MASTER IN CIVIL ENGINEERING - Faculdade de Engenharia da ...

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Symmetrical structures with symmetrical and anti-symmetrical action. Symmetrical structures with any charge. Decomposition of a charge in a symmetrical and antisymmetrical part. Chapter 4 – Energy Theorems Introduction to Energy Theorems Distortion energy and virtual work. Distortion energy due to a charge system. Deduction of the theorem of virtual work. Deduction of the theorem of Betti. Maxwell’s reciprocal theorem (1st and 2nd consequences of the theorem of Betti). Deduction of the theorem of Castigliano and its inverse. Physical interpretation of the theorem and its application to the structure analysis. Third consequence of the Theorem of Betti. Determination of displacements in hiperestatical structures using the theorem of Castigliano. Chapter 5 – Influence lines Notion of influence line. Determination of influence lines of reactions of support in isostatic structures. Determination of influence lines of transversal efforts and bending moments in isostatic structures. Determination of efforts in structures by influence lines Influence lines in hyperstatic structures. Chapter 6 – Displacement Method The displacement method as strength method’s dual method. Illustration by a simple example. Direct formulation of the displacement method in the structure analysis. Obtaining of configurations correspondent to null and unit displacement. Obtaining of an equation system. Determination of the final efforts. Notion of stiffness matrix of a beam Discussion of the minimum number of unknowns to consider in the base system set up. Application of the displacement method in the case of structures with beams with despicable axial deformability. Use of the principal of virtual work to determine the fixation forces in structures with beams with despicable axial deformation Determination of the mobility degree of a structure with beams with despicable axial deformation Master in Civil Enginerring Page 4
Soil Mechanics I Credits Contact Time Total Time 7 ECTS 75 188 Objectives, Skills and Learning Outcomes Introduction to the concepts, principles and fundamental theories describing and explaining both the mechanical behaviour (in terms of resistance and deformability) and the hydraulic behaviour of soil masses. Program Physical properties of soils. Particle size distribution. Clay minerals. Atterberg limits. Basic features of sedimentary granular soils (sands) and cohesive soils (clays). Residual soils from granite. Soil classification. Effective stress principle. At rest stress state. Elastic solutions for stresses induced in the ground by external loads. Darcy's law. Coefficient of permeability. Lab and in situ tests to evaluate soil permeability. Two-dimensional flow nets. Seepage force. Quick condition and critical hydraulic gradient. Piping and heaving. Filters. Capilarity. Confined compression of clayey layers. Oedometer test. Parameters defining soil compressibility. Normally consolidated and overconsolidated soils. Estimation of the consolidation settlement. Terzaghi theory for vertical consolidation. Secondary consolidation. Compression of unconfined clay layers. Methods of acceleration of the consolidation rate. Observation of embankments on soft ground. Mohr-Coulomb and Tresca yield criteria. Direct shear, triaxial and simple shear tests. Shear strength of sands. Liquefaction. Shear strength of clays. Drained and undrained loading. Effective stress shear strength parameters. Pore pressure parameters. Undrained shear strength of clays and its dependence on the effective at-rest stress and on the stress path. Inherent and induced anisotropy of the undrained shear strength of clays. Master in Civil Enginerring Page 5
Page 1 and 2: MASTER IN CIVIL ENGINEERING The Mas
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Page 5: Structural Analysis I Credits Conta
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Page 21 and 22: Planning and Environmental Quality
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Page 25 and 26: Maritime Works 2 Credits Contact Ti
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