Unit ADVANCED STRUCTURAL MECHANICS

DYNAMICS OF STRUCTURES

Code	A006273
CFU	6
Teacher	Federico Cluni
Teachers	Federico Cluni
Hours	48 ore - Federico Cluni
Learning activities	Caratterizzante
Area	Ingegneria civile
Sector	CEAR-06/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	English
Contents	Dynamics of single-degree-of-freedom systems. Free and forced vibrations. Response to arbitrary forces. Response spectrum. Equation of motion of multi-degree-of-freedom systems. Modal shapes and pulsations. Modal analysis. Applications to seismic analysis. Equation of motion of the beam and taut string. Modal shapes and pulsations of beam and taut string.
Reference texts	* English books - A. Chopra, "Dynamics of Structures", Prentice Hall - R.W. Clough, J. Penzien, "Dynamics of Structures", McGraw-Hill - A. Zingoni, "Vibration Analysis and Structural Dynamics for Civil Engineers", CRC Press * Italian books - L. Facchini, "Elementi di Dinamica delle Strutture", Editrice Esculapio - I. Iervolino, "Dinamica delle strutture e ingegneria sismica. Principi e applicazioni", Hoepli - G. Muscolino, "Dinamica delle strutture", McGraw-Hill (out of print, copies at the Engineering Library) - C. Gavarini, "Dinamica delle strutture", ESA (out of print, copies at the Engineering Library)
Educational objectives	The course presents the base elements and the conceptual and analytical tools for the study of the dynamics of the structures in civil engineering. The main aim of the course is to provide students with the conceptual bases and the the instruments to study the dynamics of the structures in civil engineering, with a particular reference to those responding linearly to the actions. Main knowledge acquired will be: - comprehension of the behavior of single-degree-of-freedom systems. - response in free and forced vibration. - response to arbitrary forces. - meaning and use of response spectrum - comprehension of the behavior of multi-degree-of-freedom systems - features of pulsations and modal shapes. - knowledge of modal analysis. - comprehension of the behavior of beams and taut strings. The main competence (i.e. the ability to apply the acquired knowledge) will be: - study the response of single-degrre-of-freedom system to arbitrary force. - find the pulsations and modal shapes of a multi-degree-of-freedom system. - apply the modal analysis to obtain the response under arbitrary forces. - find the response under seismic actions by means of response spectrum. - find the pulsations and modal shapes of a continuous system, beam or taut string.
Prerequisites	The Course is in the first year. The topics of the Course require the ability to solve ordinary and partial differential equations and simpe integrals. Knowledge of these techniques represents a mandatory prerequisite for students planning to follow the course with profit.
Teaching methods	The course is organized as follows: - Face-to-face lectures on all subjects of the course. The lecture notes will be available at: https://www.unistudium.unipg.it/unistudium/
Other information	-
Learning verification modality	The exam consists of an oral test consisting on an interview about half an hour long, aiming to ascertain the knowledge level and the understanding capability acquired by the student on theoretical and methodological contents as indicated on the program (elementary oscillator, discrete systems, continuous systems). The oral exam will also test the student communication skills and his autonomy in the organization and exposure of the theoretical topics and case studies. For information on support services for students with disability and/or specific learning disorders visit the page http://www.unipg.it/disabilita-e-dsa
Extended program	Single-degree-of-freedom system The laws of motion. Principle of D'Alembert. Undamped free oscillations. Free and forced oscillations with damping. Harmonic forces. Amplification factor and phase shift. Resonance. Power dissipated by the damper. Pseudo-acceleration. Response spectrum. Base displacements. Accelerometers and seismometers. Response to arbitrary force. Duhamel's integral. Solution with Fourier series. Nonlinearity: nonlinear damping (hysteresis and friction). Oscillator with nonlinear (elastic-plastic) reaction. Multi-degree-of-freedom systems Equations of motion for discrete systems. Solution in free oscillations. Properties of the eigenvectors: natural modes. Normal and principal coordinates. Modal Analysis. Rayleigh's damping. Applications of modal analysis. Modal participation factors. Modal contribution factors. Respone to base displacements. Modal analysis for seismic actions (response spectrum analysis). Push-over analysis. Mass participation factors. Continuous systems Equation of motion of the beam and taut string. Free oscillations of the beam. Mode orthogonality. Examples: simply supported beam, cantilever. Forced oscillations of the beam. Influence of axial force on the modes. Oscillations of the taut string. Respone to base displacements. Applications of structural engineering: base isolation, tuned mass dampers, suspension bridges, soil-structure interaction.
Obiettivi Agenda 2030 per lo sviluppo sostenibile

