This study presents analytical and experimental procedures and design tools for the control of flexible structure vibrations using a cantilevered adaptive truss. A specific six-actuator, octahedral-octahedral truss effects the control of different flexible structures. These structures could represent space structures or robotic manipulators or a variety of other flexible structures where unwanted structural vibration could reduce the performance of the system. Three of these structures; a slender beam, a single curved beam, and two curved beams are controlled both in simulation and with an experimental test article. The test article, comprised of the flexible structure, the adaptive truss, and the actuators shows excellent agreement between simulated and experimental responses to initial conditions in both open-loop and (LQR) closed-loop control. As a example of the ability of the truss to control the slender beam, a first mode simulated frequency of 3.11Hz (3.09Hz experimental) and damping ratio of 0.0044 (0.0044) are controlled to produce a 3.20Hz (3.14Hz) frequency and a damping ratio of 0.2876 (0.2746). This 6000% increase in damping without a significant change in the modal frequency shows the potential of the adaptive truss in vibration control. The agreement between simulated and experimental data shows the validity of the modeling and experimental procedures. From the information gained, conclusions are drawn about the uses of an adaptive truss in the control of flexible structure vibrations. / Ph. D.

[pt] Treliças espaciais de forma piramidal são um componente básico de diversas estruturas, incluindo desde nanoestruturas de carbono até domos geodésicos para cobertura de grandes espaços. Estas estruturas, tal como a treliça plana de von Mises, apresentam uma resposta altamente não linear na presença de cargas estáticas e dinâmicas. A não linearidade é particularmente significativa, mesmo para baixos níveis de carregamento, quando estas estruturas são abatidas. Neste trabalho apresenta-se uma formulação não linear exata para uma treliça piramidal composta de n barras e, a partir desta formulação, analisa-se a perda de estabilidade e vibrações não lineares destas estruturas sob cargas estáticas e dinâmicas. Para compreensão do comportamento não linear são usadas respostas no tempo e planos de fase, diagramas de bifurcação, perfis de energia e bacias de atração. Os resultados mostram a importância da não linearidade na dinâmica e estabilidade da estrutura. / [en] Spatial trusses in the form of a regular pyramid are a basic configuration of many structures, from carbon nanostructures to geodesic domes used as roof of large spaces. These structures, as the planar von Mises truss, present a highly nonlinear response when submitted to static and dynamic loads. The nonlinearity is particularly significant when these structures are shallow, even when low load levels are applied. This paper presents a exact nonlinear formulation for a pyramidal truss made of n equal bars and analyze the loss of stability and nonlinear vibrations of the structure under static and dynamic loads. To understand to nonlinear behavior of the pyramidal truss, time responses, phase planes, bifurcation diagrams, energy profiles and basins of attraction are used. The results show the importance of the nonlinearity in the dynamics and stability of the structure.

Thesis (MScEng (Civil Engineering))--Stellenbosch University, 2008. / The Southern African Institute of Steel Construction expressed concern with regard to the unit definition of the effective length factor, K, stipulated for compressive elements of parallel chord trusses in Clause 15 of SANS 10162-1:2005 - Limit state design of hot-rolled steelwork. The simplified method for truss design specified in the code assumes all compression members are pin-connected, which allows for greater design simplicity and reduces the amount of code interpretation required by the designer. In addition to this, Clause 15 requires the additional reduction in resistance of the first web compression members by a factor of 0.85. However, this approach may be considered overly conservative and in current design practice the effective length factor is often reduced to less than 1.0. This research investigates the effective length factor of web compression members in parallel chord trusses, by means of investigative structural analyses of representative trusses using ANGELINE and Prokon analytical programs, and by designing, constructing and testing six representative trusses, using current design practices. A comparative study of a number of different countries’ codified approaches to truss design is also included. The structural analyses revealed that in-plane buckling of the web compression members was the consistent mode of failure, however at a much greater applied load than the design load determined according to SANS 10162-1:2005. Contrary to the expected mode of failure, all six tests performed on the representative trusses exhibited elastic out-of-plane buckling, or strongaxis buckling, of the web compression members, but still at a much greater applied load than the design load. The unexpected out-of-plane buckling of the web members is due to the inplane stiffness of the end connections used. In order to stay true to current design practice, gusset plates and longitudinal welds were used to join the web members to the chords. The stiffness of the gusset plates therefore significantly reduced the effective length of the web compression members in-plane, but did not reduce the effective length out-of-plane. Despite the unanticipated behaviour of the tests performed, certain conclusions can still be drawn from the results. The unit definition of the effective length factor for in-plane buckling of web compression members is too conservative and a K factor of 0.8 is recommended. In addition to this an effective length factor for out-plane-buckling of web compression members of 1.1 is recommended for trusses with welded connections. The necessity of the reduction in resistance of 0.85 of the first web compression members requires further investigation. The most important conclusion to be drawn is that out-of-plane buckling of web compression members can be the dominant failure mode, which is not taken into consideration in current design practice.

