<div>In the past decade, high-strength reinforcement (fy > 60 ksi) has become more prevalent and more widely accepted. Building codes such as ACI 318-14 do not address the use of highstrength reinforcement for proper development and splicing of reinforcement. Furthermore, research on development of high-strength reinforcement is limited. The objective of the study is to develop a suitable expression for the development and splicing of high-strength reinforcement.</div><div>Of particular interest is evaluating the influence of splice length and confinement on bond strength as well as evaluating the effectiveness of high-strength transverse reinforcement on bond strength. The study tested 22 large-scale concrete beams reinforced with ASTM A615</div><div>Grade 100 deformed steel bars: 11 specimens without transverse reinforcement within the splice region (unconfined) and 11 specimens with transverse reinforcement within the splice region (confined). Splice lengths varied from 40 bar diameters to 120 bar diameters, which are some of the largest ever tested. The effect of the test variables which were systematically studied, found</div><div>that splice strength is nonlinearly related with splice length and can be represented by a power equation. Furthermore, it was found that high-strength transverse reinforcement does not improve bond strength compared with the use of Grade 60 transverse reinforcement. Considering the test results and review of historical test results, an analytical investigation was conducted which developed a simple expression for estimating the capacity of both unconfined</div><div>and confined beams. The results are compared with the current building code design expressions as well as other proposed bond strength equations. The research conducted here provides the basis for development of a design expression that will allow for the incorporation of highstrength reinforcement in future building codes.</div>

Atualmente a maioria dos veículos de passeio, pequenos e médios, são equipados com eixo traseiro do tipo interdependente. Seu baixo custo de fabricação e instalação fácil faz dele o preferido pela indústria automotiva. Normalmente, o eixo traseiro interdependente é um conjunto soldado e sua fabricação requer um controle do processo e qualidade das juntas soldadas de alto nível, devido a uma característica típica de projeto: eixos traseiros interdependentes possuem tensões críticas nos seus cordões de solda. Neste estudo, foi avaliado o quanto alterações nos parâmetros de soldagem afetam a geometria da solda e esta, por sua vez, compromete a vida à fadiga de um eixo interdependente. Através da variação dos parâmetros primários de soldagem (corrente, tensão e velocidade de soldagem), foi criado duas classes de eixos: classe A - 22V; 235A; 9mm/seg e classe B - 29V, 302A; 15mm/seg. Estes eixos foram submetidos a um ensaio de torção com carga em amplitude constante e seus desempenhos foram medidos através da curva de vida à fadiga. A variação dos parâmetros de soldagem afetou a geometria do cordão de solda, provocando nos eixos da classe B o surgimento de defeitos como baixa penetração da solda e mordedura. O resultado da análise metalográfica indica que estes defeitos influenciaram na resistência à fadiga dos eixos. A fractografia das fraturas confirmou que as falhas ocorreram por fadiga. / Nowadays most of the light, small and medium vehicles are equipped with a twist beam rear axle. Its low-cost production and easy assembly makes it the favorite axle type for the automotive industries and suspension developers. Usually the twist beam rear axle is a welded assembly and its production request a process control and high-level quality of the welded joint, due to a typical project characteristic: twist beam rear axle have critical tensions in their welds beads. It was evaluated in this study, how much the alterations in the welding parameters affects the weld bead geometry and this, for its time, affects the fatigue life of the twist beam rear axle. Through the variation of the welding primary parameters (welding current, arc voltage and welding speed), it was manufactured two classes of the axles: class \"A\" - 22V; 235A; 9mm/seg and class \"B\" - 29V, 302A; 15mm/seg. These axles were submitted the constant amplitude fatigue torsion testing and your performance were measured through the fatigue life curve. The variation of the welding parameters affected the weld bead geometry, inducing on the class \"B\" axle, the appearance of defects as low weld penetration and undercut. The metalography investigation indicates that these defects influenced in the fatigue life resistance. The fractures fractography confirmed that the flaws happened for fatigue.

