Civil and Environmental Engineering

The course aims at providing the necessary background for the interpretation of chemical phenomena, for the understanding of the structure and properties of molecules and crystalline solids, and the comprehension and handling of energetic phenomena concerning chemical and electrochemical systems.

The course aims to provide the basic knowledge necessary for the interpretation of chemical phenomena, for the understanding of the structure and properties of crystalline solids and for the understanding and calculation of energy phenomena related to chemical and electrochemical systems.

ATOM Constitution of the nucleus, structure of the hydrogen atom and atomic models (Bohr and quantum-mechanical) Quantum numbers, exclusion principle and Hundt rule Spatial form of s,p and d orbitals CLASSIFICATION OF THE ELEMENTS AND PERIODIC TABLE Electronic configuration of the elements and periodicity in the chemical and physical properties Atomic radius, ionization energy and electron affinity Subdivision into metals, non-metals and semimetals. Basics on the main groups of the periodic table and some transition metals. THE CHEMICAL BOND Bond: ionic, covalent, metallic. Intermolecular interactions. Covalent bond: single, double and triple. Molecular geometry, hybridisation and resonance. Notes on the theory of molecular orbitals. NOMENCLATURE, FORMULAS AND STOICHIOMETRY Atomic and molecular mass, the mole, Avogadro's constant. Acid-base reactions and formation of salts. Oxidation state and balancing of redox reactions. Mass relationships in a chemical reaction, limiting reagent. Combustion reactions GASEOUS STATE Ideal gas laws. State equation of ideal gases. Equilibrium distribution of kinetic energies in an ideal gas (Boltzmann). Liquefaction of a gas. LIQUID STATE Vapour pressure of pure liquids. Solutions: ways to express concentration. Dissociation and ionization degree. Colligate properties of solutions, both electrolytic and non. Definition of acid and base according to Arrhenius, Brønsted and Lewis. Ostwald dilution law. Ionic product of water, pH and pOH. SOLID STATE Unit cell and structure of simplestcrystalline solids. Crystal lattices. Classification of solids. CHEMICAL KINETICS AND CATALYSIS Reaction rate and order. Arrhenius equation. Activation energy. Catalysis and catalysts. CHEMICAL EQUILIBRIUM Mass action law. Equilibrium constant. Homogeneous and heterogeneous chemical equilibria. Le Chatelier principle and influence of the temperature on the equilibrium. CHEMICAL THERMODYNAMICS First, second and third Principle. Reaction enthalpy and Hess law. Change in entropy and free energy of a reaction. Spontaneity criterion. ELECTROCHEMISTRY Normal and effective potential of an electrode. Electrochemical cells and Nernst equation. Electrochemical force of a cell. Reactivity of metals with ocids, oxidizing or not. Electrolysis and Faraday laws. ORGANIC CHEMISTRY Nomenclature and properties of the main organic compounds. Most common functional groups and their main reactions. Isomerism: structural, geometric, conformational.

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

PRINCIPLES OF GENERAL CHEMISTRY (International Edition). Author: Martin Silberberg. Publisher: MgGraw-Hill

Lo studente deve acquisire due tipologie fondamentali di conoscenze: (i) la capacità di risolvere problemi concreti mediante programmi da implementare in un linguaggio di programmazione ed eseguire su un calcolatore; (ii) la capacità di comprendere aspetti quantitativi dell’informatica quali prestazioni, capacità di calcolo, rappresentazione dell’informazione, e l’organizzazione degli elaboratori. Queste capacità vengono applicate alla soluzione di problemi di rilevanza pratica.

L’insegnamento, obbligatorio per tutti gli studenti, si propone un duplice obiettivo: da un lato, introdurre gli studenti alle problematiche legate all’informatica sia dal punto di vista “culturale� che da quello tecnologico. Dall’altro, insegnare l’uso di un linguaggio di programmazione per un elaboratore, quale strumento per la soluzione di problemi reali.

o Teoria [9 ore] + Rappresentazione dell’informazione + Architetture dei sistemi di elaborazione + Architettura software o Problem solving e algoritmi [12 ore] + diagrammi di flusso (flow chart), pseudo-codice per la risoluzione di problemi concreti complessi o Linguaggio Python (40 ore) + Tipi di dato primitivi + Variabili e costanti numeriche + Stringhe e metodi per stringhe + Input e Output di dati numerici e di stringhe + Operatori aritmetici elementari, potenze, funzioni matematiche + Variabili booleane e operatori + Costrutti di controllo di flusso (condizionali e iterativi) + Funzioni e passaggio di parametri + Liste, Insiemi, Dizionari + Strutture complesse (dizionari di insiemi e dizionari di liste) + Lettura e scrittura di file di testo + Gestione delle eccezioni

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

• Dispense del corso a cura del docente - Concetti di informatica e fondamenti di Python (Seconda edizione), Cay Horstmann Rance D. Necaise, APOGEO, ISBN 9788891635433, http://www.apogeoeducation.com/concetti-di-informatica-e-fondamenti-di-python.html

Conoscenza della lingua inglese, attraverso l’acquisizione della certificazione IELTS 5.0, che sviluppa le quattro abilità Writing – Listening – Speaking - Reading.

Il Politecnico ha inserito la lingua inglese tra gli insegnamenti obbligatori dei corsi di laurea e richiede il superamento dell’esame IELTS con punteggio 5.0 o certificazione sostitutiva (https://didattica.polito.it/cla/it/certificazioni). A tal scopo il Centro Linguistico d’Ateneo offre una serie di percorsi didattici differenziati sulla base del livello di conoscenza iniziale sia in aula con i CEL sia in autoapprendimento.

Il risultato del test di livello attribuisce un percorso didattico: Beginner: Si consiglia di parlare con un esperto linguistico Elementary: Si consiglia di parlare con un esperto linguistico Pre-Intermediate: Lezioni in aula orientate al livello IELTS 5.0 Objective 5 (o video lezioni) Writing Tutorials Speaking Tutorials Reading Tutorials Listening Tutorials Grammar Tutorials Vocabulary Tutorials Speaking Fluency for IELTS 5.0 Intermediate: Corso IELTS Intensive – videolezioni Writing Tutorials Speaking Tutorials Reading Tutorials Listening Tutorials Grammar Tutorials Vocabulary Tutorials Speaking Fluency for IELTS 5.0 Le attività didattiche sono proposte ciclicamente in corso d’anno. I link di iscrizione sono presenti sul tab Lingue della pagina personale del Portale della Didattica quando il corso/attività è disponibile. Le videolezioni sono accessibili dalla sezione Materiale Propedeutico della pagina personale del Portale della Didattica.

Modalita di esame: Prova scritta (in aula); Prova orale obbligatoria;
Exam: Written test; Compulsory oral exam;
... Il Politecnico organizza una sessione IELTS al mese (escluso agosto). Per tutte le informazioni sulle sessioni IELTS per gli studenti del Politecnico: https://didattica.polito.it/cla/it/ielts

Beginner: Si consiglia di parlare con un esperto linguistico Elementary: Si consiglia di parlare con un esperto linguistico Pre-Intermediate: Complete IELTS Bands 4 – 5 (Student’s book with answers & CD ROM) Cambridge University Press ISBN 978 0 521 179560 Intermediate: IELTS Trainer Six Practice Tests with answers Cambridge University Press

Students will be able to know the main mineral-petrographic characteristics of the most common rocks, the morphologies and the morphological evolution of the land, the tectonic structures, to have general knowledge on geodynamics, to draw simple geological sections and to interpret a geological map.