A fully automated computer program is developed for the optimum design of steel space trusses acting compositely with a concrete slab placed on top. The program sizes the truss members to meet the requirements of the load and resistance factor design specification of the American Institute of Steel Construction using the load combinations of ANSI. Earthquake loading is not considered. The optimum size is based on minimum cost, regarding the amount of welding required at the joints and of the member itself. The total cost is based on all steel work in the truss. Once the truss configuration has been defined, and it has been ensured that linear elastic behavior exists, the structure is analyzed for the construction process, to make sure that no overstressing will take place in any structural element at any time during construction and service. The analysis and design principles are presented and an actual design case is solved. (Abstract shortened with permission of author.)

Master of Science / Department of Architectural Engineering / Kimberly W. Kramer / Trusses are an efficient way to span long distances with minimal material required. This report is a parametric study of the different design and construction aspects for a 300’-0” span, steel, Warren type truss. The study specifically examines the vertical loading on the truss, including components and cladding wind loading. The engineering variables investigated are panel point location, steel shape size and type, steel grade, member orientation, and connection design. Each of these aspects are studied independently with major results accounted for later in analysis. This allows for the most economical truss by reviewing each alternative possibly not commonly used in steel construction. However, trusses require special consideration in constructability compared to a common steel structure such as an office building. Because of this added complexity, constructability issues are also examined after all parametric studies are completed for engineering variables. Transportation regulations and restrictions, steel erecting (including the construction loading of the ASCE 37-02), and temporary structures are considered for the 300’-0” span steel truss. The results of the engineering design variables are documented showing the benefit of using W-Shape members with higher grades of steel in select members, and the rotation of members for truss stability and simplified connection detailing. Each of the multiple construction considerations are presented, providing the most recent information available at the time of this report.

Apresenta-se neste trabalho um processo de busca da solução de mínimo peso, para estruturas de aço treliçadas planas utilizando-se seções formadas por perfis comerciais comuns, dimensionadas segundo a norma brasileira para projeto e execução de estruturas de aço de edifícios. Como base do processo de otimização foi utilizado o método do gradiente inteiro, alterando-se alguns critérios, no sentido de melhorar o desempenho e levar em conta a relação não linear entre as características geométricas dos perfis. São abordados os conceitos matemáticos básicos envolvidos no processo de otimização, os de análise de estruturas treliçadas planas, bem como a formulação para o dimensionamento de barras sujeitas a tração ou compressão. São apresentadas ainda as listagens dos programas envolvidos no processo e também exemplos de aplicação para demonstrar a eficácia dos procedimentos utilizados. / This work presents a process to find a least weight solution for two-dimensional trusses composed of available steel sections, according to brazilian code for design and constructions or steel buildings structures. The optimization process is based on the method of integer gradient directions. Some modifications were introduced in order to improve the algorithm and take into account the non-linear relationship between geometric characteristics for steel cross-section. It is also presented the basic concepts of mathematics optimization to design two-dimensional trusses, as well as the formulation for designing members in tension or compression. The program listing used in this process is also presented, as well as some examples, to demostrate the efficacy of the process.

No Brasil é comum a utilização de barras tubulares com extremidades estampadas na confecção das treliças metálicas espaciais, uma vez que representam uma significativa redução de custos, quando comparado a sistemas mais elaborados, devido a sua simplicidade de fabricação e montagem, entretanto trata-se aparentemente de um sistema precário do ponto de vista estrutural, merecendo estudos que estabeleçam critérios para uma utilização segura. Neste trabalho são apresentadas análises teóricas e experimentais destas estruturas, onde foi analisada a situação construtiva usual de treliça com nós típicos (extremidade das barras estampadas, sobrepostas e unidas por um único parafuso), e com nós de aço (sistema de conexão formado por uma peça com aletas de aço soldadas). Os resultados experimentais foram obtidos em ensaios de quatro protótipos que simulam um trecho de treliça espacial, constituídos por uma malha quadrada sobre quadrada, composta de nove módulos piramidais de 2,5 x 2,5 x 1,5 (m), totalizando uma estrutura com dimensões iguais a 7,5 x 7,5 x 1,5 (m), apoiada por colunas nos vértices, permitindo comparar a rigidez, o modo de falha e a resistência entre estes protótipos. A análise teórica dos protótipos foi feita admitindo-se os casos de linearidade e também de não linearidade física e geométrica, levando-se em consideração a variação de inércia das barras junto aos nós. / In Brazil the use of tubular bars with stamping extremities is common in space steel structures, as it means a significant reduction of cost, when caompared with more elaborete system, due to its simplicity of manufacture and assembly. However it is apparently an uncertain system from a structural point of view, which requires studies establishing safe utilization criteria. This paper presents theorical and experimental analysis of this structures. The usual constructive situation of space structure with \'nós típicos\' (bars with flattened ends, superposed and connected by a unique bolt), and \'nós de aço\' (connection system formed by a piece with steel fin welded) was studied. The experimental results were obtained in tests of four prototypes which simulated a section of space structure composed of a mesh squareon- square, with nine 2.5 x 2.5 x 1.5 (m) pyramidal modules, totaliing a structure with 7.5 x 7.5 x 1.5 (m) dimensions, supported by columns in their vertices, permiting to compare the stiffness, the failure manner and the resistance of this prototypes. The theorical analysis of prototypes was carried out by assuming the cases of linearity and physical and geometric non-linearity, taking into consideration the variation of stiffness of the bars next to the nodes.

