Sulla progettazione in zona sismica di strutture dotate di dissipatori fluido-viscosi: proposta di una metodologia

CHAPTER 1:FLUID-VISCOUS DAMPERS In this chapter the fluid-viscous dampers are introduced. The first section is focused on the technical characteristics of these devices, their mechanical behavior and the latest evolution of the technology whose they are equipped. In the second section we report the definitions and the guide lines about the design of these devices included in some international codes. In the third section the results of some experimental tests carried out by some authors on the response of these devices to external forces are discussed. On this purpose we report some technical schedules that are usually enclosed to the devices now available on the international market. In the third section we show also some analytic models proposed by various authors, which are able to describe efficiently the physical behavior of the fluid-viscous dampers. In the last section we propose some cases of application of these devices on existing structures and on new-construction structures. We show also some cases in which these devices have been revealed good for aims that lies outside the reduction of seismic actions on the structures. CHAPTER 2:DESIGN METHODS PROPOSED IN LITERATURE In this chapter the more widespread design methods proposed in literature for structures equipped by fluid-viscous dampers are introduced. In the first part the response of sdf systems in the case of harmonic external force is studied, in the last part the response in the case of random external force is discussed. In the first section the equations of motion in the case of an elastic-linear sdf system equipped with a non-linear fluid-viscous damper undergoing a harmonic force are introduced. This differential problem is analytically quite complex and it’s not possible to be solved in a closed form. Therefore some authors have proposed approximate solution methods. The more widespread methods are based on equivalence principles between a non-linear device and an equivalent linear one. Operating in this way it is possible to define an equivalent damping ratio and the problem becomes linear; the solution of the equivalent problem is well-known. In the following section two techniques of linearization, proposed by some authors in literature, are described: the first technique is based on the equivalence of the energy dissipated by the two devices and the second one is based on the equivalence of power consumption. After that we compare these two techniques by studying the response of a sdf system undergoing a harmonic force. By introducing the equivalent damping ratio we can write the equation of motion of the non-linear differential problem in an implicit form, by dividing, as usual, for the mass of the system. In this way, we get a reduction of the number of variables, by introducing the natural frequency of the system. The equation of motion written in this form has two important properties: the response is linear dependent on the amplitude of the external force and the response is dependent on the ratio of the frequency of the external harmonic force and the natural frequency of the system only, and not on their single values. All these considerations, in the last section, are extended to the case of a random external force. CHAPTER 3: DESIGN METHOD PROPOSED In this chapter the theoretical basis of the design method proposed are introduced. The need to propose a new design method for structures equipped with fluid-viscous dampers arises from the observation that the methods reported in literature are always iterative, because the response affects some parameters included in the equation of motion (such as the equivalent damping ratio). In the first section the dimensionless parameterε is introduced. This parameter has been obtained from the definition of equivalent damping ratio. The implicit form of the equation of motion is written by introducing the parameter ε, instead of the equivalent damping ratio. This new implicit equation of motions has not any terms affected by the response, so that once ε is known the response can be evaluated directly. In the second section it is discussed how the parameter ε affects some characteristics of the response: drift, velocity and base shear. All the results described till this point have been obtained by keeping the non-linearity of the behavior of the dampers. In order to get a linear formulation of the problem, that is possible to solve by using the well-known methods of the dynamics of structures, as we did before for the iterative methods by introducing the equivalent damping ratio, it is shown how the equivalent damping ratio can be evaluated from knowing the value of ε. Operating in this way, once the parameter ε is known, it is quite easy to estimate the equivalent damping ratio and to proceed with a classic linear analysis. In the last section it is shown how the parameter ε could be taken as reference for the evaluation of the convenience of using non-linear dampers instead of linear ones on the basis of the type of external force and the characteristics of the system. CHAPTER 4: MULTI-DEGREE OF FREEDOM SYSTEMS In this chapter the design methods of a elastic-linear mdf system equipped with non-linear fluidviscous dampers are introduced. It has already been shown that, in the sdf systems, the response of the structure can be evaluated through the estimation of the equivalent damping ratio (ξsd) assuming the behavior of the structure elastic-linear. We would to mention that some adjusting coefficients, to be applied to the equivalent damping ratio in order to consider the actual behavior of the structure (that is non-linear), have already been proposed in literature; such coefficients are usually expressed in terms of ductility, but their treatment is over the aims of this thesis and we does not go into further. The method usually proposed in literature is based on energy equivalence: even though this procedure has solid theoretical basis, it must necessary include some iterative process, because the expression of the equivalent damping ratio contains a term of the response. This procedure has been introduced primarily by Ramirez, Constantinou et al. in 2000. This procedure is reported in the first section and it is defined “Iterative Method”. Following the guide lines about sdf systems reported in the previous chapters, it is introduced a procedure for the assessment of the parameter ε in the case of mdf systems. Operating in this way the evaluation of the equivalent damping ratio (ξsd) can be done directly without implementing iterative processes. This procedure is defined “Direct Method” and it is reported in the second section. In the third section the two methods are analyzed by studying 4 cases of two moment-resisting steel frames undergoing real accelerogramms: the response of the system calculated by using the two methods is compared with the numerical response obtained from the software called SAP2000-NL, CSI product. In the last section a procedure to create spectra of the equivalent damping ratio, affected by the parameter ε and the natural period of the system for a fixed value of exponent α, starting from the elasticresponse spectra provided by any international code, is introduced.