The course provides basic knowledge of geology and geomorphology necessary for the various typical activities of civil and environmental engineering. The course is aimed at students with a basic background and is aimed at providing knowledge regarding the nature and formation of rocks, geomorphological and geodynamic processes, notions of tectonics and stratimetry. This knowledge represents a necessary background for the subsequent courses in Geotechnics, Hydraulics and Materials Science

First part: The geochemical composition of the crust and the subdivision of the Earth on a geophysical basis (Preliminary Reference Earth Model). The general classification of minerals. Igneous (intrusive and effusive), sedimentary and metamorphic rocks. The cycle of rocks. Structure, texture and attitude of the rocks. Weathering of the rocks. (1.5 credits). Second part: Glacial landforms and desert environments. Scree, alluvial plains and alluvial fans, meanders, deltas and coastal areas (1.5 credits). Third part: Principles of tectonics (folds, faults), geodynamics (volcanism, seismicity, plate tectonics). Elements of Stratimetry (1 credit) Exercises (2 credits): Macroscopic recognition of rock samples; Drawing of hydrographic basins; Realization of geological sections

Modalita di esame: Prova scritta (in aula); Prova orale facoltativa;
Exam: Written test; Optional oral exam;
... The exam is aimed at evaluating knowledge, competences and skills acquired during the course. One question for each part of the course (0 to 9 points for each question) Evaluation of the exercises carried out during the course (from 0 to 3 points) Rules during oral exams: the student will need a paper sheet and a pen the student must show his/her identification document

Books of reference (available at Department library): Parriaux Aurele – GEOLOGY Basic for Engineers, Second Edition – CRC Press Material available on the web (portale della didattica): lecture slides, limited portions of reference books, collection of exercises.

This course wants to develop the student's ability to understand logical arguments stressing the role of the hypothesis, for example by building examples and counterexamples. The student acquires tools and techniques to work with geometrical objects (vectors in the plane and i the space, lines, planes, conics and quadrics) and with algebraic objects (linear systems of equations, matrices, polynomials, eigenvalues, eigenvectors, vector spaces and their transformations). For example, the student is able to symbolically deal with a linear system of equations and to compute its solutions: these solutions can correspond to the intersection of two lines, to the eigenvectors of a matrix or to the circles passing through two points. The student will also acquire the necessary knowledge to numerically solve, also using a computer, some basic problems in linear algebra when the “pencil and paper� method is not feasible (for example, computing the solutions of a large linear system of equations and computing the eigenvalues of a matrix). In particular, the student learns to identify an algebraic/geometric object, to recognize its theoretical properties and to choose the most fit algebraic/geometrical method to deal with the object. The implementation and the application of the numerical methods is done using the software MATLAB of which the student learns the basic aspects.

The course has two main goals. The first one is to introduce the main topics of linear algebra and geometry, training the student to follow logical deductive arguments and to use the proper formal language. The second goal is to give to the students the main concepts of some basic numerical methods of linear algebra and of their implementation in MATLAB, which is by now widely used in engineering. The course will show how theoretic, symbolic and numerical aspects interact with each other.

• Vector in 2-space and in 3-space and their operations. Dot product, cross product and box product. Lines and planes in 3-space. Orthogonal projections. • Matrices and their operations. Strongly reduced matrices. Matrix form of linear systems of equations and their solutions with geometrical applications. Matrix equations and inverse of a matrix. Determinants. • Vector spaces: definition, examples and applications. Sub-vector spaces and main operations with them. • Linear combination and linearly dependent vectors. How to extract linearly independent vectors from a set. Bases of a vector space. Dimension of a vector space. Dimension of finitely generated subspace. • Space of polynomials. Grassmann's relation. • Linear maps. Image of a linear map. Injective and surjective linear maps. Isomorphisms. • Matrix of a linear map. Endomorphism and square matrices. • Eigenvalues and eigenvectors. Eigenspaces of matrix endomorphisms. Characteristic polynomial of an endomorphism. Diagonalization of and endomorphism. • Orthonormal bases, orthonormal matrices. Gram-Schmidt's algorithm. Diagonalization of real symmetric matrices using orthogonal matrices. Quadratic forms and the sign that they can take in a point. • Metric problems: distance between two points, two lines, and a point and a line. • Quadratic geometry: conic curves, and spheres. Non-degenerate quadrics in canonical form. Recognising a quadric surface. •Machine arithmetic, machine numbers, rounding error. Conditioning of a numerical problems, Stabilty of an algorithm. •Approximation of functions and data : polynomial interpolation and piecewise polynomial interpolation (spline). Main results about convergence. •Linear systems: conditioning and numerical direct method. Matrix factorizations PA=LU, Choleski, QR and their main applications. •Eigenvalues of matrices: conditioning and numerical methods (powers, inverse power, QR (basics notions)). Singular values decomposition of matrices and its main applications.

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

A. Quarteroni, F. Saleri, P. Gervasio, Scientific Computing with MATLAB and OCTAVE, Springer, 2014. G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 2016. E. Carlini, LAG: the written exam, v1 and v2 CLUT 2019. E. Carlini, 50 multiple choices in Geometry, CELID 2011.

Ability to follow a chain of logical arguments. Knowledge of the fundamentals of differential and integral calculus for functions of one variable. Gaining an adequate ability in computation.

This course represents a bridge between high school and university. The main goal of the course is to provide the students with tools to follow the concatenation of simple logical arguments, and to introduce the fundamentals of differential and integral calculus for functions of one variable, with applications to ordinary differential equations of the first and the second order.

Preliminaries: sets, operations with sets and logical symbols. Numerical sets, maxima, minima and extrema. The completeness property of real numbers and its consequences. Functions: surjectivity and injectivity; composition of functions, inverse functions. Functions of one real variable: elementary functions, monotone functions and inverse functions. (About 15 hours) Limits and continuity: limits of functions and sequences; continuity. Theorems on limits: uniqueness of the limit, sign-preserving property and local boundedness, comparison theorems. Limits of monotone functions. Algebra of limits. Indeterminate forms. Local comparison of functions. Landau symbols. Infinite and infinitesimal functions. Order of an infinity and of an infinitesimal, principal part with respect to a test function. Asymptotes. The number e. Fundamental trigonometric and exponential limits. Functions continuous over an interval: existence of zeros and of maxima and minima. (About 24 hours) Derivatives: geometrical and physical meaning. Computation of derivatives. Derivatives of elementary functions. Derivatives and continuity. Non-differentiability points, extremal and critical points. Fermat Theorem. Functions differentiable over an interval and fundamental theorems of differential calculus (Rolle and Lagrange) and their consequences. De L'Hôpital rule. Taylor formula and fundamental Maclaurin expansions. Use of Taylor expansions in the local analysis of functions: comparison, extrema and convexity. Applications to the study of the graph of a function. (About 23 hours) Primitives and their computation; primitives of rational functions. Indefinite integral. The definite integral of a piecewise continuous function. Properties of the integral. Integral mean, the mean value theorem and the Fundamental Theorem of Calculus. Relations between definite integrals and primitives. Improper integrals: definitions and convergence tests. (About 21 hours) Complex numbers and differential equations: algebraic and trigonometric form of a complex number. Real and imaginary part, modulus and argument. Roots of complex numbers; the Fundamental Theorem of Algebra. The exponential of a complex number and the Euler formula. Ordinary differential equations: the Cauchy problem. First order ordinary differential equations, linear or with separable variables. Second order linear differential equations with constant coefficients. (About 17 hours)

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

C. Canuto, A. Tabacco. Mathematical Analysis I. Springer-Verlag UTX, 2015. Additional material will be provided by the teacher and will be available in the Internet personal page of the student.

