


Politecnico di Torino  
Academic Year 2017/18  
03CFPMX Structural Mechanics II 

Master of sciencelevel of the Bologna process in Civil Engineering  Torino 





Subject fundamentals
The course aims to improve and deepen the basics acquired from the course of Structural Mechanics.
The fundamental tools necessary for the advanced modeling of the mechanical behavior of materials and structures will be provided. The student will improve the study of statically indeterminate beamframed structures, he will learn the basic concepts for the analysis of biand tridimensional elements (plates and shells) and he will face the basic concepts of dynamics and plasticity of beam systems. 
Expected learning outcomes
The student will have to deepen the analytical and numerical topics presented during lectures, starting from the basic equations and choosing, for each problem, the most appropriate methodology to get the solution. The student must possess an appropriate scientific language.
The knowledge of a finite element code will help the student to understand the difficulties for scientific/professional modeling. 
Prerequisites / Assumed knowledge
Fundamental notions on the basic mathematical courses (Analysis 1 and 2, Geometry, Analytical Mechanics, Numerical Methods: solution of ordinary and partial differential equations, eigenvalue/eigenvector problems ; statics, kinematics and dynamics of rigid bodies,..) and engineering courses (Structural Mechanics, Structural Engineering: study of isostatic and statically indeterminate structures by the force method, differential equation of the elastic line; static, kinematic and constitutive equations for the beam; curve pressures, elastic and plastic behavior of materials,..) are required.

Contents
The course is divided homogeneously into three major topics (about 28 hours for each topic): 1. STATICALLY INDETERMINATE STRUCTURES: Method of displacements: automatic computation of beam systems. Plane trusses, plane frames, plane grids and space frames. Structural symmetry. Rotating and translating frames. Thermal loads and imposed displacements. Frames with nonorthogonal beams. 2. BI AND TRIDIMENSIONAL STRUCTURES: Beams with rectilinear and curvilinear axes: statickinematic duality. Beam on elastic foundation. Plates in flexure: statickinematic duality. SophieGermain equation with boundary conditions. Shells with double curvature. Symmetrically loaded shells of revolution: membranes and thin shells, circular plates, cylindrical shells. Finite Element Method: Principle of minimum potential energy, RitzGalerkin method, Principle of Virtual Work. 3. DYNAMICS OF STRUCTURES AND FUNDAMENTALS OF PLASTICITY: Singledegreeoffreedom linear systems. Free response. Damped response. Forced response to harmonic, periodic, impulsive or generic excitations. Nonlinear elastic oscillator. Elastoplastic oscillator. Multidegreeoffreedom linear systems: modal analysis. Rayleigh’s quotient. StodolaVianello method. Continuous systems: modal analysis of deflected beams. Membranes and plates in vibration. Finite Element Method. Dynamics of beam systems. Element of Seismic Engineering, Italian Code and practical concepts for earthquake design. Incremental plastic analysis. 
Delivery modes
Approximately one fourth of the lectures is held at LAIB to learn a finite element software. This allows the student to verify the results introduced from an analytical point of view. These lessons cover: (1) introduction of a finite element analysis on PC, thin or thick beam elements; (2) calculation of plane frames and trusses; (3) calculation of sheartype and spatial frames; (4) calculation of rectangular thin plates; (5) calculation of circular plates and hemispherical domes; (6) calculation of beam on elastic foundation and hydrostatic tanks; (7) free vibrations of a cantilever beam (mono, biand tridimensional model); (8) modal analysis of plane and space frames; (9) Modal analysis of continuous systems (arc, circular plate, hemispherical dome).

Texts, readings, handouts and other learning resources
Official textbooks:
A. Carpinteri, "Scienza delle Costruzioni 1", Pitagora Editrice, Bologna, 1992. A. Carpinteri, "Scienza delle Costruzioni 2", Pitagora Editrice, Bologna, 1992. A. Carpinteri, "Dinamica delle Strutture", Pitagora Editrice, Bologna, 1998. Recommended books: – A. Carpinteri, "Structural Mechanics: A Unified Approach", Chapman & Hall, London, 1997. A. Carpinteri, G. Lacidogna, C. Surace, "Calcolo dei telai piani – Esempi ed esercizi", Pitagora Editrice, Bologna, 2002. E. Benvenuto, "La Scienza delle Costruzioni e il suo sviluppo storico", Manuali Sansoni, Firenze, 1981 S. Timoshenko, "Theory of Plates and Shells", McGrawHill, Singapore, 1959. As regards numerical and analytical practice lessons, the material will be uploaded on the teaching portal from time to time. 
Assessment and grading criteria
The exam consists in a written exercise on statically indeterminate frames and in a oral examination on the theoretical topics. The overcoming of the writing part reveals to be a necessary condition to access the oral examination. During the written exam, it is forbidden to use cell phones, programmable calculators, books, texts, notes. Oral questions will voted to verify the level of study and of the scientific language.
Furthermore, a numerical examination will be carried out to verify the knowledge of the finite element code. The final mark will properly take into account the results obtained in both the oral and the written tests. 
