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Scienza delle Costruzioni (CA)
Structural mechanics
Fabrizio Davi'

Seat Ingegneria
A.A. 2015/2016
Credits 12
Hours 96
Period E
Language ENG

Prerequisites
Calculus, Linear Algebra, Physics

Learning outcomes
The course aims to the essential knoweledges in Solid Mechanics, applied to the elastic behavior of low-hyperstatic plane frames.

Program
Vector spaces. Scalar and vectorial products. Tensor spaces. Identity tensor. Transpose. Symmetric and skew-symmetric tensor: axial tensor. Orthogonal tensors. Kinematics. Deformation and deformation gradient. Deformations of line, surface and volume elements. Polar decomposition theorem. Kinematics of rigid bodies: degrees of freedom. Spin Tensor and angular velocity. Poisson formula. Plane rigid motion. Constraint: lagrangean coordinates. Multiple constraints. Statically determinated, undeterminated and impossible systems. Rigid body statics: internal actions in rigid systems. Work, power and energy. Force and couplke resultants. Virtual power principle. Static balance laws. Reactive forces in constrained rigid systems. Reactive forces in statically determinated rigid systems. Reactive forces and equilibrium configurations in statically impossible rigid systems. Statics of rods: internal actions, balance laws and boundary conditions. Internal action diagrams. Plane rods: archs and straight rods. Rods kinematics: kinematical descriptors, deformations measures, compatibility equations. Kirchhoff's rod. Constitutive relations: linearly elastic rods. Virtual works, energetics and variational formulations. Minimum principles. Hyperstatic plane frames; the Müller-Breslau equations as a consequence of Complementary nergy minimum principle. Tridimensional linear elasticity. Kinematics: displacement and strain. The infinitesimal strain tensor. Statics: the notion of stress. Cauchy's theorem. Virtula works for defromable systems. Linear isotropic materials. The Saint-Venant's problem for isotropic solids. The Clebsch's solution. Yield criteria . Stability of Euler beams.

Development of the examination
LEARNING EVALUATION METHODS
The final test consists of a written test and an oral colloquia. The written test requires the study of a simple hyperstatic plane frame.

LEARNING EVALUATION CRITERIA
The written test must verify the ability to resolve a statically-indeterminate plane truss, determining also the displacements of a given section and performing the safety analysis of another section. The diagrams of the stress characteristics must be correctly drawn and from the data provided in the text the displacement or rotation of a section must be correctly evaluated. The ideal Huber-Von Mises tension compatible with the admissible one must be also evaluated for a section In the oral test must verify the ability to solve problems of a theoretical or applicative nature by starting from the equations of mechanics of deformable bodies. It could also require proofs of theorems or deductions of equations, focusing more on the deductive aspects rather than on mnemonic.

LEARNING MEASUREMENT CRITERIA
n the written test the relevance of the obtained results with the solution is checked; in the oral test both the knowledge of the topics and the capability to develop solutions to proposed problem are checked.

FINAL MARK ALLOCATION CRITERIA
- For the written exam is admitted only the positive result associated with the determination of the exact solution. For the oral exam grade is assigned by taking into account the topics knowledge, the capability to apply these knowledges to solve example

Recommended reading
F. Davì, Note di Scienza delle Costruzioni, 2013 (free downloadable from University official Webpage) P. Podio-Guidugli, Lezioni di Scienza delle Costruzioni, Aracne Editrice, Seconda Edizione 2009 L. Gambarotta, L. Nunziante ed A. Tralli, Scienza delle C

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