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.

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.

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 non-orthogonal beams. 2. BI- AND TRI-DIMENSIONAL STRUCTURES: Beams with rectilinear and curvilinear axes: static-kinematic duality. Beam on elastic foundation. Plates in flexure: static-kinematic duality. Sophie-Germain 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, Ritz-Galerkin method, Principle of Virtual Work. 3. DYNAMICS OF STRUCTURES AND FUNDAMENTALS OF PLASTICITY: Single-degree-of-freedom linear systems. Free response. Damped response. Forced response to harmonic, periodic, impulsive or generic excitations. Non-linear elastic oscillator. Elasto-plastic oscillator. Multi-degree-of-freedom linear systems: modal analysis. Rayleigh’s quotient. Stodola-Vianello 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.

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 shear-type 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-, bi-and tri-dimensional model); (8) modal analysis of plane and space frames; (9) Modal analysis of continuous systems (arc, circular plate, hemispherical dome).

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”, McGraw-Hill, Singapore, 1959. As regards numerical and analytical practice lessons, the material will be uploaded on the teaching portal from time to time.

Exam: Written test; Compulsory oral exam;

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.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.