Università Roma Tre

Introduction to Structural Mechanics provides students with the basic knowledge of mechanics of materials and structures. This knowledge allows students to solve simple problems in the statics of elastic beams, and to acquire the core knowledge required for courses in structural design. The course is taught in the second year of the Degree in Civil Engineering. This degree aims at providing tools for the design, construction, maintenance and management of civil structures and infrastructures, such as buildings, bridges, tunnels, transport systems, hydraulic works and land protection. As part of this process, the course aims to provide adequate knowledge: 1) of the laws governing the equilibrium of rigid and deformable systems; 2) of beam theory; 3) methods for calculating stresses in beam framework; 4) assess the resistance of a structure. At the end of the course students will be able to: 1) be acquainted with technical language; 2) analytically represent and solve simple problems of statics of structures in civil engineering; 3) to understand the limits of the models used; 4) to assess the safety of a structural element.

P. Casini, M. Vasta, "Scienza delle costruzioni", Città Studi Edizioni 2016.
Steen Krenk & Jan Høgsberg, "Statics and Mechanics of Structures", Springer 2013.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, 1984.
E. Sacco, Lezioni di Scienza delle Costruzioni, 2016.

Vectors. Moment of a vector with respect to a point. Resultant force and resultant moment of a system of vectors. Equivalence of systems of vectors. Planar systems. Linear transformations on vector spaces. Second-order tensors. Differentiation of vector and tensor functions. Gradient and divergence. Divergence theorem. Stokes’ theorem.
Centroid of a material system. First moments and moments of inertia of a planar region. Moments of inertia of a planar region with respect to lines passing through a given point. Mohr’s circles. Polarity and involutions determined by the ellipse of inertia.
Equilibrium of a material point. Constraints. Infinitesimal rigid displacements. Euler’s theorem. Work in a rigid displacement. Equilibrium equations of rigid bodies. Beams and frames. Diagrams of the components of force and couple resultants. Forces exerted by the constraints. Principle of virtual work for rigid bodies. Statically determined structures. Graphic statics.
Deformation of a continuous body. Measures of deformation. Principal strains. Volume change. Compatibility conditions. Equilibrium equations of deformable bodies. Stress tensor. Principal stresses. Plane stress. Mohr’s circles for stresses. Constitutive equations. Hyperelastic materials. Energy functional. Clapeyron’s theorem. Equilibrium boundary-value problems. Betti’s theorem. Virtual work principle for deformable bodies. Von Mises and Tresca yield criteria.
Saint-Venant’s problem. Extension, bending, torsion, and shear of beams. Equilibrium differential equations for a beam. Limitations of the theory. Allowable stress. Euler’s critical load.
Effects of imperfect constraints and temperature variations. Mohr’s analogue. Hyperstatic beams. Continuous beams. Analysis of planar trusses and frames by means of virtual work principle, force and displacement methods.

P. Casini, M. Vasta, "Scienza delle costruzioni", Città Studi Edizioni 2016.
Steen Krenk & Jan Høgsberg, "Statics and Mechanics of Structures", Springer 2013.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, 1984.
E. Sacco, Lezioni di Scienza delle Costruzioni, 2016.