Fiber-reinforced polymeric (FRP) composites are being considered for structural members in bridge construction as lighter, more durable alternatives to steel and concrete. Extensive testing and analysis of a pultruded, hybrid double web beam (DWB) developed for use in bridge construction has been conducted at Virginia Tech. A primary purpose of this testing is the development of a structural design guide for the DWB, which includes stiffness and strength data. The design manual also includes design allowables determined through a statistical analysis of test data. Static testing of the beams, including failure tests, has been conducted in order to determine such beam properties as bending modulus, shear stiffness, failure mode, and ultimate capacity. Measuring and calculating the shear stiffness has proven to be an area of particular interest and difficulty. Shear stiffness is calculated using Timoshenko beam theory which combines the shear stiffness and shear area together along with a shear correction factor, k, which accounts for the nonuniform distribution of shear stress/strain through the cross-section of a structure. There are several methods for determining shear stiffness, kGA, in the laboratory, including a direct method and a multi-span slope method. Herein lays the difficulty as it has been found that varying methods produces significantly different results. One of the objectives of current research is to determine reasons for the differences in results, to identify which method is most accurate in determining kGA, and also to examine other parameters affecting the determination of kGA that may further aid the understanding of this property. This document will outline the development of the design guide, the philosophy for the selection of allowables and review and discuss the challenges of interpreting laboratory data to develop a complete understanding of shear effects in large FRP structural members. / Master of Science

Studies on the effective moment of inertia of girders that support concrete slabs using joist seats as the horizontal shear connections, and a cost efficiency analysis comparing composite and non-composite floor systems that meet vibrations design standards, were conducted. The first study was undertaken because over-prediction of girder effective moment of inertia was the suspected cause of several recent vibration problems in floors supported by widely spaced LH-series joists. Eight purpose-built floors of the type in question were subjected to experimental tests of girder effective moment of inertia and girder frequency. Frequencies were tested for two live loading cases. Three separate test configurations were made with each floor by changing the seat-to-girder connections between bolted, welded, and reinforced. In the study, 1) the accuracy of the current design practice is assessed, 2) a new relationship was proposed, and 3) suggestions for finite element modeling are made. In recent years, composite construction has been used to improve cost efficiency by reducing structural weight and in some cases by reducing story height. However, vibration problems are a design consideration in composite floors because lighter floors tend to be more lively. It is not clear if cost savings can be made with composite construction if vibrations are considered in the design. To compare the cost of composite and non-composite floors that satisfy AISC/CISC Design Guide criterion for walking excitation, four typical size bays were analyzed using commercial design software that finds the least expensive member configuration for a given bay size. All acceptable bay configurations of member sizes and spacing were evaluated for least non-composite and composite costs, then these results were compared. The findings show that composite construction can be more economical when initial dead load deflections do not control the design. / Master of Science

Twenty cantilever diaphragm tests were performed in the Structures and Materials Laboratory at Virginia Tech. The tests included both deep deck and cellular deck profiles with varying structural and side-lap connections. The tests were conducted with three different structural connections: screws, pins and welds and two different side-lap connections: screws and button punch. The tests were conducted and both load and deflection of the diaphragms were recorded. The current International Code Council, ICC, evaluation procedure shows that there are two different methods for measuring diaphragm deflection. The first method was by measuring specific corner displacements and making corrections to remove any rigid body motion. The second method is by measuring the deflection of the diagonals of the diaphragm. In this study both measurements were taken to do a comparison of the results that were obtained. Both strength and stiffness values were calculated based on the Steel Deck Institute (SDI) Diaphragm Design Manual (2004) and modifications described by Luttrell (2005). The paper by Luttrell (2005) only recommends modifications for the calculation of diaphragm stiffness. The data obtained from the tests were compared to the SDI calculations to distinguish any noticeable trends. Modifications are recommended regarding diaphragm strength and further research is suggested to create a better stiffness prediction of diaphragms. / Master of Science

