### Master’s Degree

*1. Mandatory Disciplines*

**Scientific Methodology** (45 horas, 3 créditos) – Common for all areas

Syllabus: Types of knowledge and research. Scientific methods and quantitative and qualitative research. Conceptual instruments in the field of knowledge production. Problems, procedures and analysis tools; the various types and strategies of investigation and the carrying out of didactic and scientific activities, with a view to technical, scientific, intellectual production and the discussion of ongoing research and the improvement of students' productions.

*2. Common elective Subjects*

**Mathematical Methods** (45 Credit Hours, 3 Credit Units)

Syllabus: Elementary Functions. Flat analytical geometry. Polynomials. Linear equations, eigenvalues, eigenvectors, singular values and matrix factorization. Differential in one variable and Taylor series. Multivariate differential, gradient, Taylor series in multiple variables. Integral in a variable. Multivariate integral in simple domains. Orthogonal representation of vectors. Least squares. Discrete Fourier Series (FFT). Fourier series for functions. Fourier transform. Orthogonal polynomials. Systems in one dimension. Linear, nonlinear, homogeneous and nonhomogeneous differential equations. Linearization and methods of disturbance. Linear equations at constant coefficients. Convolution. Laplace transform. Discretization of differential equations. Solution of difference equations. Transform Z. Filtering. Partial differential equations. Basic partial differential equations (wave, heat, deformations, etc.). Solutions by separating variables. Solutions by Fourier series. Optimization notions. Formulation of problems. Least squares. Elementary problems. Calculation of variations.

**Solid Waste Management** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: origin, production of solid waste; the problem of construction waste; ecological and epidemiological aspects. Characterization of residues: classification, composition, physical-chemical, biological, qualitative and quantitative aspects, NBR 10004/04. Methodologies and techniques of minimization, recycling and reuse of waste. Packaging, collection, transport: packaging; collect; transport; transfer station; design of a collection system; ABNT standards, case studies. Recycling of ceramic materials and building materials: application in the manufacture of concrete and mortars. Engineering Solutions: reduction of material consumption, waste / new technologies, reuse, recycling and life cycle. Project management of construction and demolition waste. Use of waste: technical, environmental, legislative and standardization aspects.

**Theory of Elasticity** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: basic operations with tensioners; tensor tension; tensor of the deformations; relationships between tensors. Two-dimensional problems: Airy voltage function; problems in Cartesian and polar coordinates; twist. Kinematics: problems in the field of small deformations; problems in the field of large deformations. Tensor of Cauchy and Piola-Kirchhoff I and II.

**Methods of Scientific Programming** (45 Credit Hours, 3 Credit Units)

Syllabus: Programming language; practice of scientific programming with development in FORTRAN 90/95; practice of scientific programming with MATLAB Software; object-oriented programming; practice of object-oriented scientific programming with development in the FORTRAN 90/95 and MATLAB languages.

**Finite Element Method** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: conceptualization; definition. Physical and variational interpretation of finite elements. Methods that minimize waste: weak form; strong form. Numerical integration: points of integration; functions weight. Interpolation elements and functions: internal nodes; elements in two dimensions; elements in three dimensions; isoparamétricos elements.

**Systems Identification** (45 Credit Hours, 3 Credit Units)

Syllabus: Overview of systems identification. Basic concepts: mean, variance, correlation, ergodicity, orthogonality. Systems of linear equations. Minimization of functions. Certain linear systems. Least squares. Adjustment of parametric curves of one and multiple variables. Polynomial, trigonometric and rational models. Static systems. Identification of linear dynamic systems. Models AR, ARX, ARMA and ARMAX. Extended MQ Estimators, Instrumental Variables, and Recursive MQ. Identification of non-linear systems. Polynomial NARMAX models. Selection of terms via error reduction rate. Orthogonal estimation of parameters. Special regression topics: PCA and PLS. Case studies and applications.

