This report is the documentation for a stiffness formulation to perform rigid diaphragm analysis for wood structures subjected to wind loads. Traditionally, rigid diaphragm analysis has been performed using a vaguely-defined superposition approach; however, this report details a more rational stiffness approach to solving for forces placed on walls resulting from a rigid diaphragm, and its implementation is via a simple spreadsheet application. In addition to the formulation of the spreadsheet, the report contains a User’s Guide and examples of the spreadsheet’s use. The purpose of the spreadsheet is not as a replacement to more sophisticated and comprehensive finite element analysis software, but as a tool to aid designers who practice engineering and may not have access to such software. In general, the application is developed for wood diaphragms as will be noted by references to wood-related codes. However, much of the approach may be used for diaphragms constructed with other materials as well. / text

No description available.

Recent investigations in nanotechnology show that carbon nanotubes (CNT) have one of the most significant mechanical, electrical and optical properties. Interactions between those areas like electrical, optical and mechanical properties are also very promising in both research and industrial fields. Those unique characteristics are built by mainly the atomistic structure of the carbon nanotubes. In this thesis, the effects of vacant atoms on single walled carbon nanotubes (SWCNT) are investigated using matrix stiffness method. In order to use this technique a linkage between structural mechanics and molecular mechanics is established. A code has been developed to construct the SWCNT with the desired chirality, extracting the vacant atoms with the corresponding atomic bonds between the neighbor nodes and calculating the effect of those vacancies on its vibrational properties. A finite element software is also utilized for validation of the code and results. In order to investigate the convergence of the effect of those vacant nodes a numerous number of analyses have been carried out with randomly positioned vacant atoms. Also consecutive vacant nodes have been positioned in order to investigate the effect on the structural properties through the length of a CNT. In addition to those, as a case study, the reduction in Young&#039 / s modulus property because of the vacancies has also been investigated and the effects are tabulated in the report. It is concluded in this study that the any amount of vacant atoms have substantial effect on modal frequencies and Young&#039 / s modulus. Chirality and the position of the vacancies are the main parameters determining the structural properties of a CNT.

Vibration-based energy harvesting using piezoelectric materials have been investigated by several research groups with the aim of harvesting maximum energy and providing power to low-powered wireless electronic systems for their entire operational life. The electromechanical coupling effect introduced by the piezoelectric vibration energy harvesting (PVEH) mechanism presents modelling challenges. For this reason, there has been a continuous effort to develop different modelling techniques to describe the PVEH mechanism and its effects on the dynamics of the system. The overall aims of this thesis are twofold: (1) a thorough theoretical and experimental analysis of a PVEH beam or assembly of beams; (2) an in-depth analytical and experimental investigation of the novel concept of a dual function piezoelectric vibration energy harvester beam/tuned vibration absorber (PVEH/TVA) or 'electromechanical TVA' and its potential application to vibration control. The salient novel contributions of this thesis can be summarised as follows: (i) An in-depth experimental validation of a PVEH beam model based on the analytical modal analysis method (AMAM), with the investigations conducted over a wider frequency range than previously tested. (ii) The precise identification of the electrical loads that harvest maximum power and that induce maximum electrical damping. (iii) A thorough investigation of the influence of mechanical damping on PVEH beams. (iv) A procedure for the exact modelling of PVEH beams, and assemblies of such beams, using the dynamic stiffness matrix (DSM) method. (v) A procedure to enhance the power output from a PVEH beam through the application of a tip rotational restraint and the use of segmented electrodes. (vi) The theoretical basis for the novel concept of a dual function PVEH beam/TVA, and its realisation and experimental validation for a prototype device. A thorough experimental validation of a cantilever piezoelectric bimorph energy harvester without a tip mass is presented under random excitation. The study provided a deep insight into the effect of PVEH on the dynamics of the system for variations in electrical load. An alternative modelling technique to AMAM, based on the DSM, is introduced for PVEH beams. Unlike AMAM, the DSM is exact, since it is based on the exact solution to the bending wave equation. It also readily lends itself to the modelling of beams with different boundary conditions or assemblies of beams of different crosssections. AMAM is shown to converge to DSM if a sufficiency of modes is used. Finally, an in-depth theoretical and experimental investigation of a prototype PVEHbeam/TVA device is presented. This device comprises a pair of bimorphs shunted by R-L-C circuitry and can be used as a tuned mass damper (TMD) to attenuate a vibration mode of a generic structure. The optimal damping required by this TMD is generated by the PVEH effect of the bimorphs. Such a device combines the advantages of conventional mechanical and electrical TVAs, overcoming their relative disadvantages. The results demonstrate that the ideal degree of attenuation can be achieved by the proposed device through appropriate tuning of the circuitry, thereby presenting the prospect of a novel class of 'electromechanical' tuned vibration absorbers.

