Mechanics 2

Code:

EC0013

Acronym:

MECA2

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2006/2007 - 1S

Active?	Yes
Web Page:	http://www.fe.up.pt/si/DISCIPLINAS_GERAL.FORMVIEW?P_CAD_CODIGO=EC0013&p_ano_lectivo=2006/2007&p_periodo=1S
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
LEC	2	Plano de estudos de transição para 2006/07	2	6	6	60	160
MIEC	334	Syllabus since 2006/2007	2	-	6	60	160
		Plano de estudos de transição para 2006/07	2	-	6	60	160

Teaching language

Portuguese

Objectives

To instruct and to develop the ability to analyse problems of dynamics of rigid bodies or rigid particles’ systems, by introducing theoretical concepts and practical methodologies to solve problems related to kinematics and kinetics.

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.

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

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

Teaching methods and learning activities

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

keywords

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

Evaluation Type

Evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	56,00
	Total:	-	0,00

Eligibility for exams

The conditions for the frequency attainment are those expressed in the article 4º of the General Norms of Evaluation of the FEUP. Furthermore, the proposed problems have to be adequatelly developed and delivered during a pre-defined period of time.

Calculation formula of final grade

The final classification is given by the written final exam result.

Examinations or Special Assignments

Two complementary exercises sheets are going to be presented for individual resolution during the period extra-lessons. The delivery of the respective resolutions, correctly done, during the pre-defined period of time is one of the indispensable conditions to frequency attainment.

Special assessment (TE, DA, ...)

The students with special status are equally evaluated as other students.

Classification improvement

The classification improvement follows the rules established in the article 10º of the General Norms of Evaluation of the FEUP.