**Numerical Methods** (45 Credit Hours, 3 Credit Units)

Syllabus: Computing error in digital systems, numerical solution of systems of linear algebraic equations: direct and iterative methods. Calculation of zeros of non-linear algebraic functions. Solution of systems of nonlinear algebraic equations. Differentiation and Numerical Integration. Linear and non-linear regression. Solution of Ordinary Differential Equation Systems: Runge-Kutta Method and Multiple-Step Method. Finite difference method for solving ordinary and partial differential equations. Applications in Engineering problems.

**Advanced Geotechnical Investigation** (45 Credit Hours, 3 Credit Units)

Syllabus: Sampling of geomaterials: collection of deformed and undisturbed samples, superficial and deep. Historical, procedures, standardization, intervening factors, advantages and limitations, critical analysis, interpretation and applications of the SPT, CPT, vane, pressiometer and dilatometer tests. Fundamentals of instrumentation and devices for measuring displacement, deformation, force, tension, pressure, velocity, acceleration and temperature. Inclinometer, tell-tales, LVDT, set-up plate and pin, tassometer, convergence meter, geophone, accelerometer, resistance strain gauge, load cell, piezometer, total pressure cell, thermocouple, RTD thermistor) and TDR. Acoustic emission, laser, optical and radar interferometry, satellite image. Remote monitoring. Instrumented static load test and dynamic load test. Non-invasive and non-destructive methods. Electrical, electromagnetic and seismic geophysical methods.

**Experiment Planning** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction. Importance of the use of methodology in multivariable processes; advantages of the factorial experiments in relation to the univariate type experiments; application potential. Basic concepts of statistics. Strategies to define the most appropriate planning according to the process under study. Full factorial planning. Definition of the variables of the process under study and its restrictions; elaboration of full factorial planning; analysis of the effects of the factors on the desired responses; statistical analysis and interpretation of results. Fractional factorial planning. Definition of the variables of the process under study and its restrictions; definition of the most appropriate resolution. Elaboration of fractional factorial planning; analysis of the effects of the factors on the desired responses. Adjusting models.

*3. Optional subjects..*

*3.1 Line: Sustainable Technologies.*

**Energy Generation and Energy Efficiency** (45 Credit Hours, 3 Credit Units)

Syllabus: Energy sources; supply and use of energy sources, forms of energy generation; small and large hydroelectric plants; wind power; hydrokinetic energy; isolated systems and rural electrification; main environmental impacts; energy efficiency - approaches of the 1st and 2nd laws of thermodynamics; energy efficiency in mining.

**Special Topics in Energy Development** (45 Credit Hours, 3 Credit Units)

Syllabus: To be specified in the program of the discipline, according to the topics to be worked, addressing specific issues related to the area of energy development.

**Turbomachines** (45 Credit Hours, 3 Credit Units)

Syllabus: Linear grids and velocity triangles; governing equations for the analysis of the flow in turbomachines; models applied to the analysis of the flow in turbomachines; flow modeling in linear grids; radial equilibrium analysis; hydraulic turbine design criteria; secondary flows in turbomachinery.

**Horizontal Axis Turbine Modeling** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction to turbine aerodynamics; Theory of the Actuator Disk, Theory BEM, Theory BEM with rotation in the mat; the corrections of Prandtl and Glauert; turbines with diffusers; modeling of the power train of horizontal axis turbines. The effect of cavitation.

**Flow of Solids and Method of Discrete Elements** (45 Credit Hours, 3 Credit Units)

Syllabus: Properties of bulk solids; stress analysis and granular medium; principles of shear tests; properties and solid flow characterization; practical aspects of bulk solids shear tests; voltages in silos; silo sizing; interactions in granular medium; introduction to the discrete element method; modeling of contact forces for application to the DEM method; applications with the EDEM and Bulk Flow Analyst software.

**Computational Fluid Dynamics** (45 Credit Hours, 3 Credit Units)

Syllabus: Review and classification of flows. Conservation equations: mass, momentum and energy. Fundamentals of numerical simulation of flows. Finite difference and volume concepts. Discretization of equations. Numerical formulations for the approximation of the convective term. False diffusion. Permanent and transient regime (explicit and implicit methods). Speed-pressure coupling: SIMPLE, SIMPLEC, FLOOR and trailer. Incompressible iterative algorithms for flow. Segregated and coupled methods. Stability and precision of the numerical solution. Structured and unstructured meshes. Generation of mesh. Turbulence: mean Reynolds equations, turbulence models. Application of commercial software for solving problems of fluid mechanics and heat transfer.