A theoretical study has been conducted to investigate the effect of flat bars supports on the dynamic response of a heat exchanger U-tube. The tube is modelled using three dimensional, six degrees of freedom per node straight beam finite elements. A new method, the stiffness method, is introduced to compute the impact forces at the supports. It is compared with the previously used external force method. Modal analysis is employed to investigate the modal energy dissipation in the higher modes. Time response of the U-tube is analysed using a Fast Fourier Transform algorithm. The effects of clearance, excitation magnitude, and mode coupling through friction at the supports are investigated. / Thesis / Master of Engineering (ME)

Z-sections are widely used as secondary members in metal building roof systems. Lateral restraints are required to maintain the stability of a Z-section roof system and provide resistance to the lateral forces generated by the slope of the roof and the effects due to the rotation of the principal axes of the Z-section relative to the plane of the roof sheathing. The behavior of Z-sections in roof systems is complex as they act in conjunction with the roof sheathing as a system and as a light gage cold formed member, is subject to local cross section deformations. The goal of this research program was to provide a means of predicting lateral restraint forces in Z-section supported roof systems. The research program began with laboratory tests to measure lateral restraint forces in single and multiple span sloped roof systems. A description of the test apparatus and procedure as well as the results of the 40 tests performed is provided in Appendix II. To better understand the need for lateral restraints and to provide a means of testing different variables of the roof system, two types of finite element models were developed and are discussed in detail in appended Paper I. The first finite element model is simplified model that uses frame stiffness elements to represent the purlin and sheathing. This model has been used extensively by previous researchers and modifications were made to improve correlation with test results. The second model is more rigorous and uses shell finite elements to represent the Z-section and sheathing. The shell finite element model was used to develop a calculation procedure referred to as the Component Stiffness Method for predicting the lateral restraint forces in Z-section roof systems. The method uses flexural and torsional mechanics to describe the behavior of the Z-section subject to uniform gravity loads. The forces generated by the system of Z-sections are resisted by the "components" of the system: the lateral restraints, the sheathing and Z-section-to-rafter connection. The mechanics of purlin behavior providing the basis for this method are discussed in appended Paper II. The development of the method and the application of the method to supports restraints and interior restraints are provided in appended papers III, IV and V. / Ph. D.

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-23T12:33:24Z No. of bitstreams: 1 DissAJRC.pdf: 3333263 bytes, checksum: 705b9ce01810131eee4f42918ca5f807 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:36:15Z (GMT) No. of bitstreams: 1 DissAJRC.pdf: 3333263 bytes, checksum: 705b9ce01810131eee4f42918ca5f807 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:36:21Z (GMT) No. of bitstreams: 1 DissAJRC.pdf: 3333263 bytes, checksum: 705b9ce01810131eee4f42918ca5f807 (MD5) / Made available in DSpace on 2016-09-26T20:36:27Z (GMT). No. of bitstreams: 1 DissAJRC.pdf: 3333263 bytes, checksum: 705b9ce01810131eee4f42918ca5f807 (MD5) Previous issue date: 2015-05-05 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / It’s presented in this work a graphic program that allows the analysis (calculation of forces and displacements) of concrete slabs by the equivalent grid model. The surface is considered as monolithic without the traditional discretization of the structure, i.e., the separation of the various structural members (beams, columns and slabs). Only the pillars are considered as unmovable in the direction of its principal axis. The graphical environment designed for this is pioneering, developed by objectoriented programming and will be distributed freely and with listings available. The system allows the designing of the structure as a model, allowing an easier perception of its different structural components and the definition of the different stresses on it. The program establishes an interface adapted to the calculation module, that initially was developed by Igor Stayanov Cotta in 2006,.and thus allows the graphic view of the efforts, displacements and stresses acting over the model. / Apresenta-se neste trabalho um programa gráfico que permite a análise (cálculo de esforços e deslocamentos) de lajes de concreto pelo modelo da grelha equivalente. O pavimento é considerado como monolítico sem a tradicional discretização da estrutura, ou seja, a separação dos diversos elementos estruturais (vigas, lajes e pilares). Apenas os pilares são considerados como indeslocáveis na direção do seu eixo principal. O ambiente gráfico idealizado para tal é pioneiro, desenvolvido por meio da programação orientada a objetos e será livre (gratuito e com listagem disponível). No sistema é possível lançar a estrutura como se desenham as fôrmas de uma estrutura, permitindo assim, de forma fácil, a caracterização das diferentes propriedades dos materiais e a definição das ações atuantes na estrutura. O programa estabelece uma interface para o módulo de cálculo adaptado que, inicialmente, foi desenvolvido por Igor Stayanov Cotta em 2006.e assim permite a visualização dos esforços, dos deslocamentos e dos gráficos de tensões na tela do monitor.

