| Code |
16150
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| Year |
2
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| Semester |
S2
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mechanics and Thermodynamics
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Entry requirements |
N.A.
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Learning outcomes |
Starting from matrix algebra and statics, the main objective is the study of solid mechanics using the concepts of continuum mechanics. In particular, different methodologies are used to describe the change in shape of a solid and the continuity conditions to define the strain at each point, to describe the internal stresses and equilibrium conditions with the stress state at each point, and the constitutive relationships that allow to relate stresses with strains, in particular the theory of elasticity. These concepts are applied to plane stress states, to determine stresses and strains in slender bars due to axial force, torsional moment, bending moment and shear force. These concepts are applied to the analytical structural calculus of simple geometry objects, and will allow in the future to extrapolate to the numerical structural calculus of generic geometry structures and boundary conditions.
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Syllabus |
Review of vector and matrix algebra: Operations between scalars, vectors and matrices. Cartesian tensor. Eigenvalues ??and eigenvectors. Coordinate transformation. Tensor decomposition.
State of deformation at a point. Displacement and deformation gradients. Deformation Tensors. Decomposition of the infinitesimal strain tensor into spherical and anti-spherical. Eigenvalues and eigenvectors. Invariants. Coordinate transformation. Continuity equations. Saint-Venant and Bernoulli kinematic hypotheses for bars in tension, torsion and pure bending.
Stress tensor. Equilibrium equations for tensile, torsional and bending loads. Decomposition of the stress tensor. Coordinate transformation. Mohr's Circle. Principal stressses and directions. Overlapping loads.
Linear elastic relationship between stress and strain tensors. Lame constants. Young's modulus and Poison's ratio. Shear and volumetric module. Tensile and torsional stiffness. Equation of the deflection line in beams.
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Main Bibliography |
Bower, A. F. 2012, Applied Mechanics of Solids, CRC Press
Beer, J. e DeWolf, 2003. Mecânica dos Materiais, McGraw-Hill
Nash W. A. e Potter M. C. Resistência dos Materiais, Bookman
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Language |
Portuguese. Tutorial support is available in English.
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