**Machine Dynamics** (45 Credit Hours, 3 Credit Units)

Syllabus: Instrumentation for measuring vibration. Global and spectral level monitoring. Characteristic defect frequencies of rotating and alternate machine components. Diagnosis of defects in rotating and alternative machines. Pattern Recognition. Turbine power train dynamics.

**Signal Processing** (45 Credit Hours, 3 Credit Units)

Syllabus: Systems: classification. Properties. Relationships between input and output of linear systems. Signs: definitions and classification. Fourier analysis: Fourier series and Fourier transform. Stochastic processes: probability distribution function, mathematical hope and statistical moments, probability density function, correlation functions and spectral density. Digital signal processing: signal analyzer, filters, discretization of signals, sampling theorem, discrete Fourier transform, Fast Fourier transform (FFT) and window functions. Errors in estimation of frequency response functions.

**Dynamics of Granular Systems** (45 Credit Hours, 3 Credit Units)

Syllabus: Granular systems, basic concepts and examples of problems in Civil Engineering. Introduction to simulation methods, Equations of motion in granular systems and numerical methods for solving ordinary differential equations: Euler, Runge-Kutta and Leapfrog method. Simulation via molecular dynamics, History, Fundamentals of molecular dynamics and Simulation methodology. Simulating simple initial systems, Potential Functions, Calculating Interactions, and Simulating Initial Conditions. Dynamics Granular, Interactions in normal and tangential direction, Rotation and friction implementation and Simulating a vibrating granular layer (2D version).

*3.2 Line: Infrastructure*

**Materials Science** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction to materials science: classification of materials, classification based on structure, new materials applied to Engineering: Lucalox, optical fibers, Nylon, semiconductor chips and Kevlar®. Atomic structure: structure of the atom, electronic structure, interatomic distance, atomic mass and atomic number. Chemical bonds: coordination numbers, ionic bonds, covalent and metallic bonds, Van der Walls Force. Crystalline structure of materials: cubic, hexagonal and other crystal systems; amorphous materials: glass. Phase diagrams of pure substances, phase rule, binary eutectic alloys. Characteristics and structure of materials: polymers, composites, metal alloys and glasses. Mechanical, electrical, magnetic and optical properties of materials: tensile and deformation, hardness, plastic and elastic deformation; electrical conductivity and semiconductor devices; electromagnetic spectrum, refraction and absorption.

**Dynamics of Structures** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: fundamental concepts, types of loading, characteristics of the dynamic problem; discretization methods; equations of motion: systems of one degree of freedom: free vibration, response to harmonic loads, response to periodic loads, response to impulsive loads, response to general dynamic loads; systems of various degrees of freedom: formulation of motion equations, structural property matrices, free non-damped vibrations.

**Computational Analysis of Concrete Structures** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: introduction to the finite element method; computational modeling of concrete structures; precision and modeling errors; state of the art and future prospects. Modeling of concrete structures: models with lattice and bar elements; models with plate and membrane elements; models with three-dimensional solids. Models of connecting rods based on computational analysis: method revision; general aspects of modeling; practical examples. Introduction to nonlinear analysis of concrete structures: concrete behavior; constitutive models for concrete under tension and compression; cracked concrete behavior; cracking models; constituent models for steel; adhesion between steel and concrete. Practical applications of concrete structure modeling.

**Waste Utilization** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction; alternatives to waste recycling as building materials; classification of waste; environmental risk of the waste, in the initial stage; environmental risk of new products; environmental risk of the production process; techniques for chemical, physical and environmental characterization of waste; development of new products from waste; microstructure analysis; study of mechanical performance; evaluation of durability; different waste used in construction.

