The course aims at introducing the fundamental concepts of structural mechanics, limiting the analysis to plane structures and under the hypotheses of small displacements and linear elasticity. The goal is to provide the basic concepts and tools for the analysis and the mechanical modeling of structures, identifying constraint reactions, internal forces, deformations, and displacements. The knowledge acquired during the course is the basis for all courses, both of theoretical and design-oriented character, typical of structural engineering.
Course Prerequisites
Knowledge of Calculus, Geometry and Algebra, Physics, Analytical Mechanics.
Teaching Methods
Blackboard lectures
Assessment Methods
Joint written examination for modules A and B, possibly followed by an oral examination (or oral examination in special situations identified by the teacher).
Texts
Lecture notes. P. Casini e M. Vasta, Scienza delle costruzioni. Città Studi. A. Taliercio e U. Perego, Fundamentals of Structural Mechanics. Esculapio.
Contents
1. introduction to the course a. notations and preliminaries (surface centroid and inertia, vector operations, differential equations) b. definition of beam, structure, constraint (internal, external) c. kinematic analysis, structure classification (statically determinate/indeterminate) 2. isostatic structures a. constraint reactions b. internal actions c. reticular structures d. beam equilibrium equations 3. deformable beam theories a. Euler Bernoulli beam (compatibility, constitutive relations, and Navier formula, elastic curve theory) b. Timoshenko beam c. thermal loads 4. principle of virtual works a. displacements in statically determinate structures b. constraint reactions in statically indeterminate structures 5. Mohr's analogy 6. introduction to displacement method