• Knowledge and understanding (acquisition of theoretical and experimental skills in mechanics, fundamentals of electrostatics and thermodynamics and critical understanding of their laws; start understanding the scientific method, the nature and modalities of research in Physics). - Practical application of the acquired knowledge (ability to identify the essential elements of a phenomenon, in terms of magnitude order and required level of approximation; ability to apply laws and theorems to practical situations through problem solving).

The main objective of the Physics I course is to provide the students with a solid scientific base, aimed to mature understanding and quantitative description of the fundamental laws of nature, concerning mechanics, electrostatics and thermodynamics.

INTRODUCTION The experimental method and the physical quantities. The measurement process. Dimensions of physical observables and units of measurement. Uncertainty (statistical and systematic errors) and uncertainty propagation. Particle KINEMATICS. Review of vector calculus. Reference frames. Position, displacement, velocity, and acceleration in 1, 2 and 3 dimensions. Uniform motion. Motion with constant and variable acceleration. Polar and cylindrical coordinates. Tangent and normal components of acceleration, radius of curvature. Circular motion. Velocity and acceleration composition laws. Particle DYNAMICS Mass and force. Inertial reference frames. Newton’s Laws. Gravitational force. Coulomb’s force. Elastic force. Constraints. Static and kinetic friction. Viscous resistance. Non inertial reference frames: fictitious forces. Work and kinetic energy: definition of work, work-energy theorem. Potential Energy and energy conservation: conservative force fields and potential energy. Mechanical-energy conservation. Examples and applications. Harmonic oscillator: harmonic motion, damped and driven harmonic motion. Resonance. Linear momentum and angular momentum: impulse-momentum theorem. Moment of a force (torque) and angular momentum. Angular momentum theorem. Newton’s Law of Gravitation and Coulomb’s Law. Kepler’s laws. Law of universal gravitation, inertial and gravitational mass. Coulomb’s law and charge. Superposition principle of forces. Gravitational and electrostatic fields. Field lines and flux. Gravitational and electrostatic potential: Gauss’ theorem, charge distributions with spherical symmetry and other examples. DYNAMICS and STATICS of many-particle systems and COLLISIONS. Continuous and discrete systems. Internal and external forces. Equation of motion of the center of mass. Total momentum of many-particle systems. Center of mass and linear momentum conservation. Angular momentum of many-body systems: Angular momentum theorem and conservation. Angular momentum and kinetic energy in the center-of-mass frame. Collisions: momentum and kinetic energy in collision processes. Elastic and inelastic collisions. DYNAMICS of a rigid body. Definition of rigid body. Translation and rotation about a fixed axis of a rigid body. Moment of inertia. Parallel-axis theorem. Rigid-body kinetic energy. Pure rolling motion. Rolling motion with slipping. Conservation laws in the rigid-body motion. Mechanical equilibrium of a rigid body. Examples and applications. MECHANICS OF FLUIDS. Pressure. Statics of fluids: hydrostatic pressure (Stevin’s law). Pascal’s law and Archimedes principle. Dynamics of ideal fluids: flux lines and flux tube. Equation of continuity. Bernoulli’s theorem. Examples and applications. Viscosity. THERMODYNAMICS: calorimetry, First Law of Thermodynamics and ideal gases. Basic concepts in thermometry and heat transfer. Thermodynamic equilibrium and variables of state. Reversible and irreversible thermodynamic transformations. Adiabatic, isothermal, isobaric and isochoric transformations. First Law of Thermodynamics, internal energy. Calorimetry. Ideal (or perfect) gases. Kinetic theory of gases, work and internal energy. Applications of the first law to ideal gases. THERMODYNAMICS: Second Law of Thermodynamics and Entropy. Second Law of Thermodynamics: Kelvin and Clausius statements. Heat engines and refrigerators. Thermal efficiency. Carnot’s cycle and other cycles. Carnot’s theorem. Thermodynamic temperature. Clausius’ theorem. Entropy.

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

• DC Giancoli, "Physics for scientists & engineers, 4th ed., Prentice Hall, 2009 - R Resnick, D Halliday, KS Krane, "Physics", vol. 1, 5th ed., John Wiley & Sons 2002 - SJ Ling, J Sanny, W Moebs, "University Physics", vols. 1-2, Rice University 2018

The students will be able to apply the acquired knowledge to understand and evaluate the criticalities deriving from the interaction between anthropic activities and environmental matrices and to select the proper treatment technologies in order to avoid any environmental damages. He/she will be able to perform preliminary dimensioning concerning waste, wastewater and gaseous emissions plants.

The aim of the course is to build the basic knowledge concerning organic and inorganic pollutants and the related possible interaction with the environment due to physical and chemical properties. The main sources of pollutants will be examined too. Applied treatments concerning waste, waters and gaseous emissions will be presented with the objective to increase the environmental sustainability of activities and processes involving environmental and civil engineers.

Introduction: Organic and inorganic pollutants and related properties. Interaction with soil, water and air. Main pollutants sources (1,5 cfu); Measure units, reaction kinetics, mass balances, concentration balances, energy balances, ideal reactors (1,5 cfu); Water and wastewater treatment (2 cfu) • primary treatments: equalization, separation of coarse solids, sedimentation, flotation; • biological treatments: aerobic fermentation, anaerobic fermentation, suspended and adhered biomass systems; • tertiary treatments: nitrification, denitrification, dephosphating, adsorption, disinfection, filtration, chemical and membrane treatment. Gaseous effluents (0.5 cfu): • particulate removal: cyclones, mechanical filters, electrofilters, washing towers; - gas removal: absorption, adsorption, oxidation, biofiltration; - chemical treatments: catalytic conversion, combustion. Solid effluents and waste (1,5 cfu): • material recovery: material recycling, conditioning, leaching; • energy recovery: incineration; inertization; • biological processes: composting, anaerobic fermentation. Polluted soil (1 cfu): • Characterization and risk analysis • Remediation technologies Applied cases and preliminary dimensioning (2 cfu)

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

Material available on the web (portale della didattica): lecture slides, limited portions of reference books; scientific papers as further readings.

Knowledge about (i) fluids at rest, (ii) modelling of ideal and Newtonian fluids, (iii) pressurized and free-surface streams and (iv) motion in porous media. Students will be able to evaluate the static and dynamic actions of fluids on walls, design and verify streams in pipes and free-surface channels and tackle simple problems of flows in porous media.