Studio di ausili tecnologici compensativi di supporto all'iter di apprendimento matematico secondario e universitario degli studenti con dislessia

Data coming out from various researches carried out over the last years in Italy on the problem of school dispersion in secondary school show that difficulty in studying mathematics is one of the most frequent reasons of discomfort reported by students. Nevertheless, it is definitely unrealistic to think we can do without such knowledge in today society: mathematics is largely taught in secondary school and it is not confined within technical-scientific courses only. It is reasonable to say that, although students may choose academic courses that are, apparently, far away from mathematics, all students will have to come to terms, sooner or later in their life, with this subject. Among the reasons of discomfort given by the study of mathematics, some mention the very nature of this subject and in particular the complex symbolic language through which it is expressed. In fact, mathematics is a multimodal system composed by oral and written verbal texts, symbol expressions, such as formulae and equations, figures and graphs. For this, the study of mathematics represents a real challenge to those who suffer from dyslexia: this is a constitutional condition limiting people performances in relation to the activities of reading and writing and, in particular, to the study of mathematical contents. Here the difficulties in working with verbal and symbolic codes entail, in turn, difficulties in the comprehension of texts from which to deduce operations that, once combined together, would lead to the problem final solution. Information technologies may support this learning disorder effectively. However, these tools have some implementation limits, restricting their use in the study of scientific subjects. Vocal synthesis word processors are currently used to compensate difficulties in reading within the area of classical studies, but they are not used within the area of mathematics. This is because the vocal synthesis (or we should say the screen reader supporting it) is not able to interpret all that is not textual, such as symbols, images and graphs. The DISMATH software, which is the subject of this project, would allow dyslexic users to read technical-scientific documents with the help of a vocal synthesis, to understand the spatial structure of formulae and matrixes, to write documents with a technical-scientific content in a format that is compatible with main scientific editors. The system uses LaTex, a text mathematic language, as mediation system. It is set up as LaTex editor, whose graphic interface, in line with main commercial products, offers some additional specific functions with the capability to support the needs of users who are not able to manage verbal and symbolic codes on their own. LaTex is translated in real time into a standard symbolic language and it is read by vocal synthesis in natural language, in order to increase, through the bimodal representation, the ability to process information. The understanding of the mathematic formula through its reading is made possible by the deconstruction of the formula itself and its “tree” representation, so allowing to identify the logical elements composing it. Users, even without knowing LaTex language, are able to write whatever scientific document they need: in fact the symbolic elements are recalled by proper menus and automatically translated by the software managing the correct syntax. The final aim of the project, therefore, is to implement an editor enabling dyslexic people (but not only them) to manage mathematic formulae effectively, through the integration of different software tools, so allowing a better teacher/learner interaction too.