Università Roma Tre

Kinematics of rigid bodies. Planar rigid displacements. Systems of rigid bodies.

Kinematic characterization of a constraint. External constraints and internal constraints.
Lability.

Statics of rigid bodies. External forces. Force, moment of a force, systems of forces, force density, distributed loads.
Static characterization of constraints. The static problem. Cardinal equations of statics. Static classification.

Evaluation of internal actions. Differential equilibrium equations in scalar and vector format. Direct method. Internal action diagrams.

Reticular trusses. Node method. Ritter method.

Beam kinematics. Displacement, rotation, hypothesis of small displacements. Kinematic conditions. Deformation measurements. Axial deformation. Angular scroll. Curvature. Equations of congruence. Model of Euler-Bernoulli. Vector representation of congruence equations. The kinematic problem for the beam.

Constitutive equations. Phenomenology of the response of a material. The uniaxial test. Elastic behavior. Plastic behavior and rupture. Ductile and fragile materials.

Constitutive equations for the elastic beam. Axial behavior, flexural behavior, shear behavior. Uniform thermal variation, affine thermal variation.

The elastic problem for the beam and its formulation.

Displacement method. Equation of the tension beam. Inflexion of a beam in the Euler-Bernoulli model. Extension to the Timoshenko model. Connection conditions and problem formulation for beam systems. Kinematic and static performance of internal constraints.

Three-dimensional continuous bodies. Cauchy's concept of traction. Partwise balance. Cauchy's Lemma. The stress tensor. Differential equations of equilibrium. Principal stresses and principal directions. Voltage states. Lamé's ellipsoid of tension. Isostatic lines. State of plane or biaxial tension. Purely tangential tension state. Uniaxial voltage state. Mohr's circles for the stress.


The problem of Saint Venant. Postulate of Saint Venant. The semi-inverse method. Normal force. Flexure. Torsion of compact and hollow circular sections. The Neumann problem. Elliptical sections. Polygonal sections. The hydrodynamical analogy. Thin rectangular section. Open sections composed of thin rectangles. Thin-walled sections: Bredt's theory.

Bending and shearing. Distribution of normal tractions. Distribution of tangential tractions: Jourawsky formula and its applicability.
Thin sections open. Thin rectangular section. Thin double T section. U and H shaped sections. Thin sections closed. Symmetrical closed section. Symmetrical compact sections. Determination of the shear center.

Rupture and yielding criteria for fragile materials and ductile materials.

P. Casini, M. Vasta, "Scienza delle costruzioni", Città Studi Edizioni 2016.
Steen Krenk & Jan Høgsberg, "Statics and Mechanics of Structures", Springer 2013.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, 1984.
E. Sacco, Lezioni di Scienza delle Costruzioni, 2016.
Solved problems.