The course provides the basic knowledge of fluid mechanics, concerning the static and dynamic behavior of ideal and real-Newtonian fluids. Particular attention is paid to practical applications and engineering aspects with particular reference to Civil and environmental Engineering.

Fluids and their characteristics. Definition of fluid; fluid as a continuous; typical variables of fluid mechanics; motion regimes; deformations, deformation celerity and stresses in a fluid; state equation. Fluid statics. Local and global force balances; Stevin law; pressure measurements; resultant on flat surfaces and curved surfaces; buoyancy; stability of floats. Kinematics. Eulerian and Lagrangian approaches. Eulerian acceleration, flow field; currents; continuity equations in local and global form. Dynamics of ideal fluids. Euler equation; global equation; Bernoulli's theorem and its applications and extensions. Power of a stream. Dynamics of Newtonian fluids. Navier-Stokes equations; global equation for Newtonian fluids; Reynolds number. Laminar flow. Definition; global equation; analytical solutions. Turbulence. Reynolds experience: general characteristics; temporal and ensemble average; Reynolds-averaged equations; Reynolds stresses; dimensional analysis; velocity profile. Pressurized currents. Empirical approach; Moody's diagram; dissipations; empirical formulas; piezometric and total load behaviors. Pipeline network. Definitions; design problems; emblematic cases, networks; Tank design; flow measurements. Open channel flows. Basic concepts; de Saint Venant equations; uniform motion; critical motion; Froude number; critical slope. Permanent motion; depth profiles; hydraulic jump; typical cases; flow measurements. Potential flows. Definition; potential and stream functions; Chauchy-Riemann relations; differential modelling; complex formalism; examples (motion in corners, well-source, vortex, flow around a body and a cylinder). Filtration. General characteristics and approaches; Darcy equation; hydraulic conductivity tensor; analytical solutions.

Modalita di esame: Prova scritta (in aula);
Exam: Written test;
... The exam is WRITTEN ONLY and includes numerical problems as well as theoretical questions (this includes derivations) that the students have to address in 2 HOURS. The students are allowed to bring only a pen and a calculator (lengthy empirical formulae will be always provided in the exam script). The exam is passed provided that a minimum score of 18/30 is achieved.

The slides of the curse will be made available on the Polito Teaching Portal https://didattica.polito.it Suggested reading: Fluid Mechanics: Fundamentals and Applications. Second Edition in SI Units. Y.A. Çengel and J. M. Cimbala, McGraw-Hill, New York, 2010.

Expected acquired knowledge: - Definition, properties, and convergence criteria for numerical series. - Definition, properties, and convergence criteria for sequences and series of functions, power series, and Fourier series. - Definition and main properties of Laplace transform. - Properties and analysis of functions of several variables. - Definition and properties of double, triple, line, and surface integrals. - Conservative vector field; Green, Gauss, and Stokes theorems. Expected acquired ablities: - to classify the asymptotic behaviour (e.g., converge or the lack thereof) of numerical series, sequences of functions, and series of functions using the criteria introduced in class; - to infer the set and type of convergence of sequences and series of functions; - to compute the power series approximation of a function and the Fourier series approximation of a periodic function; - to compute the Laplace transform of simple functions and compare their properties; - to analyze a function of several variables; find and classify its critical points; - to compute double, triple, line, and surface integrals; - to reproduce, discuss, and explain theoretical results presented in class and apply them to solve simple problems.

This course first completes the theory of functions of one variable which was developed in the Mathematical Analysis course, by introducing the student to basic concepts of numerical series, power series, Fourier series, and Laplace transform. The course then introduces basic topics in the mathematical analysis of functions of several variables including differential calculus in several variables, the theory of multiple integration, line, and surface integration.

• Laplace transform. - Numerical series: definition and convergence criteria. Power series and Taylor series. Fourier series. - Review on vectors and elementary notions of topology of R^n. Functions of several variables, vector fields. Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient, and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, unconstrained maxima and minima. - Double and triple integrals, center of mass. Length of a curve and area of the region under the graph of a function. Line and surface integrals (for graphs of functions only). Circulation and flux of a vector field. - Conservative vector fields. Green, Gauss, and Stokes theorems.

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

The following textbook covers the topics of the course and will be used as a reference: - C. Canuto, A. Tabacco, "Mathematical Analysis II", Springer` Other material will be suggested in class and made avalaible thorugh the Portale della Didattica.

• Knowledge of electrostatics in dielectrics media and of magnetostatics. - Knowledge of basic principles of time-dependent electric and magnetic fields. - Knowledge of Maxwell's equations. - Knowledge of wave optics as a consequence of Maxwell's equations. - Knowledge of wave optics laws and of properties of electromagnetic waves. - Ability to apply the acquired knowledge to solve elementary problems.

Aim of the course (1st semester, 2nd year) is to provide the students with the theoretical concepts concerning basic physics subjects such as (i) electrical properties of materials (ii) electromagnetism nd Maxwell's equation and (iii) waves and wave optics.

ELECTROSTATICS (1 CFU) Static electric field in matter: conductors. Capacitance and capacitors. Energy density of the electric field. Dielectric materials: electrical polarization. Electric current. Conduction. Current intensity and current density. Direct current (DC). Resistance. Ohm’s law. Resistivity and conductivity. Electric power. Joule effect. MAGNETOSTATICS (1,5 CFU) Magnetic field and magnetic induction. Second Maxwell’s equation. Force on a charge moving in a magnetic field: Lorentz’s force. Magnetic force on a current-carrying conductor. Sources of magnetic field. Field of a straight current-carrying conductor: Laplace’s law, and its applications. Magnetic field of a circular current loop. Magnetic dipole. Torque on, and potential energy of, a magnetic dipole in a magnetic field. Forces between parallel currents. Ampère’s law and its applications. Magnetic fields in matter: diamagnetism, paramagnetism and ferromagnetism. TIME-DEPENDENT ELECTRIC AND MAGNETIC FIELDS (2 CFU) Faraday – Henry – Lenz law of electromagnetic induction and its applications. Third Maxwell’s equation. Inductance and self-inductance. Energy in an R-L circuit. Energy density of the magnetic field. Ampère-Maxwell law: fourth Maxwell’s equation. ELECTROMAGNETIC WAVES (1.5 CFU) Wave equation for electric and magnetic field. General characteristics of a wave. Electromagnetic waves. Propagation and attenuation of the electromagnetic waves in conductors and dielectrics. Wave optics. Interference, electromagnetic waves interference and its applications. Diffraction: the basic principles. Fraunhofer’s theory of a double slit interference and of a single slit diffraction. Polarization of light: the basic principles.

E' possibile sostenere l?esame in anticipo rispetto all?acquisizione della frequenza

• "Physics for Scientists and Engineers with Modern Physics" FISHBANE, GASIOROWICZ, THORNTON, Ed. Pearson, Prentice Hall Learning material distributed by teacher.