Concrete has established itself as the most widely used structural material. There is hardly any place where human life and concrete structure do not exist together. It's use is seen in wide variety of structures like buildings, bridges, dams, nuclear structures, floating and submerged structures and so on. Hence, in view of safety, serviceability and economy, proper understanding of the behaviour of concrete is imperative in designing these complex structures. Current reinforced concrete codes are based on strength and serviceability concepts. The tensile strength of concrete is totally neglected in the limit state method of analysis. The concrete in tension is assumed to be fully cracked and conservative method of design is adopted. The crack causes a considerable degradation of stiffness of overall structure and gives rise to regions of stress concentration, which are not accounted for, in the present design methods. Besides, it is found that the size of the structural component significantly influences the stress at failure. It has been fairly well established that large specimens fail by catastrophic crack propagation while small specimens tend to fail in a ductile manner with considerable amount of slow crack growth preceding fracture. Initial attempts to understand the cracking of concrete through the principles of fracture mechanics was made in 1960's. It was concluded that the LEFM and small scale yielding fracture mechanics which are developed for metals are inapplicable to concrete structures except for certain limiting situations such as the behaviour at extremely large sizes. The reasons for the inapplicability of LEFM principles to concrete structures are attributed to slow crack growth, formation of nonlinear fracture process zone, and softening behaviour of concrete in tension. Several analytical and numerical models have been proposed to characterize the fracture behaviour of concrete. In the present work a simple numerical method is proposed to analyse the Mode-I fracture behaviour of concrete structures, using finite element method. The stiffness matrices calculated at the beginning of the analysis are used till the end without any modification. For this reason, the method is named as Initial Stiffness Method (ISM). An attempt has also been made to modify the lattice model existing in literature. The contents of the thesis are organised in six chapters. In chapter 1, a brief introduction to basic principles of fracture mechanics theory is presented. This is included mainly for the completeness of the thesis. In chapter 2, a brief review of literature regarding the application of principles of fracture mechanics to concrete structures is presented. The need for the introduction of fracture mechanics to concrete is presented. Early work, applying LEFM principles to concrete structures is discussed. The reasons for the inapplicability of linear elastic fracture mechanics principles to concrete structures are discussed. Necessities for nonlinear fracture mechanics principles are pointed out. Attention is focused on the influence of the factors like slow crack growth, formation of nonlinear fracture process zone and softening behaviour of concrete in tension on the fracture behaviour. Besides a possible use of fracture energy as an alternative fracture criterion for concrete is contemplated. Several analytical and numerical models (assuming concrete as homogeneous continuum), proposed so far to characterize the fracture behaviour of concrete, are presented and discussed in detail. Different heterogeneous models presented so far are also discussed. In chapter 3, a simple numerical method to analyse the fracture of concrete (strain softening material) in Mode-I, using FEM is proposed. The stiffness matrices are generated only once and are used till the end of the analysis. This feature makes the model simple and computationally efficient. A new parameter namely, strain softening parameter α has been introduced. It is found that this strain softening parameter ‘α’ is a structural property. The results obtained from the present method are found to converge with increasing number of elements thus making the method mesh independent, and thus objective. The method was validated by analysing the beams tested and reported by various researchers. The predicted values of maximum load by the present method are found to agree well with the experimental values. Initially, all the beams are analysed using uniform meshes and load-deflection diagrams are plotted. All the beams are again analysed using graded meshes. The load-deflection, load-CMOD diagrams are plotted from the results obtained from the analysis using graded meshes. In chapter 4, the results obtained in chapter 3 are analysed for size effect. Literature regarding size effect of concrete structures has been reviewed. In addition to the size effect on nominal stress at failure which exists in literature, two new parameters namely, post peak slope and softening slope parameter α have been used to confirm the size effect. This does not exist in the literature. In chapter 5, an attempt is made to modify the lattice model existing in literature. This is done with a view to model concrete as a heterogeneous medium, which would be nearer to reality. The softening property of concrete has been incorporated. The model was validated against some of the experimental results existing in literature. The results are found to be encouraging. The results from this model show the post peak softening similar to the experimentally observed ones. The effects of different probabilistic distributions to the properties of mortar on the maximum load of the beam are studied. It is found that normal distribution of properties to mortar gives the best results. A study is made regarding the sensitivity of various properties of mortar on the maximum load of the beam. It is concluded that load carrying capacity of the beam can be increased by using a mortar of higher tensile strength. Finally in chapter 6, general conclusions and suggestions for further investigations are discussed.

The diploma thesis deals with static analysis of the Black bridge in Hodonín city. The creation of the numerical model in ANSYS sw. is described according to the existing project documentation, followed by the application of loading and boundary conditions (including the solution of foundation soil placed on the piles). The selection of the loading is used according ČSN EN standards for analysis and verification of the main construction parts. This work also includes verification of the piles deformations calculated both in ANSYS sw. and by the direct stiffness method (MS Excel is used) and their comparison is done. Amongst other attachments, the verification of the load carrying capacity of the structure (respecting the current traffic limitation allowing only one vehicle to be on the bridge structure) is also provided.

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.