Environmental decay in porous masonry materials, such as brick and mortar, is a widespread problem concerning both new and historic masonry structures. The decay mechanisms are quite complex dependng upon several interconnected parameters and from the interaction with the specific micro-climate. Materials undergo aesthetical and substantial changes in character but while many studies have been carried out, the mechanical aspect has been largely understudied while it bears true importance from the structural viewpoint. A quantitative assessment of the masonry material degradation and how it affects the load-bearing capacity of masonry structures appears missing. The research work carried out, limiting the attention to brick masonry addresses this issue through an experimental laboratory approach via different integrated testing procedures, both non-destructive and mechanical, together with monitoring methods. Attention was focused on transport of moisture and salts and on the damaging effects caused by the crystallization of two different salts, sodium chloride and sodium sulphate. Many series of masonry specimens, very different in size and purposes were used to track the damage process since its beginning and to monitor its evolution over a number of years Athe same time suitable testing techniques, non-destructive, mini-invasive, analytical, of monitoring, were validated for these purposes. The specimens were exposed to different aggressive agents (in terms of type of salt, of brine concentration, of artificial vs. open-air natural ageing, …), tested by different means (qualitative vs. quantitative, non destructive vs. mechanical testing, punctual vs. wide areas, …), and had different size (1-, 2-, 3-header thick walls, full-scale walls vs. small size specimens, brick columns and triplets vs. small walls, masonry specimens vs. single units of brick and mortar prisms, …). Different advanced testing methods and novel monitoring techniques were applied in an integrated holistic approach, for quantitative assessment of masonry health state.

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In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After a brief introduction to the subject, the attention is focused on the constitutive relations both for the isotropic and the orthotropic cases. In particular, a novel approach based on energetic arguments , able to automatically select appropriate constitutive relations in accordance with the GBT kinematics, is presented. Furthermore, the concept of consistency of a GBT-based model is introduced and a consistency analysis is conducted. This provides a formal basis to investigate the effects of various families of cross-section deformation modes in terms of predictive capabilities of the GBT model. Later, a new finite element for GBT beams is presented. The element is based on the hybrid complementary energy functional, involving nodal displacements and equilibrating stresses within the element as indipendent variables. Assumed stresses are rationally derived basing on the stresses associated to analytical solutions of some particular cases. The numerical results show the high performance of the proposed element. Subsequently, in the framework of cold-formed stability verification, a verification approach called Embedded Stability Analysis is shown. The verification approach, based on the GBT, is an interesting alternative to the simplified procedures provided by current standards and it is applicable in a simple and general way. A synthetic parameter allows the designer to evaluate when it is more appropriate to consider the distortional effects in thin-walled stability check. Finally, in the framework of cold-formed stability analysis, a new version of the so-called approach ECBL (Erosion of the Critical Load Bifurcation), based on the GBT, is presented. The numerical results show an excellent agreement between the new version ECBL approach and the experimental results.

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Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities. This dissertation, concentrates on some of the fractural aspects of shaft and composite which have being increasingly used in modern structures, consists four chapters within two parts. Chapters 1 to 4 are included in part 1. In the first chapter, the basic knowledge about the stress and displacement fields in the vicinity of a crack tip is introduced. A review involves the general methods of calculating stress intensity factors are presented. In Chapter 2, two simple engineering methods for a fast and close approximation of stress intensity factors of cracked or notched beams under tension, bending moment, shear force, as well as torque are presented. New formulae for calculating the stress intensity factors are proposed. One of the methods named Section Method is improved and applied to the three dimensional analysis of cracked circular section for calculating stress intensity factors. The comparisons between the present results and the solutions calculated by ABAQUS for single mode and mixed mode are studied. In chapter 3, fracture criteria for a crack subjected to mixed mode loading of two-dimension and three-dimension are reviewed. The crack extension angle for single mode and mixed mode, and the critical loading domain obtained by SEDF and MTS are compared. The effects of the crack depth and the applied force ratio on the crack propagation angle and the critical loading are investigated. Three different methods calculating the crack initiation angle for three-dimension analysis of various crack depth and crack position are compared. It should be noted that the stress intensity factors used in the criteria are calculated in section 2.1.

