Learning objectives
The aim of the course is to provide the fundamental notions to understand the structural behavior (knowledge) and to analyze the state of stress in simple structures (competence).
The students will also be able to autonomously study further aspects related to the structural analysis of more complex situations not covered in the course (learning ability).
Prerequisites
It is necessary to have at least attended the course: FUNDAMENTALS OF MATHEMATICS.
Course unit content
Fundamentals of the equilibrium of statically determined structures. Internal actions. Stress and strain in a continuous medium. De Saint Venant's problem (axial force, bending, shear and torsion). The strength of materials.
Full programme
1. Systems of forces, resultant and resultant moment, balanced systems.
2. Geometry of the masses. Mass systems (discrete and continuous). First order moment: static moment,
center of mass (center of gravity). Second order moments: axial, centrifugal, polar moment of inertia.
Transposition formulas. Rotation formulas, directions and main moments of inertia, problem of
maximum and minimum, circle of Mohr.
3. Simple one-dimensional structures (beams) and composite structures (frames). Plane beams. Equilibrium problem: kinematic aspects (valence of constraints and degrees of freedom) and static aspects (constraint reactions and cardinal equations of thestatic). Isostatic, statically indeterminate and labile structures. Superposition principle.
Resolution of statically determined beam systems: equations of equilibrium; kinematic check.
4. Internal actions. Conventions on signs and diagram drawing. Special problems. Flat trusses. Axial and polar symmetry, antisymmetric cases.
5. Analysis of stress. Definition of stress, local stress tensor, Cauchy equations, reciprocity principle. Principal stresses and their directions. Plane stress state and circle of Mohr. Boundary equations and indefinite equations of equilibrium.
Deformation analysis. Deformation Tensor. Deformation components: expansion and distortion. Principal strains and principal strain directions
6. Laws of elasticity (for deformable three-dimensional solids). Elastic, linear, homogeneous and isotropic material, constitutive equations for an elastic material. Physical meaning of elastic constants.
7. The problem of De Saint-Venant. Main hypotheses, De Saint-Venant principle, indefinite equations of equilibrium, elasticity equations and boundary conditions. Special cases: axial force, bending, shear and torsion. Combined cases.
8. Strength criteria of materials. Rankine, Tresca, Von Mises, Mohr-Coulomb criteria.
9. Displacement evaluation in beams. Some basic concepts on the resolution of statically indeterminate structures; equilibrium stability.
Teaching methods
The course is organized in theoretical and practical lessons (by making use of electronic presentations); the exercises are either developed by the teacher and autonomously in class and at home by the students.
For every topic, the practical activities are properly scheduled in order to provide the students the ability to solve the proposed problems on the basis of the previously explained theoretical concepts.
Assessment methods and criteria
The final exam consists in a written test