**Concrete Armor I** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction and sizing process: introduction; mechanics of reinforced concrete; historical development; objectives and design process; structural safety and boundary states; probabilistic calculation; sustainability and useful life. Materials: behavior and compressive strength of concrete; tensile strength and under multiple stress state of the concrete; stress-strain curves for concrete; creep and retraction; tensile and compressive behavior of steel; strength and ductility. Adherence, anchoring and splicing of reinforcement: mechanisms of force transfer; adhesion; straight anchorage, with hooks and mechanics; continuity of armatures and requirements for structural integrity; of the reinforcement. Beam flexure behavior and resistance: beams flexion theory; elastic analysis of tensions in beams; cracking; resistant moment of beams with simple reinforcement; definition of balanced sections; moment-curvature; double reinforced beams; beams with section T. Pillars: combined action of axial load and moment; interaction diagrams for reinforced concrete pillars; dimensioning of short pillars; pillars under biaxial flexion; behavior of svelte pillars in rigid frames.

**Concrete Armor II** (45 Credit Hours, 3 Credit Units)

Syllabus: Beam shear: mechanical behavior; rupture modes; trellis models; standards for shear design; suspension armature; beams with variable height. Different approaches for the shear design of concrete elements: introduction; compression field methods; truss models with concrete contribution; friction-shear; connecting rods and tie rods. Torsion: introduction and basic theory; behavior of concrete elements under torsion; dimensioning of elements to the torsion; thin walled pipes and trellis models; standards for the torsion dimensioning of concrete elements. Bidirectional slabs: behavior of slabs under bending; analysis and distribution of moments; moments for dimensioning in finite element models; flexural sizing; shear dimensioning of slabs; joint action of moment and shear on slabs. Theory of rupture lines: introduction; armor, behavior and conditions in the ultimate limit state; analysis by the principle of virtual works; analysis by equilibrium equations; applications for two-way panels; applications for point loads and slab-pillar connections.

**Concrete Dosing** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction; internal structure of concrete; relations between structures and properties of the hardened paste; materials for dosage; pozzolanic materials; additions; dosage methods; experimental methods; quality control, dosing of conventional concretes; dosing of high-performance concrete.

**Precast Concrete Structures** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: fundamental concepts; materials; advantages and disadvantages; historical development and future prospects. Production of precast concrete structures: manufacturing; transport; Assembly. Design of precast concrete structures: general principles; geometry of the elements; tolerances and clearances; structural analysis and design; transitional situations; stability. Connections between precast elements: general aspects; types of connections; anchoring and splicing of bars; transfer of localized forces; steel connectors subjected to traction, shear stress and bending moment. Models of rods and rods for analysis of elements and pre-cast connections: introduction; general analysis and sizing procedure; dimensioning of rods, rods and knots; applications for dimensioning Gerber consoles, walls and teeth.

**Instability of Structures** (45 Credit Hours, 3 Credit Units)

Syllabus: Stability theory of structures: conceptualization and definition; stability criteria; physical and geometric nonlinearity; boundary and bifurcation points; critical and post-critical behavior; sensitivity to imperfections; multiple bifurcations and modal coupling; vibrations of structural elements sensitive to buckling. Structural stability problems: stability of slender columns; stability of rectangular plates; stability of beams and frames in the plane. Computational modeling of stability problems: approximate methods; problems of eigenvalue in stability and use of finite elements; geometric matrices for the various structural elements; analysis of nonlinear systems.

**Pathology of Materials** (45 Credit Hours, 3 Credit Units)

Syllabus: Concept (pathological manifestation, useful life, durability). Mechanisms, symptomatology, prevention and recovery of pathological manifestations of concrete structures, masonry, mortar coverings and ceramic coatings. Concrete pathology: surface wear, cracking, leaching, alkali-aggregate reaction, sulfates and corrosion of reinforcement. Pathology of masonry: cracking and efflorescence. Pathology of coatings: detachment, cracking, pulverulence, expansion by moisture and efflorescences.

**Plasticity of Concrete** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction to Plasticity Theory: constitutive equations; extreme principles for rigid-plastic materials; plasticity problems; reinforced concrete structures. Flow conditions: concrete; flow conditions for beams and slabs; dimensioning of reinforcements. Theory for flat concrete: geometric and static conditions; principle of virtual works; constitutive equations; flat deformations for Coulomb materials. Beams: Beams under bending; shear beams; torsion beams; combined action of bending, shearing and torsion. Lajes: conditions of staticity, geometric; constitutive equations; exact solution for isotropic slabs; upper limit solutions for isotropic slabs; lower bound solutions for isotropic slabs; orthoptic slabs.

