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.
teacher profile teaching materials
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.
Programme
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.
Core Documentation
Notes written by the teacher. Files employed for the lectures are published on the “moodle” page of the course.Reference Bibliography
Reference texts are given in the bibliography of the notes; in particular, the students may consult the following textbooks: - L. Boscotrecase - A. Di Tommaso, Statica applicata alle costruzioni, Patron, Bologna, 2012. - P. Podio-Guidugli, Lezioni di Statica, Aracne, Roma, 2014. - E. Viola, Lezioni di Scienza delle Costruzioni, Pitagora, Bologna, 2003. - V. Franciosi, Fondamenti di Scienza delle Costruzioni, Volume II, Liguori, Napoli, 1987. - V. Franciosi, Problemi di Scienza delle Costruzioni, Volume I, Liguori, Napoli, 1975. - E. Viola, Esercitazioni di Scienza delle Costruzioni, Volumi I e II, Pitagora, Bologna, 1993.Type of delivery of the course
Lessons concern theory and applications. The "moodle" learning platform is used to offer additional didactic material to the students and to give them the possibility of developing discussions with the teacher.Type of evaluation
The final evaluation of the students is made by means of a written test, usually regarding applications, and an oral examination, more oriented towards the theoretical fundaments. The evaluation has the objective of verifying that the students are able to determine stress resultants, stresses and deformations in simple structures, and that they possess the basic knowledge needed for subsequent structural courses.