An experimental testing program was conducted to determine the compression member performance in post-buckling region. These results are compared with an analytical computer program developed by Portland State University under Bonneville Power Administration Contract 79-80BP 24005. The paper presents the sensitivity of the performance of single angle compression members to various parameters such as length to radius of gyration ratio, eccentricity, end conditions and yield stress. The effect of local buckling on long member performance is also documented.

Double-layer grid systems are three-dimensional pin-jointed structures, which are generally used for covering roofs having large spans. In this study, evolution strategies method is used to optimize space trusses. Evolution strategies method is a type of evolutionary algorithms, which simulate biological evolution and natural selection phenomenon to find the best solution for an optimization problem. In this method, an initial population is formed by various solutions of design problem. Then this initial population starts to evolve by using recombination, mutation, and selection operators, which are adopted for optimization of space trusses by modifying some parameters. Optimization routine continues for a certain number of generations, and best design obtained in this process is accepted as optimum solution. OFES, a design and optimization software developed for optimum design of steel frames, is modified in this study to handle space truss systems. By using this v software, six design examples taken from real-life industrial applications with element numbers changing between 792 and 4412 are studied. The structural systems defined in examples are optimized for minimum weight in accordance with design provisions imposed by Turkish Specification, TS648. The optimization is performed based on selecting member sizes and/or determining the elevation of the structure and/or setting the support conditions of the system. The results obtained are compared with those of FrameCAD, a software which is predominantly used for design of such systems in national current design practice.

The recent improvement of additive manufacturing has allowed designers to achieve a level of complexity and customizability that is difficult or impossible to accomplish using traditional manufacturing processes. As a result, much research has been conducted on developing new methods to utilize the larger design space brought by additive manufacturing. One such research area is in the design of mesoscale lattice structures. Mesoscale lattice structures are a type of cellular structure with support element sizes on the order of magnitude of centimeters. These types of structures are engineered for high performance and have applications in industries where both low weight and high strength are desired. However, due to the small size of their struts, these structures can easily have hundreds to thousands of individual struts. As a result, design poses a unique challenge. Current methods approach design of mesoscale lattice structures as a topological optimization problem, treating each strut diameter in the structure as a design variable. For structures with a fewer number struts, these optimization methods can converge, but will generally be very time-consuming. For structures with a large number of struts, the optimization problem becomes too large for current algorithms to solve. In previous research, a new, highly efficient design method for mesoscale lattice structures was presented that eliminates the need for global size or topological optimization. This method, termed the Size, Matching and Scaling method, used a unique combination of a solid-body finite element analysis and a library of pre-defined lattice configurations, termed the "unit-cell library," to generate lattice topologies. The results from this method were highly promising: design time was significantly reduced when compared to optimization methods. Furthermore, lattices designed using the SMS method had performance results that were either comparable or better than their optimized counterparts. However, the method developed was highly conceptual, lacking a true systematic methodology for generating topologies and suffering from some gaps in implementation. In this research, we present a modified Size Matching and Scaling (SMS) design method. Firstly, we introduce and outline the modified methodology. This methodology particularly includes an optimization step for determining strut diameters that replaces the manual search used in the original method. Secondly, we expand and explore the unit-cell library in an attempt to improve the performance of lattices generated using the SMS method. In particular, we optimize several unit-cell configurations and compare their performance in the context of the SMS method. Finally, we test the updated SMS methodology and unit-cell library using various design examples. Results from the various example problems indicate that optimization is not only a viable systematic method for determining diameter values, but is actually preferred to the manual, iterative process used in the original method. Furthermore, various optimization algorithms and approaches yield different results. Between the two optimization algorithms utilized in this method: constrained optimization and least-squares minimization, constrained minimization converges faster, but least-squares minimization yields slightly improved performance results. In addition to these algorithms, a one-variable approach using an untested, simplifying assumption, dubbed the "28% approach," was tested. Results indicate that this assumption was incorrect and cannot be utilized. Finally, results from the expanded unit-cell library indicate that the best unit-cell configuration is still the same original unit-cell configuration utilized in the first SMS method. The addition of more unit-cell does not improve the performance of structures generated using the SMS method. In fact, both performance and design time worsen when additional configurations are utilized.