**Repair and Reinforcement of Concrete Structures** (45 Credit Hours, 3 Credit Units)

Syllabus: Maintenance of structures: important aspects; mechanisms of deterioration; establishment of shelf life and safety levels. Methodology for diagnosis and intervention: methodology; inspection; investigations and trials; project verification; strategies for interventions. Interventions: determination of intervention techniques; surface protection; repair; reinforcement; demolitions. Basis for reinforcement design with Fiber Reinforced Polymers (PRF): general aspects; properties of PRF reinforcement systems; criteria for designing PRF reinforcements. Reinforcement to flexion with PRF: flexural strength; determination of modes of rupture; reinforcement detailing; in-service behavior of the element. Reinforcement to shear with PRF: shear strength of reinforced elements with PRF; procedure for designing and detailing reinforcement. Confinement with PRF: confinement for axial reinforcement; design procedure for circular pillars; confinement of columns under flexo compression.

**Sustainability Applied to Materials** (45 Credit Hours, 3 Credit Units)

Syllabus: Sustainable development: history and concept of sustainability. Socio-environmental responsibility: the use of materials and products that minimize risks to human health and ecosystems. General information on construction, materials and environment: measures and feasibility of the use of sustainable materials. Environmental impact: impact assessment; legislation, EIA / RIMA. Ecological materials: clean technologies, biodegradable polymers, alternative materials. Ecological economics: economic valuation in environmental management, environmental valuation methods, conservation versus development. Sustainability applied to the development of materials: sustainability indicators, new clean technologies.

**Microscopic Materials Analysis Techniques** (45 Credit Hours, 3 Credit Units)

Syllabus: Introduction: Methods of microscopic analysis of materials: classical and instrumental; calibration methods: external and internal standard, selection of analytical method. Linear regression models. Validation of analytical methods: performance characteristics, analytical parameters of validation, selectivity, linearity, precision, accuracy, robustness. Infrared and Fourier transform infrared spectroscopy: spectral regions, applications, molecular vibration study, absorbance and transmittance, instrumentation, sample preparation, spectra interpretation and case studies. Atomic absorption spectroscopy: Beer's law, instrumentation, absorbent species, quantitative analysis, applications. Methods of thermal analysis: classification of thermoanalytical techniques, instrumentation, coupled techniques, applications, Thermogravimetry - TG, Differential Thermal Analysis - DTA and Differential Exploration Calorimetry - DSC.

**Special Topics in Energy Development** (45 Credit Hours, 3 Credit Units)

Syllabus: To be specified in the program of the discipline, according to the topics to be worked, addressing specific issues related to the area of energy development.

**Special Topics in Infrastructure** (45 Credit Hours, 3 Credit Units)

Syllabus: To be specified in the program of the discipline, according to the topics to be worked, addressing specific subjects related to the area of infrastructure.

#### 4*. Other Activities.*

**Proficiency Exam.**

Syllabus: The student must present satisfactory knowledge in English.

**Teaching Internship** (15 Credit Hours, 1 Credit Unit)

The student must teach a minimum of 30 hours of classes in subjects related to his / her research line in undergraduate courses.

**Short Course** (15 Credit Hours, 1 Credit Unit)

Syllabus: Specific for each course.

**Publication of Scientific Articles A1 to A2** (60 Credit Hours, 4 Credit Units)

Syllabus: Development and Publication of Articles in Qualis CAPES Periodicals A1 to A2

**Publication of Scientific Articles B1 to B2** (30 Credit Hours, 2 Credit Units)

Syllabus: Development and Publication of Articles in Qualis CAPES B1 to B2 Periodicals.

**Defense of Master's Thesis Qualification.**

Syllabus: Development and defense of master's thesis

**Defense of Master Dissertation** (90 Credit Hours, 6 Credit Units)

Syllabus: Development and defense of master's thesis