As indústrias têxteis desempenham um importante papel na economia nacional e mundial. Entretanto, do ponto de vista ambiental, suas atividades são consideradas como potencialmente poluidoras e utilizadoras de recursos naturais. Os corantes azo reativos são os principais corantes utilizados no setor para o tingimento do algodão no Brasil e no mundo. Devido à sua baixa fixação à fibra e a variações no processo de produção, cerca de 30 % da concentração inicial utilizada nos banhos de tingimento são perdidos e vão compor o efluente final. Esses compostos apresentam uma baixa biodegradabilidade e elevada solubilidade em água e, por isso, não são completamente removidos pelos processos biológicos convencionais. Os corantes quando descartados sem tratamento adequado no corpo dágua receptor podem causar modificações estéticas, alterar a fotossíntese e a solubilidade dos gases, além de serem tóxicos e genotóxicos para a biota. Os principais objetivos do trabalho foram avaliar a toxicidade e genotoxicidade de dois diferentes corantes azo reativos (Remazol Preto B RPB e Remazol Alaranjado 3R R3AR) e a eficiência de redução da cor e toxicidade após o uso da radiação com feixe de elétrons. Também foi analisada a toxicidade dos corantes em diferentes formas químicas, que podem ser encontradas nos efluentes. Os ensaios de toxicidade aguda realizados com Vibrio fischeri, Daphnia similis e Biomphalaria glabrata evidenciaram diferentes padrões de resposta para os corantes. Os dois corantes em suas formas químicas foram levemente tóxicos para Vibrio fischeri, com exceção da forma vinilsulfona do corante RPB que foi tóxico (CE(I)5015min = 6,23 mg L-1). Nos ensaios com Daphnia similis, o corante RPB foi levemente tóxico na sua forma original, sulfatoetilsulfona (CE(I)5048h = 91,25 mg L-1) e não apresentou toxicidade nas demais formas químicas. Entretanto, o corante RA3R foi tóxico para o dafnídeo, sendo muito tóxico na forma vinilsulfona (CE(I)5048h = 0,54 mg L-1). Não foi observada toxicidade nos ensaios com o organismo Biomphalaria glabrata. A toxicidade crônica foi avaliada com o organismo Ceriodaphnia dubia e o corante RPB apresentou valores de CENO e CEO iguais a 12,5 e 25 mg L-1, respectivamente, para a forma sulfatoetilsulfona. Após a hidrólise do corante (vinilsulfona e hidroxietilsulfona) foi observado um aumento os valores obtidos de CENO e CEO. Não foi verificado efeito crônico para o corante R3AR e suas formas químicas. O teste do cometa adaptado para o caramujo Biomphalaria glabrata foi utilizado para avaliar a genotoxicidade dos corantes. O corante RPB apresentou genotoxicidade nas concentrações mais elevadas (1 e 2 g L-1), com valores de dano quantitativo de 117 e 112 e o R3AR não foi genotóxico. O uso da radiação com feixes de elétrons demonstrou eficácia na remoção da cor dos corantes. Com a dose de 10 kGy foi possível uma redução de 97,64 % para RPB e de 96,8 % para R3AR. Após irradiação do corante RPB com a dose de 10 kGy foi evidenciada uma redução de 59,52 % da toxicidade aguda avaliada com Vibrio fischeri. Nas demais doses não houve redução significativa, assim como na avaliação com Daphnia similis, onde os valores de CE(I)5048h obtidos foram menores que o corante não irradiado. O corante R3AR apresentou diminuição da toxicidade mais acentuada após a radiação quando comparado com o RPB, com reduções de 82,95 % (V. fischeri) e 71,26 % (D. similis) com 10 kGy. / The textile industries play an important role in national and global economy. But, their activities are considered potentially polluting. The use of large volumes of water and the production of colored wastewater with high organic matter are among the main issues raised, especially during the stage of dyeing and washing of the textile process. The reactive azo dyes are the main colors used in the industry for dyeing of cotton in Brazil and worldwide. Because of its low setting and variations in the fiber production process, about 30% of the initial concentration used in the dyeing baths are lost and will compose the final effluent. These compounds have a low biodegradability, are highly soluble in water and therefore are not completely removed by conventional biological processes. In addition, other processes do not promote degradation but the tranference to solid environment. The dyes discarded without treatment in the water body can cause aesthetic modifications, alter photosynthesis and gas solubility, as well as being toxic and genotoxic. The main objectives of this study were to evaluate the toxicity and genotoxicity of two reactive azo dyes (Remazol Black B - RPB and Remazol Orange 3R R3AR) and the percentage of color and toxicity reduction after the use of electron beam radiation. The acute toxicity assays performed with Vibrio fischeri, Daphnia similis and Biomphalaria glabrata showed different response patterns for dyes. The different chemical forms of dyes were slightly toxic to Vibrio fischeri and only the RPB dye (vinylsulphone) was toxic (EC5015min = 6,23 mg L-1). In tests with Daphnia similis, the dye RPB was slightly toxic in its patern form, sulphatoethylsulphone, (CE5048h = 91,25 mg L-1) and showed no toxicity in other chemical forms. However, the RA3R dye was toxic to the dafnids