STRUCTURAL PLASTICITY AND STABILITY

Code	A006274
CFU	9
Teacher	Federico Cluni
Teachers	Federico Cluni
Hours	72 ore - Federico Cluni
Learning activities	Caratterizzante
Area	Ingegneria civile
Sector	CEAR-06/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	English
Contents	Plasticity. Yield criteria. Postulates of plasticity. Limit analysis with applications to frame structures. Plane problems. Structural stability
Reference texts	* English books - R. Hill, "The mathematical Theory of Plasticity", Oxford Classic Texts - W.F. Chen, D.J. Han, "Plasticity for structural engineers", Springer - G.J. Simitses, D.H. Hodges "Fundamentals of Structural Stability", Elsevier Butterworth-Heinemann * Italian books - R. Baldacci, G. Ceradini, E. Giangreco, "Plasticità", Cisia - R. Baldacci, G. Ceradini, E. Giangreco, "Dinamica e stabilità", Italsider
Educational objectives	The course presents the base elements and the conceptual and analytical tools for the study of the civil engineering structures in the elasto-plastic range and the evaluation of the safety of structures with regards to instability. Main knowledge acquired will be: - modeling of the behavior of materials in elasto-plastic range; - use and limits of the main yield criteria; - limit analysis, both with upper- and lower-bound approaches; - modeling of plane problems; - stability of structural elements and structures. The main competence (i.e. the ability to apply the acquired knowledge) will be: - estimation of critical load of structural elements; - estimation of the collapse load and the collapse mechanism of structures; - assessment of the strains/stresses in plane problems; - estimation of instability load.
Prerequisites	The Course is in the first year. The topics of the Course require the ability to solve ordinary and partial differential equations and simple integrals. Moreover it is required the of structural mechanics and strength of materials (mechanics of solids materials, stress analysis, strain analysis, linear elasticity, mechanics of beam). Knowledge of these techniques represents a mandatory prerequisite for students planning to follow the course with profit.
Teaching methods	The course is organized as follows: - Face-to-face lectures on all subjects of the course. The lecture notes will be available at: https://www.unistudium.unipg.it/unistudium/
Other information	-
Learning verification modality	The exam consists of an oral test consisting on an interview about half an hour long, aiming to ascertain the knowledge level and the understanding capability acquired by the student on theoretical and methodological contents as indicated on the program (plastic analysis, limit analysis, plane problems, instability). The oral exam will also test the student communication skills and his autonomy in the organization and exposure of the theoretical topics and case studies. For information on support services for students with disability and/or specific learning disorders visit the page http://www.unipg.it/disabilita-e-dsa
Extended program	Plasticity. Yelding Function. Description of the Yelding Function. Deviatoric stresses. Yeld criteria: Rankine, Grashof, Tresca, Huber-Von Mises-Hencky, Hill, Coulomb, Drucker-Prager. Constitutive relations. Elasto-plastic material. Levy-Mises equations. Prandtl-Reuss equations. Stable material (Drucker). Postulates of plasticity. Plastic potential, convexity, normality. Limit analysis. Lower bound theorem. Upper bound theorem. Elasto-plastic internal forces. Plastic hinge. Application of limit analysis to frame structures. Plane problems. Strain plane problem. Stress plane problem. Generalized plane problem. Mechanics of cable. Mechanics of membrane and plate. Structural stability. Influence of shear deformability. Influence of imperfections. Elasto-plastic analysis of stability.
Obiettivi Agenda 2030 per lo sviluppo sostenibile