Scienza delle Costruzioni
The course aims at providing the theoretical basis and the operational tools for the analysis of strain and stress state in a continuous body. In particular, the analysis of structural systems consisting of beams and rods is addressed. The course includes both theoretical and practical sessions. Students will be provided with the tools necessary to classify a framed structure, to carry out the relevant stress analysis, to compute the deformed shape and to understand the relationships that allow relating the one-dimensional structural models to Saint-Venant’s theory.
Contents of the courses of Calculus 1 and 2, Rational Mechanics.
Internal stresses and stress resultants. Sign conventions for stress resultants. Computation of stress resultants via direct method and analytical method. Differential equilibrium equations. Boundary conditions and jump conditions. Computations of stress resultants via Lagrange method. Formulation of a structural problem. Elastic equilibrium of rods. Beams in bending. The Euler-Bernoulli beam model. Shear deformation. The Timoshenko beam model. The deflection curve. The Fundamental identity of Mechanics for rods and beam models. Applications of the virtual work theorem. Maxwell-Betti reciprocity theorem. Hyperstatic structures. Kinematic compatibility equations. Stress-based formulations. Introduction to elastic instability. Euler’s beam buckling. Influence lines.
Saint-Venant’s problem. Geometric and constitutive assumptions. Assumptions on external loads and internal stress state. Momentum balance and boundary conditions. Stress resultants. Saint-Venant’s Postulate. Axial force. Flexure. Biaxial bending. Eccentric axial force. Torque. Analogies with other physical phenomena. Shear. Approximate formulation and Jourawski’s formula. Extension of Saint-Venant’s results.
Stress analysis in structures;
Structural models and methods of analysis;
Saint Venant problem.
Theoretical and practical sessions.
P. Casini, M. Vasta, Scienza delle Costruzioni, Città Studi; D. Bernardini, Introduzione alla Meccanica delle Strutture, CittàStudi; L. Ascione, Sulla statica delle travi e dei sistemi di travi, Liguori; C. Comi, L. Corradi Dell'Acqua, Introduzione alla meccanica strutturale, McGraw-Hill; Further reading: L. Corradi Dell'Acqua, Meccanica delle strutture, vol 1, McGraw-Hill (Il problema di Saint Venant);
MAX [0.2 × P1 + 0.2 × P2 + 0.6 × PF; PF]