation is optional. All the components are expressed in a 0 to 20 scale.

The final classification is computed using the following formula:

CF = max {CT ; EF}

where,

CT = PA / 2 x CAD1 + PA / 2 x CAD2 + PF x EF

CAD1 – classification of test 1;
CAD2 – classification of test 2;
EF     – classification of final exam (ordinary and appeal).

Being PA and PF the weights associated to the classifications CAD1, CAD2 e EF:

PA = 0,25 (25%)
PF = 0,75 (75%)

NOTE 1: The tests that correspond to CAD1 and CAD2 are optional. If a student doesn’t respond to any of them, the correspondent weights are added to PF.

NOTE 2: The formulation is valid for all the students registered in this curricular unit.

NOTE 3: The classification of the distributed evaluation obtained in the previous school year won’t be valid in the present school year.

NOTE 4: The final maximum grade that any student can obtain through written tests/ exam is 17. To obtain a grade of 18 or higher, the student must take an oral exam. Only students with a grade of 18 or higher obtaind through written exams are admitted to an oral exam.

Examinations or Special Assignments

The students are not obliged to do tests 1 and 2 (CAD1 and CAD2) that are part of the distributed evaluation of the curricular unit. This component will only be considered in the Final Classification if it is obtained during the current school year.

Special assessment (TE, DA, ...)

See NOTE 2 of item "Cálculo da Classificação Final".

Classification improvement

It is not foreseen any test to improve the classification of the distributed evaluation, but only of the ordinary final exam that may be obtained through the appeal final exam.

Observations

Estimated working time outside classes: 4 hours.