and the vinylsulphone form very toxic (EC5048h = 0,54 mg L-1). No toxicity was observed in Biomphalaria glabrata assays. Chronic toxicity was assessed with the organism Ceriodaphnia dubia and the NOEC and OEC values of RPB dye (sulphatoethylsulphone) were 12.5 and 25 mg L-1, respectively. After hydrolysis of the dye (vinylsulphone and hydroxyethylsulphone) was shown to increase the values obtained from the NOEC ans OEC. There was no chronic effect for the R3AR dye and its chemical forms to C. dubia. The comet assay adapted to hemocytes of Biomphalaria glabrata was used to assess the genotoxicity of the dyes. The RPB dye was genotoxic at highest concentrations (1 and 2 g L-1), with quantitative values of DNA damage equal to 117 and 112 and the R3AR dye was not genotoxic. The use of radiation with electron beams have proven effective in removing the color dyes. With a dose of 10 kGy a reduction of 97.64% and 96.8% for R3AR and RPB, respectively, was achievied. Possibly, the color removal was mainly due to the interaction of reactive species such as hydroxyl radicals generated in the radiolysis of water after the radiation beam of electrons. After radiation of the RPB dye a dose of 10 kGy reduced 59.52 % of the acute toxicity measured with Vibrio fischeri. For the other doses there was no significant reduction, as well as with Daphnia similis, where the values of EC5048h obtained were smaller than the non-irradiated dye. The R3AR dye showed better decreased toxicity after radiation when compared with the RPB, with reductions of 82.95% (V. fischeri) and 71.26% (D. similis) with 10 kGy.

O bagaço de cana de açúcar é uma fonte de energia renovável e matéria prima promissora na produção de biocombustível, pois representa cerca de 30% de glicose contida na planta com potencial de ser hidrolisado e convertido em etanol. Os principais constituintes do bagaço de cana são a celulose, formada por cadeia linear de glicose, a hemicelulose, um polímero amorfo constituído de xilose, arabinose, galactose e manose e a lignina, um polímero complexo formado por unidades de fenilpropanos que atuam como revestimento impermeabilizante nas fibras, difícil de ser removido por sua característica recalcitrante. O objetivo do presente trabalho foi avaliar a eficiência da irradiação com feixe de elétrons como pré-tratamento do bagaço de cana para hidrólise enzimática da celulose. O pré-tratamento do bagaço de cana é uma das etapas mais importante para torná-lo economicamente viável e competitivo na produção de energia. Como pré-tratamento o processamento por feixe de elétrons pode fragilizar a estrutura da hemicelulose e lignina, pela ação de radicais altamente reativos que quebram as ligações químicas, reduzindo o grau de polimerização das fibras. Foram avaliados os efeitos da radiação na estrutura e composição do bagaço, assim como a combinação do processamento por feixe de elétrons com o pré-tratamento de esplosão à vapor. Para hidrólise enzimática utilizou-se enzimas comerciais fornecidas pela Novozymes. O processamento por feixe de elétrons levou a alterações na estrutura e composição do bagaço de cana aumentando a solubilidade pela degradação de celulose alfa e hemicelulose e aumentando também o rendimento da hidrólise enzimática. No caso do bagaço explodido, não houve alteração no rendimento da hidrólise enzimática, mas o processamento por feixe de elétrons promoveu uma redução de 67% no furfural, que é formado no processo de explosão a vapor. / The sugar cane bagasse is a renewable energy source and a raw material promise in the biofuel production, once represents about 30% of glucose contained in the plant with the potential to be hydrolyzed and then converted to ethanol. The bagasse is composed of cellulose, straight chain of glucose, of hemicellulose, an amorphous polymer consisting of xylose, arabinose, galactose, and mannose, and of lignin, a complex polymer consisting of fenilpropans units that acts as waterproof coating on the fibers, which is hard to remove due its recalcitrant nature. The aim of this work was to study the electron beam processing as a pretreatment of sugarcane bagasse to enzymatic hydrolysis of cellulose. The pretreatment of sugarcane bagasse is one of the most importante steps to make this material economically viable and competitive on the energy production. As a pretreatment the electron beam processing can weak the hemicellulose and lignin structures by the action highly reactive radicals that breaks the links, reducing the degree of polymerization fibers. It was evaluated the chemical and structural modifications on fibers caused by the irradiation, the enzymatic hydrolysis of electron beam as the only pretreatment and combined to steam explosion. For enzymatic hydrolysis it was used the commercial enzymes from Novozymes. The radiation processing promotes changes in structure and composition of sugarcane bagasse, increasing the solubility, that is related to hemicellulose and cellulose cleavage, and also increasing the enzymatic conversion yield. In the case of exploded bagasse there is no changes in the enzymatic hydrolysis yield, however the electron beam processing promoted a 67% reduction of furfural, that is formed in the steam explosion process.

