The goal of this course is the introduction of the basic principles of continuum mechanics, specialised to the case of solids, under the hypothesis of linear elasticity. The objective is to give basic concepts and methods to comprehensively elastic solids, and their stress and strain state, building the necessary bases 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 examinitaion (or just oral examination in special situations identified by the teacher).
Texts
- Lecture notes; - M. Capurso, Lezioni di Scienza delle Costruzioni. Esculapio; - A. Taliercio and U. Perego, Fundamentals of Structural Mechanics. Esculapio.
Contents
0. Course introduction; notations; preliminaries. 1. Kinematics of deformable bodies: - Continuum deformation process; - Strain tensor and properties; - Principle strains and directions; - Compatibility equations. 2. Statics of deformable bodies: - Cauchy continuum and stress vector; - Cauchy stress vector and properties; - Principle stresses and directions; - Mohr's circle; - Equilibrium differential equations and boundary conditions. 3. Virtual work principle. 4. Linear elastic constitutive laws. 5. Linear elastic problem. 6. Plane stress and plane strain. 7. Allowable stress criteria. 8. Saint-Venant problem: - Problem formulation; - Axial force; - Simple symmetrical bending; - Simple unsymmetrical bending; - Combined axial force and bending; - Torsion; - Bending with constant shear; - General case.
