


Politecnico di Torino  
Academic Year 2017/18  
01RVRMX Structural Mechanics II 

Master of sciencelevel of the Bologna process in Civil Engineering  Torino 





Subject fundamentals
The course aims to improve and deepen the basic knowledge acquired in the course of Structural Mechanics at the Bachelor Degree. The fundamental tools necessary for the advanced modeling of the mechanical behavior of materials and structures will be provided. The student will study highly statically indeterminate beamframed structures, will learn the basic concepts for the analysis of bidimensional elements (plates and shells) and will face the basic concepts of dynamics 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 from the bachelor mathematical courses (Mathematical Analysis 1 and 2, Geometry, Linear Algebra, Analytical Mechanics, Numerical Methods) and engineering courses (Structural Mechanics: study of isostatic and statically indeterminate structures by the force method, differential equation of the elastica) are required.

Contents
1. ONEDIMENSIONAL STRUCTURES. Statically Indeterminate Structures: Method of forces, Method of displacements, mixed Method. Structural symmetry. Rotating and translatingnode frames. Thermal loads and imposed displacements. Frames with nonorthogonal beams. Stiffness matrix of the beam. Automatic computation of beam systems. Beams with curvilinear axes. Beam on elastic foundation.
2. BIDIMENSIONAL STRUCTURES: Plane stress and plane strain. Plates loaded in their plane: plates with a circular hole; concentrated force acting on a semiinfinite plane. Plates loaded orthogonally to their plane: Sophie Germain equation for plates in bending, boundary conditions. Symmetrically loaded shells of revolution: membranes and thin shells, circular plates, cylindrical shells. 3. DYNAMICS OF STRUCTURES: 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. Continuous systems: modal analysis of deflected beams. Dynamics of beam systems. 
Delivery modes
Approximately three fourth of the lectures are given in classroom (mainly at blackboard) whereas one fourth are held at LAIB to learn the use of a finite element software. This allows the student to check the results obtained analytically during the course. 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 textbook:
 A. Carpinteri, "Advanced Structural Mechanics", CRC Press, 2017. (Chapter 1 to 6) Recommended books: – A. Carpinteri, "Structural Mechanics Fundamentals", CRC Press, 2013. (it covers what students are expected to know from the bachelor course in structural mechanics) A. Carpinteri, G. Lacidogna, C. Surace, "Calcolo dei telai piani – Esempi ed esercizi", Pitagora Editrice, Bologna, 2002 (useful for the written examination). S. Timoshenko, "Theory of Plates and Shells", McGrawHill, Singapore, 1959. (worldwide known structural mechanics book) As regards numerical and analytical practice lessons, material will be uploaded on the teaching internet site. 
Assessment and grading criteria
The exam consists in a written exercise on statically indeterminate frames and in an oral examination on the theoretical topics. The overcoming of the writing part is a necessary condition to access the oral examination. During the written exam, it is forbidden to use cell phones, programmable calculators, books, texts, notes (except the formulary provided during the course). Oral questions will assess the knowledge level and the scientific language of student. Furthermore, a numerical examination will be carried out to check 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.