The main aim is to supply the student with a robust background on materials, able to couple scientific and technological knowledge in a synergic way, providing general guidelines for translating scientific knowledge into technological tools for engineering design. The student should then: - know the chemical and atomic nature of the materials and the strong dependence of the macroscopic features and properties from it; - know how to exploit this scientific background in controlling the material properties up to the tailoring of material features for a specific application; - be conscious of the role of material selection in matching design requirements; - know a deep English vocabulary on Materials Science and Technology.

The course aims at providing the basic knowledge for a proper selection and use of materials for Civil Engineering. Starting from an essential introduction to the structure and properties of various classes of materials, tools for a rational selection of materials in terms of mechanical, physical and durability performance are provided. The relationships among materials structure, microstructure and performances and, as a consequence, the potentialities of engineering design able to exploit traditional and innovative materials through the tailoring of their microstructure are described and discussed. Indeed, it is intended that students also gain an understanding of the complexity of materials, the origin of their properties, to know which material properties are intrinsic and which can be manipulated through manufacturing, processing and post-treatments. Several case studies (e.g. famous buildings and infrastructures) will be exploited, considering their relevance in the structural field, to achieve a deep knowledge and analyse the performance of materials in various engineering contexts.

The program of the course can be summarised as follows: Part 1: Introduction to Material Science and Technology. Chemical bond and its influence on the properties of materials. Structure of crystalline and amorphous materials. Crystal defects. Relationship between material structure and elastic behaviour. Relationship between material structure and plastic behaviour. Relationships between material structure and other properties (chemical, physical). Modification of the material properties: microstructural constituents (solid solutions, intermediate phases,...), phase diagrams and transformations (melting/solidification, precipitation hardening), basic knowledge on thermal treatments, microstructural evolution and effect on properties. Part 2: General discussion of the principal classes of the engineering materials (metals, ceramics, polymers), with specific examples on the most interesting materials. Building materials (aerial and hydraulic binders, such as gypsum, lime, hydrated lime, Portland and blended cements) will be analysed. Particular attention will be paid to concrete. Stones, traditional ceramics, glasses, metallic materials (mainly steel, but also cast iron and some other metal alloys – such as aluminium, copper and titanium alloys will be discussed), wood, polymeric and composite materials. For each class of materials, the processing (production and shaping), the properties, the durability, the environmental impact, the possible technological solutions to maximize the materials performance and durability will be explained.

Modalita di esame: Prova scritta (in aula);
Exam: Written test;
... Learning will be assessed by a written exam of 1h and 30 min that comprises questions with open and closed answers covering all the topics explained during the course. Theoretical as well as simple analytical problems and exercises will be proposed. The evaluation aims to verify the level of learning and the degree of assimilation of the subjects presented and is based on the level of knowledge acquired, on the correctness of expression and terminology, and on the ability to connect the concepts. Particular attention will be given to the evaluations of the knowledge of the physical-microstructure characteristics of the most used materials and their durability but also the knowledge of the mechanical properties of the most used building materials. An example of a typical exam will be reviewed at the end of the course.

The following textbooks are recommended: W.D. Callister, Jr. D. G. Rethwisch, Materials science and engineering. An introduction, John Wiley & Sons Inc (10th Edition, 2018); M. Soutsos, P.L.J. Domone, Construction Materials: Their Nature and Behaviour, CRC Press, Taylor & Francis Group (Fifth Edition, 2018); G.D. Taylor, Materials in construction: an introduction, Pearson Education (3rd Edition, 2000). Other reading materials will be provided by the professor during the course.

The student will be able to determine the constraint reactions and the diagrams of internal actions (normal stress, shear stress and bending moment), and to plot the deflection curve for any plane system of isostatic beams; to calculate the stresses in the beams on the basis of De Saint Venant theory; to apply the strength criteria for generic stress states; to investigate a slender bar subjected to a buckling load.

The teaching aims to provide the basic knowledge needed to compute a structure and to assess its safety, by defining the parameters that describe the applied loadings and the strength of materials. The calculation methods used to assess the stress state in simple structural elements are presented, with focus on examples of civil/environmental interest (structures, infrastructures, plants) and failure under monotonic loading.

STATICALLY DETERMINATE BEAM SYSTEMS: statics and kinematics, plane constraints, hypostatic systems, determination of constraint reactions with auxiliary equations and with the graphical method; internal beam reactions; indefinite equations of equilibrium for plane beams; trusses. ANALYSIS OF STRAIN AND STRESS: strain tensor; dilations and shearing strains; principal directions of strain; cubic dilation. Measures by extensometers. Stress tensor; principal directions of stress; plane stress condition; Mohr’s circle. Indefinite equations of equilibrium; boundary equations of equivalence; principle of virtual work for deformable bodies. ELASTIC CONSTITUTIVE LAW AND STRENGTH CRITERIA: experimental techniques to characterize the mechanical behavior of materials. Traction test. Linear elasticity; elastic potential; Young modulus and Poisson’s coefficient; problem of a linear elastic body: Clapeyron’s theorem; Betti’s reciprocal theorem; isotropy; Tresca’s and Von Mises’ strength criteria. GEOMETRY OF AREAS: centroid, static moment, moment of inertia, product of inertia, principal axes and moments of inertia. SAINT-VENANT PROBLEM: fundamental hypotheses; centered axial force; flexure; eccentric axial force and biaxial flexure; central cores of inertia; torsion; shearing force; beam strength analysis. CALCULUS OF ELASTIC DISPLACEMENTS AND SIMPLE STATICALLY UNDETERMINATE BEAM SYSTEMS: equation of the elastica; determination of elastic displacements; method of forces; equations of congruence written with the principle of virtual works; Simpson’s integration rule. ELASTIC INSTABILITY: compressed beams with different constrain conditions.

Modalita di esame: Prova scritta (in aula); Elaborato scritto individuale; Prova scritta in aula tramite PC con l'utilizzo della piattaforma di ateneo;
Exam: Written test; Individual essay; Computer-based written test in class using POLITO platform;
... Written exam on paper lasting 2 hours and classroom supervision (for students in presence) Oral exam in person.

Notes, exercises, formularies will be downloadable from the website of the course. Optional textbooks: A. Carpinteri (2013) Structural mechanics Fundamentals, CRC Press.

At the end of the course, the student is expected to be able: - to correctly describe the kinematics of a mechanical system, to identify the degrees of freedom and to choose the most suitable generalized coordinates, - to introduce formally the forces acting on a mechanical system, - to compute the mechanical quantities of a system, - to formulate the proper mathematical equations underlying the mechanical problem, choosing the most appropriate solution method. The overall target is to possess a solid knowledge of the theoretical mechanics of systems with a finite number of degrees of freedom.

Aim of this course is to teach the students the fundamental laws of Classical Mechanics: the equations of motion of a mechanical system with a finite number of degrees of freedom, with an emphasis on statics. The teaching addresses kinematics, statics, and dynamics of a rigid body and of systems of rigid bodies. Equations of balance of momentum and moment of momentum are derived for a rigid body from a system of constrained particles. Emphasis is given to the notions of equilibrium and stability thanks to the principle of virtual work. A large number of exercises and examples favours a deeper understanding of the subject.

