Architecture

The program is composed of the following items: 1. Linear elastic beam Definitions: beam geometry, boundary conditions, and external forces. Kinematics: displacements of rigid beams, deformations. Strain-displacement relations, kinematic characterization of boundary conditions. Statics: internal axial and shear forces and bending moment, internal equations of equilibrium, static characterization of boundary conditions. Internal forces-strain relations, axial experimental test, fragile materials, ductile materials. Linear elastic relations for beam under axial loads and under bending moment. Methods of solution of the elastic problem. 2. Continuum mechanics Analysis of strain: displacement and deformation, deformation gradient, displacement equation, displacement gradient, strain-displacement relations. Analysis of stress: body forces, surface forces, internal forces, stress at a point, special stress components, Cauchy theorem, differential equation of equilibrium, stress boundary conditions, principal stresses and principal planes, two-dimensional state of stress, example of stress states. Stress-strain relations: elastic materials, homogeneous materials, materials symmetry, isotropy, orthotropy. Solution of the elastic problem. 3. Beam of De Saint Venant Definition of the De Saint Venant’s beam: geometry, loads, material, boundary condition. The De Saint Venant’s problem and postulate. Semi-inverse formulation of the problem. • Combined axial load and bending moment: hypothesis on the strain distribution, stress state, equations of boundary conditions, Navier’s equation for stress under axial load and bending moments, neutral axis equation, deflection plane and moment plane. Stress and strain distributions for materials with no tensile strength. • Torsion. Circular cross section: Coulomb’s solution, Displacement, strain, stress. Thin-wall hollow section: Bredt’s solution. Rectangular sections and sections composed of thin rectangular sections (outline). • Shear. Bending and shear: Jourawsky’s approximate theory. Shear and torsion: torsion center. 4. Concept of structural stability (outline) Definition of equilibrium types. The Euler’s column: stability equation, Euler’s critical force. Euler’s hyperbole. Effect of end conditions.

It is essential that the student possesses the following knowledge, obtained by passing the exams of the Mathematics II and Structural Mechanics courses (elements of linear algebra: vectors, matrices, systems of linear equations; elements of tensor algebra: linear transformations, sum, product for a scalar, composition, scalar product, trace, tensor of the second order symmetrical, antisymmetric, transposed; static: kinematics and static systems of rigid bodies, in particular beams and beam systems).

Main book Casini P., Vasta M. “Scienza delle Costruzioni” CittàStudiEdizioni, Novara, 2011.

Attendance is optional but strongly recommended.

During the course three extemporaneous tests are carried out.