As estruturas tubulares, muitas vezes, têm sua aplicação restrita a construções onde a concepção arquitetônica determina o seu uso, no entanto há algumas vantagens do ponto de vista estrutural que podem justificar a sua aplicação. A reduzida área exposta ao fogo e aos ambientes agressivos, boa resistência a compressão axial com baixa tendência ao desenvolvimento de instabilidades localizadas, são algumas das vantagens da utilização destas estruturas. O objetivo principal deste trabalho é analisar numericamente o comportamento da ligação entre viga de seção I com coluna tubular circular, para tanto são consideradas configurações usuais de ligação com anéis externos transversais e chapa de alma. É ainda objetivo trazer um panorama das estruturas tubulares em geral, com o desenvolvimento histórico das pesquisas, e principalmente estabelecer uma compilação dos procedimentos analíticos de cálculo e classificação apresentados pelas normas Eurocode 3 e ANSI/AISC. A análise numérica foi realizada por meio dos pacotes comerciais TRUEGRID® e ANSYS®, os quais aplicam o método dos elementos finitos. Foram empregados modelos que consideram as características mecânicas do aço, como plastificação e encruamento, e ainda as não-linearidades geométricas e de contato. Os resultados numéricos apresentaram coerência razoável com os modelos analíticos normativos. Foi possível o conhecimento do comportamento M-\'fi\' (momento-rotação) das ligações, bem como a determinação dos parâmetros que caracterizam tal relação, como resistência, rigidez inicial e ductilidade. Os estudos comprovaram a eficácia dos anéis externos na distribuição dos esforços oriundos do engastamento parcial da viga, fazendo com que a coluna não seja comprometida. / The application of tubular structures is usually restricted to constructions on which the architectural conception demands them. However, there are also several structural advantages which justify their usage, such as a) reduced exposed area concerning fire and agressive environments; b) high axial compression resistance; c) high local buckling resistance. The aim of this work is the numerical analysis on the behavior of the I beam-circular hollow column connection, usually constituted by an external ring with single plate. It is presented a general view about the researchers development over the years on tubular structures focusing the compilation of the analytical design procedures and Eurocode 3 and ANSI/AISC classification as well. Finite element method softwares TRUEGRID and ANSYS are used for the numerical analysis in order to consider steel mechanical properties such as yielding, hardening and also geometric and contact nonlinearities. Numerical results present good agreement to codes\' analytical models. Analysis lead to understanding the connection\'s moment-rotation behavior and some of its parameters such as resistance, initial stiffness and ductility. It is shown external rings significantlly improve the semi-rigid connections stress distribution at the columns face.

Structures made of plate-like components are common in a variety of industries where the impacts of structural failures are severe. In many cases these structures are surrounded and only partially accessible, such as storage tanks and bridges, making them difficult to inspect frequently. The application of ultrasonic Guided Waves (GWs) in the evaluation and monitoring of relatively large plate-like structures is evermore a feasible option with the continuous development of transducer arrays. The use of transducer arrays is however complex due to directional control and the existence of many GW modes. Aimed at the evaluation of plate-like structures, in this research two piezoelectric transducer arrays respectively capable of omnidirectional and unidirectional control of the fundamental GW shear mode in plates (SH0) with above 20 dB mode purity are successfully designed, produced and validated. Omnidirectionality facilitates full structural evaluation coverage and can lead to defect mapping of large volumes with relatively few transducers. A unidirectional beam with relatively high mode purity facilitates evaluation of specific structural locations. Preference to the SH0 mode was given because of its non-dispersive and in-plane propagation properties making it more suitable than other GW modes to propagation in structures surrounded by fluid material. To enable the array development, a number of monolithic piezoelectric thickness-shear transducers of varied area were characterised with respect to GW mode directionality, amplitude and SH0 mode purity. The characterisation of each thickness-shear transducer allows for optimised superposition manipulation for specific applications. A single characterised shear transducer was selected for use in the development of omnidirectional and unidirectional SH0 mode transducer arrays. To aid development a linear superposition analysis model was produced and used to predict for a circular array design the optimum parameters for omnidirectional SH0 mode transmission with significant mode purity. A range of parameter combinations were evaluated and their predicted influence on array performance was characterised. The same method was employed to optimise a dual row linear array design for the unidirectional transducer array. All results were validated by FE models and later with empirical data. Both developed transducer arrays were characterised with respect to GW mode directionality, magnitude and SH0 mode purity. Both their detection sensitivity to pertinent defects and structures was validated, demonstrating relevance to Non Destructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications.

