


Politecnico di Torino  
Academic Year 2017/18  
01CFOMC Structural Mechanics 

1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Torino 





Subject fundamentals
This course operates as an hinge between the basic subjects (mathematics and physics) and the subjects taught in the following academic terms, which are oriented to design and applications. The goal of the course is to provide basical theoretical principles which, if well understood and applied, allows the student to analyse the mechanical behaviour of elastic solids and in particular of plane beam systems.

Expected learning outcomes
The student have to be able to determine the support reactions, tension, shear and bending diagrams and deflection curve for a statically determinate plane system of beams; to determine stress fields in a beam according to De Saint Venant's principle; to apply failure criteria in a triaxial state of stress; to verify a reinforced concrete beam under bending; to verify a slender column under compression.

Prerequisites / Assumed knowledge
The student have to know the kinematic, static and dynamic theory of the material point, vectorial operations (sum, scalar multiply, inner product, cross product), matrix operations, basic issues of linear algebra, analytic geometry, differential geometry. With reference to functions of one variable the students have to know the concept of limit, differentiation rules, integration rules, Taylor series and solution techniques of differential equations in case of constant coefficients. With reference to functions of several variables the students have to know differentiation rules, integration rules and Taylor series.

Contents
The basic topics of geometry of areas and of kinematics and statics of rigid body systems The mechanics of linear elastic solids −beams, plates, and threedimensional solids− examined using a matrix approach. The analysis of strain and stress around a material point. The linear elastic constitutive law, with related Clapeyron's and Betti's theorems. Kinematic, static, and constitutive equations. The implication of the principle of virtual work. The De Saint Venant’s problem. The theory of beam systems, statically determinate or indeterminate. Methods of forces and energy for the examination of indeterminate beam systems. Elastic buckling of columns (Euler’s formula). Reinforced concrete beams under bending.

Delivery modes
Practical classes:
Geometry of areas; Kinematics and statics of rigid body systems; Statically determinate beam systems; Thrust line; Beams subjected to combined uniform and nonuniform axial, flexure, shear, and torsional loads; Statically indeterminate beam systems; Determination of elastic displacements; Thermal loads and imposed displacements; Reinforced concrete beams under bending. 
Texts, readings, handouts and other learning resources
Texts:
 Carpinteri, A. (1992) Scienza delle Costruzioni, Voll. 1 e 2, Pitagora, Bologna.  Carpinteri, A. (1997) Structural Mechanics: A Unified Approach, E. & F.N. Spon, London.  Carpinteri, A., Lacidogna, G., Paggi, M. (2009) Calcolo delle Strutture Isostatiche, Pitagora, Bologna.  Carpinteri, A., Lacidogna, G., Surace, C. (2002) Calcolo dei Telai Piani, Pitagora, Bologna. Readings:  Belluzzi, O. (1966) Scienza delle Costruzioni, Vol. 1, Zanichelli, Bologna.  Benvenuto, E. (1981) La Scienza delle Costruzioni ed il suo Sviluppo Storico, Sansoni, Firenze.  Bertero, M., Grasso, S. (1984) Esercizi di Scienza delle Costruzioni, Levrotto & Bella, Torino.  Capurso, M. (1971) Lezioni di Scienza delle Costruzioni, Pitagora, Bologna.  Corradi Dell’Acqua, L. (2010) Meccanica delle Strutture, Voll. 1, 2 e 3, Mc GrawHill, Milano.  Timoshenko, S.P., Goodier, J.N. (1970) Theory of Elasticity, Mc GrawHill, Auckland.  Viola, E. (1985) Esercitazioni di Scienza delle Costruzioni, Voll.1 e 2, Pitagora, Bologna. 
Assessment and grading criteria
The exam consists of a written test and an oral test. The written test is based on the solution of problems similar to those discussed during the practical classes. The themes developed from past exams are available through the website of the course.
The written test includes a statically determinate beam system, a statically indeterminate beam system, and the determination of principal axes of inertia and stresses in the section of a De Saint Venant solid. The oral test is based on two or three theoretical questions. 
