Università Roma Tre

Linear elastic beam models: local deformation measures and local equilibrium equations. Cases examined: axis having shape of a linear segment or an arch of circumference with orthogonal sections. Linear axis and sections with a generic orientation.
Displacement method for the solution of statically indeterminate problems.
Beam models for the analysis of structural elements relevant for the historic buildings: arches, flat-arches, masonry structures (with one or more leafs) having one prevailing dimension. Analysis of the effect of the shear deformation on their mechanical behaviour.

Beam systems of relevant interest in the historic constructions: analysis of wooden trusses and floors and the unfolding of the rôle of their components.
Analysis of some sample problems by means of SAP2000 and Mathematica softwares.
The Cauchy continuum: local deformation and stress measures.
Principal stresses and principal deformation: the Mohr circumference.
The strain gage rosettes.
Uniaxial stress and strain cases. Constitutive relationships for masonry.
Linear elastic relationships. Material symmetries: orthotropic, isotropic materials. Lamé constants, Young modulus and Poisson coefficient.
Masonry damage analysis: direction of the cracks triggered by combined shear and normal stress components. Stresses induced by sinking.

Teacher's notes.
Gurtin: An introduction to continuum mechanics
Benvenuto: An Introduction to the History of Structural Mechanics