This thesis presents the results of a numerical investigation of the whole range, large deflection behaviour of axially and rotationally restrained RC beams and interactions between beams and columns in RC frame structures exposed to fire. The dynamic explicit time integration algorithm implemented in the general finite element package ABAQUS/Explicit solver was used so as to overcome various modelling challenges including temporary instability, local failure of materials, non-convergence and long simulation time. Either load factoring or mass scaling may be used to speed up the simulation process. Validity of the proposed simulation model was checked by comparison of simulation results against relevant test results of restrained RC beams at ambient temperature and in fire. The validated ABAQUS/Explicit model was then used to conduct a comprehensive study of the effects of different levels of axial and rotational restraints on the whole range behaviour of RC beams in fire, including combined bending and compression due to restrained thermal expansion, bending failure, transition from compression to tension when catenary action develops and complete fracture of reinforcement at ultimate failure. The numerical results show that different bending failure modes (middle span sagging failure, end hogging failure due to fracture of tensile reinforcement, end hogging failure due to concrete crushing) can occur under different levels of boundary restraints. Furthermore, release of a large amount of energy during the rapid transition phase from compression to tension in a beam prevents formation of a three hinge mechanism in the beam under bending. The numerical results have also revealed that reliable catenary action develops at large deflections following bending failure only if bending failure is governed by compressive failure of concrete at the end supports whereby a continuous tension path in the beam can develop in the top reinforcement. To allow fire engineering practice to take into consideration the complex restrained RC beam behaviour in fire, a simplified calculation method has been developed and validated against the numerical simulation results. The proposed method is based on sectional analysis and meets the requirements of strain compatibility and force equilibrium. The validation study results have shown that the simplified method can satisfactorily predict the various key quantities of restrained beam axial force and beam deflection-fire exposure time relationships, with the simplified method generally giving results on the safe side. The validated explicit finite element model in ABAQUS was also used to investigate structural interactions between beams and columns within an RC frame structure with different fire exposure scenarios. When fire exposure involves beams and columns located in edge bays of a frame, catenary action cannot develop. Also due to thermal expansion of the connected beam, additional bending moments can generate in the columns. Furthermore, very large hogging moments can be induced at the beam end connected to the internal bay. It is necessary to include these bending moments when designing beams and columns under such fire conditions. Catenary action can develop in interior beams of the frame when fire exposure is in interior bays where the beams have high degrees of axial restraint.

Selective electron beam melting (SEBM) is a promising powder bed Additive Manufacturing technique for near-net-shape manufacture of high-value titanium components. An extensive research program has been carried out to characterise in 3D the size, volume fraction, and spatial distribution of the pores in model samples, using X-ray computed tomography (XCT), and correlate them to the SEBM process variables. The average volume fraction of the pores (97.5 %) where fatigue cracks would initiate based on the relative stress intensity factor of all the pores. In contrast, crack growth was found to be insensitive to porosity, which was attributed to the much higher stress concentration generated by the crack in comparison to the pores. Some crack diversion was associated with the local microstructure, with prior β grain boundaries often coincident with crack diversion.