Tow-placement machines have made it possible to manufacture curved-fiber composite tow paths. A composite structure with curved-fiber tow paths can be formed in a manner similar to filament winding. The result is a laminate with spatially varying stiffness and response. This manufacturing method can also result in overlap regions between adjacent tow paths. In previous research, a closed-form solution was developed to determine the response of these variable-stiffness laminates, but the overlap regions were not included in this model. Additionally, the fiber-orientation angle throughout the panel was based on individual fiber path definitions and not tow path definitions. In this thesis, a method of creating a finite element model of tow-placed variable-stiffness composite panels is presented. This method provides a representation of the overlap regions and an accurate model of the fiber-orientation angle change throughout the laminate. The GENESIS finite element analysis and design package is used to solve for the static response of the models created. The results of these analyses compare favorably with the results of the previous research and give some insight into the interaction of the thickness and fiber-orientation variation. Additionally, some of the advanced design capabilities of the finite element modeling method, and some results of those designs are demonstrated. / Master of Science

No / Closed-form expressions are derived for the torsional stiffness, radial stiffness and tilting stiffness of annular rubber flanged bushes of finite length in three principal modes of deformation, based upon the classical theory of elasticity. Illustrative numerical results are deduced with realistic physical data of typical flanged bushes.

No / This paper presents a series of test results of elliptical concrete filled steel tubular (CFST) beams and columns to explore their performance under bending and compression. A total of twenty-six specimens were tested, including eight beams under pure bending and eighteen columns under the combination of bending and compression. The main parameters were the shear span to depth ratio for beams, the slenderness ratio and the load eccentricity for columns. The test results showed that the CFST beams and columns with elliptical sections behaved in ductile manners and were similar to the CFST members with circular sections. Finally, simplified models for predicting the bending strength, the initial and serviceability-level section bending stiffness of the elliptical CFST beams, as well as the axial and eccentric compressive strength of the composite columns were discussed.

<p>Detta examensarbete har utförts på Fläktwoods AB i Växjö, som producerar stora axialfläktar för olika industriapplikationer. Syftet är att öka kunskapen om fettsmorda axiella kullager genom FE analyser.</p><p>Projektet har genomförts i fem delsteg för att avgöra påverkan av en eller några få parametrar i taget. De studerade parametrarna är: elementstorlek, kontaktstyvhet, last, lagergeometri (dvs. oskulation), ickelinjär geometri och ickelinjära materialegenskaper (dvs. plasticitet).</p><p>Slutsatsen är att elementstorleken bör väljas fint nog för att ge ett jämnt resultat men grovt nog för att beräkningstiden skal vara rimlig. Kontaktstyvheten har inte stor, men tydlig, inverkan på kontakttrycket och penetrationen. Förändringar av oskulationen leder till förändringar i kontaktellipsens form medan olika laster inte påverkar formen på ellipsen, utan snarare storleken. När det handlar om plasticitet är sträckgränsen den viktigaste faktorn att beakta.</p> / <p>This thesis project was carried out at Fläktwoods AB in Växjö who produces large axial fans for different industry applications. The purpose is to increase the knowledge of grease lubricated axial ball bearings through FE analyses.</p><p>The project was executed into five sub steps to determine the influence of one or few parameters at a time. The studied parameters are: mesh density, contact stiffness, load, bearing geometry (i.e. osculation), geometrical nonlinearity and material nonlinearity (i.e. plasticity).</p><p>It is concluded that the mesh density should be selected fine enough to give a smooth result but course enough to give a reasonable calculation time. The contact stiffness has not a major, but a clear, impact on the contact pressure and penetration. Changes of the osculation lead to changes of the contact ellipse shape and applying different load level does not affect the shape of the ellipse but rather the size. When dealing with plasticity the yield strength is the most important factor to take in consideration.</p>