1. Elements of linear algebra. vector calculus in R^3, tensor algebra, second order tensors. 2. Kinematics. Kinematics of a point particle and of a system of point particles. Holonomic and non-holonomic constraints, generalized coordinates and degrees of freedom. The constraint of rigidity. Generalized coordinates of a rigid body. Rigid velocity distribution. Poisson’s formulas. Analysis of some rigid motions. Characterization of rigid velocity distributions. Infinitesimal rigid displacements and virtual displacements. Plane rigid motions. 3. Statics. Statics of a point mass and of a system of point particles, reaction forces, friction. Equivalent systems of forces and their reduction. Center of mass. Balance equations of statics. Statics of articulated systems. Internal stresses. Principle of virtual work, equilibrium of holonomic systems, conservative forces. Equilibrium and stability using the potential energy. 4. Dynamics. Fundamental law of dynamics. Dynamics of a point mass. Mechanical quantities of mechanical systems: mass, center of mass, moment of inertia, linear and angular momentum, kinetic energy, work, power. Balance equations of dynamics. Dynamics of a rigid body. Lagrangian mechanics. Dynamics of holonomic systems; Lagrange’s equations, first integrals.

Modalita di esame: Prova scritta (in aula);
Exam: Written test;
... The final exam consists of a written test and an oral exam. In the written test, the student will be asked to solve problems related to the statics and dynamics of systems of rigid bodies, together with a question on theoretical aspects. The written test is followed by a mandatory oral discussion, where the understanding of the theory will be assessed. Only students who pass the written test will be admitted to the oral discussion.

A. Romano, Classical mechanics with Mathematica, Springer

To pass the exam, the student must demonstrate: Knowledge and understanding • Have memorized the essential concepts of the methodological approach of integrated digital modelling for the comparison of different technological solutions. • To be able to compare contents, tools and methods for the BIM-based design process. Competencies and skills • Master the interoperable management of project data. • Being able to work in a team to achieve a common goal. Judgment and Approach • To be able to use the critical thinking to develop a project from general to detail by interpreting information from different disciplines. • Demonstrate creativity in setting up a technical sheet to summarize the project developed and the work-flow used.

The aim of the course is to provide students with the essential knowledge of the methodological use of Building Information Modeling (BIM) as a design method based on the exchange of information between tools and between people (interoperability). Students, working in team, will deal of the modelling of a building using an integrated approach paying attention to sustainability, comparing different construction technologies and related costs.

The course program is divided into four macro fields: BIM-based process (6CFU) 1. BIM as process: As Designed, As Built, As Is models and interoperability for new and existing buildings 2. Introduction to BIM at urban and building scale: contents, tools and methods 3. Graphical and information standards: LOD and LOIN 4. Data hierarchy in BIM: Work Breakdown Structure (WBS) and Object Breakdown Structure (OBS) 5. Worksharing 6. Dimensions of BIM focusing on 5D Elements of Building Physics (4CFU) 7. Elements of building energetics 8. Psychrometry 9. Elements of heat transfer in building components 10. Thermal characterisation of envelope components 11. Energy and mass conservation in buildings 12. Elements of HVAC systems 13. Elements of building climatology Integrated sustainable design approach (2CFU) 14. Introduction to Integrated Sustainable Design 15. Comparing different technologies: foundation 16. Comparing different technologies: floor 17. Comparing different technologies: roof 18. Comparing different technologies: internal and external wall Cost Management approach (2CFU) 19. Cost Management 20. Cost Analysis 21. Quantity Take Off

Modalita di esame: Prova orale obbligatoria; Elaborato grafico prodotto in gruppo;
Exam: Compulsory oral exam; Group graphic design project;
... The oral exam, starting from the technical sheet created during the semester, aims to verify the achievement in terms of responsibility and autonomy, according to the following evaluation matrix (Technical sheet: 40% | Oral exam: 60%): Knowledge and understanding Knowledge of the essential concepts of the methodological approach of integrated digital modelling for the comparison of different technological solutions (Oral exam: 30%). Understanding of contents, tools and methods for the BIM-based design process (Technical sheet: 20%). Competencies and skills Competence in the interoperable management of project data (Oral exam: 20%). Skyll to work in a team to achieve a common goal (Technical sheet: 10%). Judgment and Approach Ability to use the critical thinking to develop an interdisciplinary project from general to detail (Oral exam: 10%). Creatively approaching the setting of the technical sheets illustrating the theoretical contents (Technical sheet: 10%).

DEL GIUDICE MATTEO, (a cura di), Il disegno e l’ingegnere. BIM handbook for building and civil engineering students, Levrotto e Bella, Torino, 2019.

The course purposes are: 1. Assuming the porous medium as a mixture of superposed continua, to learn the stress partition between the phase components (effective stress principle); 2. To learn the difference between fine and coarse grained soils, the meaning of drained and undrained conditions and the relative implications; 3. To understand the soil mechanical behaviour through the critical state theory, to relate effective stress and volume changes, to assimilate key concepts as peak strength, dilatancy and critical state. 4. To set the limit analysis problems within the plasticity theory; 5. To understand the influence of geological history on the mechanical behaviour of natural soils.

The course is aimed at providing the basic notions of Soil Mechanics for the assessment of the mechanical behaviour of soils and the soil-structure interaction.

First part: soil description and classification - Origin, index properties and geological history; - Soil phases and their relations; - Soil classification and index properties; - Natural deposits; Second part: the behaviour of the elementary volume - Soil mechanical behaviour; - Effective stress: definition and postulate; - Oedometer test: preconsolidation stress and compressibility. Application to the calculation of one-dimensional settlement; - Stress paths; - Shear strength and stress-strain behavior. Third part: boundary problems: - Porous media seepage; - Seepage under steady state conditions; - Theory of consolidation; - Applications of plasticity theory; - The collapse of soil structures: theorems of plasticity theory, active and passive limiting states of stress. - Coulomb and Rankine theories and practical calculation of earth pressures; - Bearing capacity of shallow footings.

Modalita di esame: Prova scritta (in aula); Prova orale obbligatoria;
Exam: Written test; Compulsory oral exam;
... The final exam consists of a written test and an oral discussion, which cover all the topics presented during the lectures and classroom exercises. The written test is aimed at verifying the ability of the students to apply the theoretical concepts to solve simple problems concerning the analysis of the state of stress and strain, the interpretation of the laboratory and in situ test results, the stability of shallow foundations and retaining structures, and the calculation of the settlement of shallow foundations. The written test consists in solving 4 exercises, within a maximum time of 2 hours. To be admitted to the oral discussion, an overall score of the written test not lower than 15/30 is required (maximum overall score equal to 30/30). During the written test, the use of notes, textbooks and scientific calculators is allowed. The use of smartphones, tablets and laptops is not allowed. The oral discussion lasts about 20 minutes and consists in 3 or 4 questions to each candidate, which can be answered orally or through the execution of short calculations. The oral discussion is aimed at verifying the knowledge of the theoretical principles that govern the mechanical behaviour of soils and the soil-structure interaction. The final mark is determined as an average value of the scores attributed to the written test and the oral discussion.

The slides of the course (presentations, notes and exercises) are made available on the teaching portal. The reference textbooks of the course are reported here below: Lancellotta, R. (2008). Geotechnical engineering. Routledge, London. Atkinson, J. (2007). The mechanics of soils and foundations. Routledge, London. Lambe, T.W., Whitman, R.V. (1969). Soil mechanics. John Wiley & Sons, Hoboken, New Jersey.