A caracterização do strain (deformação) em estruturas cristalinas em filmes finos semicondutores apresenta importantes aplicações tecnológicas, como por exemplo: a formação de defeitos, modificação da estrutura das bandas de condução e valência, e consequentemente modificando a mobilidade de portadores no material. Técnicas de espalhamento com íons de H e He têm sido amplamente empregadas para determinar a deformação, visto que mudanças na canalização ou nas direções de bloqueio podem ser facilmente relacionadas com as deformações no parâmetro de rede. Um novo método, chamado de cartografia-MEIS, é utilizado para determinar a intensidade da deformação estrutural em uma rede cristalográfica. A partir desta técnica, a projeção estereográfica de um único cristal pode ser medida com uma técnica MEIS padrão para um determinado elemento atômico e determinada profundidade. Aqui demonstramos que esta técnica pode ser expandida para caracterizar heteroestruturas SiGe tensas com alta precisão. Em nosso método, não só as principais direções cristalinas são analisados, mas também os índices mais elevados. O método também proporciona sensibilidade elementar com resolução de profundidade e pode ser utilizado em materiais nanoestruturados. A determinação da deformação baseia-se na posição das muitas linhas de bloqueio, ao contrário dos métodos tradicionais, onde duas direções são utilizados. Nós também fornecemos um método para determinar o melhor ajuste nos dados para a deformação na rede, verificando estes resultados a partir de simulações de Monte-Carlo. / The characterization of the strain in the crystal structures of thin semiconductor films has important technological applications such as, for example, the formation of defects, changes in the structure of the conduction and valence bands, and therefore modifying the mobility of carriers in the material. Scattering techniques with H and He ions have been widely used to determine the deformation, as changes in drains or the blocking directions can be easily related to the deformation of the lattice parameter. A new method, called cartography-MEIS, is used to determine the intensity of the structural deformation in a crystallographic structure. From this technique, the stereographic projection of a single crystal can be measured with a standard MEIS technique for a particular atomic element and given depth. Here we demonstrate that this technique can be expanded to characterize strained SiGe heterostructures with high accuracy. In our method, not only the main crystalline directions are analyzed but also the higher index ones. The method also provides elemental sensitivity with depth resolution and can be used in nano-structured materials. The determination of the strain is based on the position of the many blocking lines contrary to the traditional methods where two directions are used. We also provide a method to determine the lattice deformation fitting the data best and checked it against full Monte-Carlo simulations.

A principal característica de cabos é a sua capacidadede suportar grande carga na direção longitudinal e são utilizadas em, por exemplo, concreto comprimido, plataformas e pontes. Usualmente, sua estrutura básica é formada por um elemento central (núcleo) e reto juntamente com outros componentes dispostos ao seu redor em forma de hélice. Existe uma variedade de geometrias que podem ser utilizadas, assim como número de camadas. Seguindo a teoria de vigas espaciais e parametrizando a geometria, a linha média de apenas uma dessas hélices foi analisada analiticamente. Essa simplificação é valida visto que o contato e deslizamento não são incluídos nesta teoria, produzindo uma primeira abordagem ao problema da modelagem dessas estruturas. Sendo assim, as equações de equilíbrio foram deduzidas e seu sistema diferencial foi resolvido com o objetivo de representar o comportamento mecânico da estrutura. Utilizando a tríade de Frenet-Serret para definir um sistema de coordenadas local, as condições de contorno foram aplicadas buscando determinar as constantes de integração resultantes da solução analítica das equações diferenciais. Essa solução foi comparadas com resultados numéricos obtidos pelo Método dos Elementos Finitos (FEM) para validação dos casos de carga concentrada e distribuída em duas geometrias, o arco plano e a hélice. Em ambos os casos resultados apresentaram boa concordância para forças, momentos, rotações e deslocamentos. Considerando o caso do arco, o seu raio foi aumentado, de forma que a geometria se aproximasse de uma viga reta. O modelo proposto também foi utilizado para simular uma mola sob compressão. / A high number of structures uses cables due to their ability to bear large load in the longitudinal direction, for example, prestressed concrete, offshore systems and bridges. Its basic structure is formed by a central straight element surrounded by strands laid helically. A variety of geometries can be used, as well as the number of layers. Using the theory of spatial beams and parameterizing the geometry, the center line of only one of these helixes was analyzed analytically, since contact and slip are not included in this theory, obtaining a first approach in order to model these structures and to determine its mechanical behavior. Thus, the equilibrium equations were deduced and the differential system was solved with the objective of representing the mechanical behavior of the structure. Using the Frenet-Serret triad to define a local coordinate system, the boundary conditions were applied aiming the determination of the integration constants. The expressions obtained were compared with results obtained by the Finite Element Method (FEM) for validation applying concentrated and distributed loads. All cases presented good agreement FOR forces, moments, rotations and displacements. Considering the arc case, its radius was increased until a straight beam. The proposed model was also used to simulate a spring under compression.