: Les travaux présentés dans cette thèse traitent du contrôle de systèmes dynamiques soumis à des excitations harmoniques et transitoires en utilisant des absorbeurs de type Nonlinear Energy Sink (NES). Plusieurs aspects ont été développés : la conception et la réalisation d'un nouveau design pour le NES cubique, l'étude de la location et du transfert irréversible d'énergie sur un NES bistable et le développement d'un critère de conception pour un NES à Vibro-Impact (VI). Dans un premier temps, un critère de conception est proposé pour le NES à raideur cubique. Le design proposé est basé sur des ressorts coniques ou des ressorts à pas variable. Un mécanisme à raideur négative est aussi introduit pour supprimer la partie linéaire et avoir une raideur cubique pure. Dans un deuxième temps, le concept du NES est validé expérimentalement par des essais statiques et des essais dynamiques. Une analyse de sensibilité est aussi menée sur la longueur des ressorts précontraints, elle dénote parfois un état bistable de l'oscillateur. Ensuite, le NES bistable ainsi obtenu est étudié plus en détail. Ce type d'absorbeur s'avère être très robuste pour différents types d’excitation. Des études expérimentales sont aussi menées afin d'explorer le comportement dynamique. Enfin, un critère de conception est proposé pour le NES à Vibro-Impact. Des calculs analytiques détaillés sont proposés pour contrôler les vibrations sous différentes excitations. L'étude expérimentale montre une bonne cohérence avec les résultats théoriques. / The work presented in this thesis deals with the passive control of dynamics systems subjected to harmonic and transient excitations using a Nonlinear Energy Sink (NES). Several research aspects have been developed: design theory and experimental study of a novel NES, efficient Targeted Energy Transfer (TET) of bistable NES and design criteria for optimally tuned Vibro-Impact (VI) NES. Firstly, a design criterion intended to provide optimal nonlinear stiffness is proposed. Then a novel design of NES system yielding cubic stiffness with conical springs or variable pitch springs and negative stiffness mechanism is developed. Secondly, the experimental procedures for static and dynamic test are presented and applied to validate the concept of NES system. Then a sensitivity analysis is performed with respect to the pre-compressed length of springs. Thirdly, the optimal design of the above device with negative stiffness (termed as bistable NES) is studied. This type of NES is proved to work robustly for different types of excitation, and experimental study of semi-active control are explored. Finally, design criteria for optimally tuned VI NES are studied. Detailed analytical calculations of clearance to control the vibration under different excitations are proposed. A good correspondence between theoretical and experimental results is observed.

Detta examensarbete har utförts på Fläktwoods AB i Växjö, som producerar stora axialfläktar för olika industriapplikationer. Syftet är att öka kunskapen om fettsmorda axiella kullager genom FE analyser. Projektet har genomförts i fem delsteg för att avgöra påverkan av en eller några få parametrar i taget. De studerade parametrarna är: elementstorlek, kontaktstyvhet, last, lagergeometri (dvs. oskulation), ickelinjär geometri och ickelinjära materialegenskaper (dvs. plasticitet). Slutsatsen är att elementstorleken bör väljas fint nog för att ge ett jämnt resultat men grovt nog för att beräkningstiden skal vara rimlig. Kontaktstyvheten har inte stor, men tydlig, inverkan på kontakttrycket och penetrationen. Förändringar av oskulationen leder till förändringar i kontaktellipsens form medan olika laster inte påverkar formen på ellipsen, utan snarare storleken. När det handlar om plasticitet är sträckgränsen den viktigaste faktorn att beakta. / This thesis project was carried out at Fläktwoods AB in Växjö who produces large axial fans for different industry applications. The purpose is to increase the knowledge of grease lubricated axial ball bearings through FE analyses. The project was executed into five sub steps to determine the influence of one or few parameters at a time. The studied parameters are: mesh density, contact stiffness, load, bearing geometry (i.e. osculation), geometrical nonlinearity and material nonlinearity (i.e. plasticity). It is concluded that the mesh density should be selected fine enough to give a smooth result but course enough to give a reasonable calculation time. The contact stiffness has not a major, but a clear, impact on the contact pressure and penetration. Changes of the osculation lead to changes of the contact ellipse shape and applying different load level does not affect the shape of the ellipse but rather the size. When dealing with plasticity the yield strength is the most important factor to take in consideration.

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influ­ence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of sys­tems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assess­ment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understand­ing phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with diffi­culties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further com­pounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the for­mulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochas­tic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is consid­ered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the pre­vious chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteris­tics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinc­tive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical so­lutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been ac­cepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.