Le informazioni dettagliate sull’insegnamento tirocinio sono consultabili sulla GUIDA STUDENTI, sezione TIROCINIO, dell’anno accademico in corso.

Modalita di esame: Accertamento (esame senza voto);
Exam: Check;

Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Roads, Railways and Airports - module The aim of this module is to develop the ability to recognize the technical characteristics of transport infrastructure, as well as the ability to identify the reference theories for evaluating their performance. Topics will be presented to develop strong analytical skills, useful for solving problems with typical professional implications. The module will allow students to acquire the following skills: - ability to analyze transport demand for the purpose of pre-design the infrastructure and its components in functional and structural terms; - ability to evaluate the interaction between moving entities and infrastructures (roads, railways and airports) for geometric design purposes; - ability to assess physical and mechanical characteristics of construction materials. - knowing how to make and motivate design choices, - ability to identify the orders of magnitude of the numerical values that characterize the system variables, -ability to represent in graphic form the design entities; - knowing technical terminology Water Infrastructures - module Roads, Railways and Airports/Water infrastructures (Water infrastructures)This course is devoted to analyzing water infrastructures. Three perspectives will be considered. The first perspective is a qualitative and broad understanding of the technological components that made up different type of water infrastructures. The second perspective is on the modelling tools to analyze the hydraulic behavior of water infrastructures. The third and last perspective is the design of simple water infrastructures. In particular, upon completion of this course, students will be able to: - Describe the components of water infrastructures and explain their hydraulic behavior; - Describe the physical principles and phenomena that affect the behavior of water infrastructures and explain their hydraulic/hydrological significance; - Select the most appropriate model to be used to analyze different types of water infrastructures; - Implement (with commercial software/spreadsheet) a model of water infrastructures, and interpret the obtained results; - Assess the data required to build a model of a water infrastructure; - Design (from an hydraulic point of view) components of a water infrastructure; - Develop a preliminary design of a water infrastructure, considering other factors external to hydraulics and hydrology such as the technical and economic feasibility.

Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Roads, Railways and Airports - module This module aims at providing basic knowledge in the geometrical design and construction of transportation infrastructures such as roads, railways and airports. Particular attention will be given to the safe interaction between moving entities and transportation infrastructures and, more generally, to expected performance levels from the functional and structural point of view. Water Infrastructures - module Roads, Railways and Airports/Water infrastructures (Water infrastructures)One of the main duty of civil engineers is to design and manage water. Water infrastructures are built for this purpose, and this module presents the corresponding design schemes for some widely adopted infrastructures. The focus is therefore on structures devoted to the collection, transport, and distribution of water, and at the management of extreme hydrologic events, as stormwater and floods.

Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Roads, Railways and Airports - module 1. Types of transportation infrastructures and their general technical characteristics; 2. Organization of infrastructure networks, identification of mobility demand, quantification and analysis of the supply in terms of capacity and quality of service; 3. Characteristics of the driver-moving entity-infrastructure-environment system and interaction methods; 4. Fundamentals of geometric design; 6. Physical properties and constitutive models of construction materials. Water Infrastructures - module Roads, Railways and Airports/Water infrastructures (Water infrastructures)- Introduction and classification of water infrastructures (2 hrs) - Estimation of water availability and water demand (3 hrs) - Water intakes and water storage schemes (6 hrs) - Design of open flow channels (7 hrs) - Design of pipelines, water mains, pumping mains (6 hrs) - Water distribution networks (6 hrs) - Fundamentals of hydrology for small catchment analysis (7 hrs) - Infrastructures for stormwater management (7 hrs) - Hydraulic works for flood risk mitigation (6 hrs)

Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Modalita di esame: Prova scritta (in aula); Prova orale obbligatoria; Roads, Railways and Airports/Water infrastructures (Water infrastructures)Modalita di esame: Prova scritta (in aula);
Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Exam: Written test; Compulsory oral exam; Roads, Railways and Airports/Water infrastructures (Water infrastructures)Exam: Written test;
... Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)The written test will be composed of closed-answer tests and exercises to attest the ability of students to apply the concepts objective of the course. The oral exam will be dedicated to verify the knowledge acquired from theoretical lectures. The final grade will derive from the average between the written and the oral part. To pass the exam it is necessary to reach a sufficient grade for both the written and the oral part of the exam.Roads, Railways and Airports/Water infrastructures (Water infrastructures)The exam consists of a written test. In the written test (duration 1.5 hours) student will be asked to (i) solve a practical problem concerning water infrastructures (50% of the mark); (ii) answer a theoretical question (50% of the mark). The practical problem aims at assessing student’s ability to model the behavior of components of water infrastructures; design components of a water infrastructure; and critically assess the data required to build a model of a water infrastructure. The theoretical question aims at assessing student’s ability to describe the components of water infrastructures and explain their hydraulic behavior; and describe the physical principles and phenomena that affect the behavior of water infrastructures and explain their hydraulic/hydrological significance. In order to pass the exam, both the theoretical question and the practical problem must be sufficient (score >18/30) to pass the exam. Final score: The final score will derive from the weighted mean with respect to the number of credits of the two modules (7 CFU for Roads, Railways and Airports and 5 CFU for Water Infrastructures )

Roads, Railways and Airports/Water infrastructures (Roads, Railways and Airports)Slides of the lectures and additional material provided by the teacher.Roads, Railways and Airports/Water infrastructures (Water infrastructures)Slides of the lectures, course notes and additional material provided by the teacher.

The student will acquire the fundamentals for the assessment of the behavior and reliability of reinforced concrete and steel structures. This knowledge will be gained from the analysis of the issues related to the effects of the actions applied to the structures, depending on structural schemes, materials and construction technologies.

The course aims to provide the skills necessary to develop the analysis of the behavior of reinforced concrete and steel structures.

The following topics are taught during the course: • Structural reliability (10 hrs): definition of structural reliability, deterministic and probabilistic reliability methods. • Structural mechanics (10 hrs): deflections of beams, lines of influence of displacements, support reactions and stresses in beams. • Basis of design according to EN1990 (10 hrs): definition of limit state, design values of actions, material properties, geometrical dimensions of structures, combination rules of the actions for ultimate and serviceability limit states. • Actions according to the Italian design code NTC2008 (5 hrs): definition of the characteristic values of the permanent actions, wind and snow loads. • Structural effects of shrinkage and creep (5 h): analysis of shrinkage and creep phenomena in concrete elements, the three principles of linear viscoelasticity, evaluation of the structural effects of shrinkage and creep in steel-concrete composite structures. • Plasticity (5 hrs): the elastic-plastic constitutive law of steel, the concept of plastic hinge, application of the static and kinematic theorems for the calculation of the failure load. • Materials (5 hrs): characterization of the properties of concrete and steel in relation to the structural behaviour. • Analysis of r.c. sections for ultimate and service limit states (20 hrs). • Analysis of steel sections for ultimate and service limit states (10 hrs).

Modalita di esame: Prova orale obbligatoria;
Exam: Compulsory oral exam;
... Oral exam on the topics taught during the course.