Il presente lavoro di tesi ha riguardato una riformulazione teorica, una modellazione numerica e una serie di applicazioni della Generalized Beam Theory per lo studio dei profili in parete sottile con particolare riguardo ai profili in acciaio formati a freddo. In particolare, in questo lavoro è proposta una riscrittura della cinematica GBT che introduce in una forma originale la deformabilità a taglio della sezione. Tale formulazione consente di conservare il formato della GBT classica e introducendo uno spostamento di warping variabile lungo lo spessore della generica parete della sezione trasversale, garantisce perfetta coerenza tra la componente flessionale e tagliante della trave. E' mostrato, come tale riscrittura consente in maniera agevole di ricondursi alle teorie classiche di trave, anche deformabili a taglio. Inoltre, in tale contesto, è stata messa a punto una procedura di ricostruzione dello sforzo tridimensionale in grado ricostruire la parte reattiva delle componenti di tensioni dovuta al vincolamento interno proprio di un modello a cinematica ridotta. Sulla base di tali strumenti, è stato quindi proposto un approccio progettuale dedicato ai profili in classe 4, definito ESA (Embedded Stability Analysis), in grado di svolgere le verifiche coerentemente con quanto prescritto dalle normative vigenti. Viene infine presentata una procedura numerica per la progettazione di sistemi di copertura formati a freddo. Tale procedura permette di effettuare in pochi semplici passi il progetto dell'arcareccio e dei dettagli costruttivi relativi alla copertura. / The present work has revolved around a theoretical formulation, a numerical model and a series of applications of the Generalized Beam Theory for the analysis of thin walled profiles with particular emphasis on cold-formed steel profiles. In particular, this work presents a revised set of GBT kinematics that introduces in an original form the shear deformability of the section. Such kinematics preserves the classic GBT format and introduces a variable warping displacement along the wall thickness, thus guaranteeing perfect coherence between bending and shear behavior. It is shown how such a formulation permits to easily recover classical beam theories, even those that are shear deformable. Additionally a stress recovery procedure has been presented which allows for tridimensional reconstruction of the reactive components of stress resulting from internal constraints in the kinematics. Based on these procedures, a design approach is proposed for class 4 profiles. This approach is called ESA (Embedded Stability Analysis) and takes into account all aspects of the current code. Finally, a numerical procedure for the design of cold formed profiles is presented. The procedure allows to calculate in few simple steps all structural aspects of a purlin interaction with a roof system.

The inherent stochastic character of most of the physical quantities involved in engineering models has led to an always increasing interest for probabilistic analysis. Many approaches to stochastic analysis have been proposed. However, it is widely acknowledged that the only universal method available to solve accurately any kind of stochastic mechanics problem is Monte Carlo Simulation. One of the key parts in the implementation of this technique is the accurate and efficient generation of samples of the random processes and fields involved in the problem at hand. In the present thesis an original method for the simulation of homogeneous, multi-dimensional, multi-variate, non-Gaussian random fields is proposed. The algorithm has proved to be very accurate in matching both the target spectrum and the marginal probability. The computational efficiency and robustness are very good too, even when dealing with strongly non-Gaussian distributions. What is more, the resulting samples posses all the relevant, welldefined and desired properties of “translation fields”, including crossing rates and distributions of extremes. The topic of the second part of the thesis lies in the field of non-destructive parametric structural identification. Its objective is to evaluate the mechanical characteristics of constituent bars in existing truss structures, using static loads and strain measurements. In the cases of missing data and of damages that interest only a small portion of the bar, Genetic Algorithm have proved to be an effective tool to solve the problem.