The fundamental concepts and principles of Mechanics and force systems. Centroids, centre of gravity, and second moments of area and moments of inertia. Equilibrium of rigid bodies. Elastic behaviour of solids. Internal forces in structural members: trusses and beams.
Theoretical and practical contents
Chapter I: THE FUNDAMENTALS CONCEPTS AND PRINCIPLES OF MECHANICS. I.1. Introduction to physical magnitudes. I.2. Definition of force. Dynamics: Newton’s laws. I.3. Scalar and vectorial magnitudes I.4. Basic vectorial algebra and analytical geometry. I.5. Dot product and cross product. Double cross product.
Students must to know this chapter for applying in the subject contents. It will facilitate documents of theory and exercises to practice. Doubts will be answer during tutorial hours.
Chapter II: SLIDING VECTORS. II.1. Definition. II.2. Moment of a sliding vector. II.3. Systems of sliding vectors. II.4. Invariants of a given system of sliding vectors. II.5. Equation of the central axis. II.6. Classification of systems of sliding vectors. II.7. Varignon’s theorem.
Chapter III: CENTRE OF GRAVITY OF PLANE SURFACES. III.1. Centre of gravity of plane surfaces. III.2. Systematic calculation of centres of gravity. III.3. Theorems of Pappus and Guldinus. III.4. Static moments and centre of gravity of a surface.
Chapter IV: MOMENTS OF INERTIA OF AREAS. IV.1. Moments of inertia of plane surfaces. IV.2. Radius of gyration of an area. IV.3. Change of the reference system. Steiner’s theorem. IV.4. Product of inertia. IV.5. Geometric and mass moments of inertia.
Chapter V: PRINCIPALS MOMENTS AND DIRECTIONS OF INERTIA OF PLANE SURFACES. V.1. Principal moments of inertia of a section. V.2. Principal axes and principal directions of inertia. V.3. Properties of the principal axis of inertia. V.4. Calculation of de principal directions of inertia.
Chapter VI: EQUILIBRIUM OF RIGID BODIES. VI.1. Basic principles of static equilibrium. VI.2. Support and connection types. VI.3. Friction. VI.4. Free-body diagrams.
Chapter VII: ANALYTICAL TECHNIQUES TO SOLVE COPLANAR FORCE SYSTEMS. VII.1. Graphical solution for coplanar force systems. VII.2. General case. VII.3. Concurrent force systems. VII.4. Parallel force systems. VII.5. Distributed forces. VII.6. Stability and overturn.
Chapter VIII: GRAPHICAL TECHNIQUES TO SOLVE COPLANAR FORCE SYSTEMS. VIII.1. Analytical solution for coplanar force systems. VIII.2. Polygon of forces. VIII.3. Funicular polygon. VIII.4. Graphics conditions of equilibrium. VIII.5. Properties of the funicular polygon. VIII.6. Applications of graphical techniques.
Chapter IX: MECHANICAL PROPERTIES OF SOLIDS. IX.1. Elastic behaviour of solids. IX.2. Method of sections. IX.3. Normal stress and shear stress. IX.4. Axial deformation: Young’s modulus.
Chapter X: INTERNAL FORCES IN STRUCTURAL MEMBERS: PLANE TRUSSES. X.1. Plane trusses. Introduction. X.2. Assumptions made in truss analysis. X.3. Isostatic and hyperstatic systems. X.4. Method of joints. X.5. Method of Maxwell-Cremona. X.6. Method of Ritter or method of sections.
Chapter XI: INTERNAL FORCES IN STRUCTURAL MEMBERS: ISOSTATIC PLANE BEAMS. XI.1. Isostatic beams. Introduction. XI.2. Reactions at supports. XI.3. Types of loads on beams. XI.4. Internal forces in beams. Sign convention. XI.5. Loads, shear and axial forces. XI.6. Bending moments. XI.7. Graphical analysis of a beam. XI.8. Elastic curve of a beam.
PROGRAMME OF PRACTICALS
Practice 1: Introduction to the experimental measurements and its uncertainties.
Practice 2: Error analysis. Application to direct and indirect measurements.
Practice 3: Experimental measurements and its uncertainties: method of least squares. Application to the determination of the elastic constant of a spring by the static method.
Practice 4: Determination of the elastic constant of a spring by the dynamic method.
Practice 5: Determination of the centre of gravity of a homogeneous solid.
Practice 6: Moments of inertia. Steiner’s theorem.
Practice 7: Deflection of a beam with a single load.
Practice 8: Simple pendulum. Determination of the acceleration due to gravity.