• Probability, Reliability and Statistical Methods in Engineering Design / Haldar, Mahadevan - John Wiley & Sons, 2000. • Design for robustness / Knoll, Vogel – Zurich: IABSE-AIPC-IVBH, 2009. • CEB design manual on structural effects of time-dependent behavior of concrete / CEB – Saint-Saphorin: Georgi Publishing Conpany, 1984. • Time effects in concrete structures / Gilbert – Amsterdam: Elsevier, 1988. • Plastic theory of structures / Horne – London: Nelson, 1971. • Handouts of the course, produced by the professor, are available.

The students will be able to understand circular economy strategies and activities, as well as use basic sustainability assessment tools to evaluate the outcomes in terms of resource efficiency. At the end of the course, the student is expected to understand how resources and engineering can contribute (positively or negatively) to sustainable development through a more circular economy. He/she should be able to conduct a Material Flow Analysis and interpret the results using selected Circular Economy indicators.

The objective is to build on basic concepts of circular economy as they apply to natural resources with focus on minerals and energy, and related engineering projects towards the achievement of desired SDGs. The overarching framework for this course is sustainable engineering, i.e., the theory and practice of engineering within a complex, interconnected world that faces many economic, environmental and social challenges. The course provides knowledge, competences and skills necessary to understand and evaluate circular economy strategies and their socio-economic-environmental consequences.

Introduction: Role of natural resources in the economy, in a circular economy and in a net-zero economy (0.5 cfu); Circular Economy, definitions, basic concepts, strategies (0.5 cfu). Circular Economy indicators, what they measure, what should be measured and what can be measured (0.5 cfu). Circular Economy Action Plans of the EU in the context of the EU Green Deal (0.5 cfu). Critical Raw Materials and the Circular Economy, EU policies on CE and on Raw Materials (0.5 cfu). Sustainable Engineering and Sustainability Assessment tools (2 cfu). Material Flow Analysis and basics of Life Cycle Thinking, Life Cycle Assessment and Life Cycle Sustainability Assessment (0,5 cfu). Corporate Sustainability Management, Carbon Footprinting and Sustainability Reporting (0,5 cfu) Product and Organisation Environmental Footprint (PEF and OEF) in the context of Greening the EU single market (0,5 cfu)

Modalita di esame: Prova scritta (in aula); Prova orale facoltativa;
Exam: Written test; Optional oral exam;
... The exam is aimed at evaluating knowledge, competences and skills acquired during the course. The final examination consists of a written test (1,5 hours) made of open (essay) questions and short exercises (oral exam not allowed).

Material available on the web (portale della didattica): lecture slides, limited portions of reference books; scientific papers (tutorial and basic papers) as further readings, collection of exercises; homework assignments.

The expected learning outcomes are designed to provide students with both professional and academic skills. Students will gain competence in environment description, mapping, and representation on the ground, in the subsurface, and underwater. For this purpose, methods and techniques for topographic/land survey and geophysical data acquisition will be taught. The main expected learning outcomes are: - **Survey planning and design** :Capability to select appropriate methods, design optimal sampling plans, and plan data acquisition, processing, and interpretation strategies for various engineering problems related to land survey and environmental analysis. - **Tools and equipment** : Competence with traditional and innovative survey equipment and technologies (Total Station, Leveling, GNSS receivers), and the ability to use them in the field. - **Field acquisition** : Capability to manage and execute the field acquisition of topographical and geophysical data. - **Survey data processing** : Ability to process field topographic and geophysical data using standard or specifically implemented processing tools, incorporating statistical analysis and signal processing techniques. - **Modeling and inversion techniques** : Ability to implement simple modeling tools or run codes for more complex modeling of topographic and geophysical data, and the capability to handle inversion methods. - **Spatial data representation and mapping** : Metrical representation of objects and phenomena using mapping techniques and digital data in technical or thematic cartographic representation.

The use of geospatial data for mapping ground, underground, and underwater properties and systems is of paramount importance in the design, planning, and management of land and the environment. The course provides methodological competencies and practical skills in survey methods based on topographical and geophysical techniques. Students will learn survey design and execution, data processing, interpretation, data visualization, metrical representation, and mapping through a mix of classroom hours, fieldwork, team assignments, and computer lab exercises. The fundamentals of statistics related to experimental errors, geodesy, cartographic representation, and signal processing required for methodological and practical implementations will also be provided.

Common topics: 1) Introduction to terrestrial and geophysical survey methods and applications 2) Statistical data analysis 3) Fundamentals of signal processing 4) Topics of Topographic Land Surveying: - Basics of Geodesy and Reference Systems - Cartographic representation - Topographic survey methods (Levelling, Total station, GNSS positioning) 5) Topics of Geophisical Land Surveying: - Seismic wave propagation - Seismic refraction tomography - Seismic surface wave methods - Seismic borehole methods - Resistivity and electric field interaction with subsurface - Electrical Resistivity Tomography 6) Field acquisition of topographic and geophysical data 7) Lab works on the processing of topographic data 8) Lab works on the processing of geophysical data

Modalita di esame: Prova orale obbligatoria; Elaborato progettuale in gruppo;
Exam: Compulsory oral exam; Group project;
... Exam: (A) Team public oral presentation of the assignments + (B) Team assignment report + (C) Compulsory oral exam (A) Before the exam, students, divided into teams of 4-5 members, will present their solutions to the assigned task/problem to the lecturers and classmates. This presentation will be graded and will constitute 20% of the final score. (B) Prior to the exam, students, also divided into teams of 4-5 members, will submit their assignment report to the lecturers. This report will be graded and will account for 30% of the final score. (C) If the combined score from (A) and (B) is positive (≥18), the student will be admitted to the mandatory oral exam, which will be graded separately and make up 50% of the final score. The oral exam will include three questions covering the entire theoretical program and/or a discussion of the results presented in the team report. With respect to the report, questions will focus on strategies for data processing and interpretation. The oral exam aims to assess the learning outcomes and skills related to data processing and interpretation, including the use of simplified modeling and processing tools. The final grade will be computed as follows: (20% from A) + (30% from B) + (50% from C).

Material available on the web (portale della didattica): lecture slides, limited portions of reference books, collection of papers. We recommend the following textbooks:: • Manzino A. M. Quaderni di Topografia, (2017) Volume 1 Levrotto e Bella, ISBN 978-88-8218-194-9 • Manzino A. M. Quaderni di Topografia, (2019) Volume 2 Levrotto e Bella, ISBN 978-88-8218-202-1 • Manzino, A. M. Esercizi di Topografia svolti in MATLAB® (2013) Ebook Otto Ed. ISBN 9788895285443 • Cina, A. (2002). Trattamento delle misure topografiche. CELID, Torino. ISBN 88-7661-534-2 For further information: • Cina, A. (2014) – Dal GPS al GNSS (Global Navigation Satellite System) per la Geomatica. Torino, CELID • Barzaghi, R. Pagliari, D. Pinto, L. (2022): elementi di Topografia e trattamento delle osservazioni. Milano, Città Studi. • Sansò, F., Betti, B. Albertella A. (2019): Positioning. Posizionamento classico e satellitare. Milano, Città Studi.