This thesis presents research on the force and deflection behavior of beams with rectangular cross-sections undergoing lateral torsional buckling. The large 3-D deflection path of buckling beam tips was closely approximated by circular arcs in two planes. A new chain algorithm element was created from pseudo-rigid-body segments and used in a chain calculation that accurately predicted the force deflection relationship of beams with large 3-D deflections.

Understanding how different parameters affect the dynamic response of high-speed railway bridges is crucial to selecting an efficient structural form. Despite existing numerous publications within this field, only few address the importance of torsional deformations. The main objective of this thesis is to investigate the influence of the torsional resistance of the deck on the dynamic response of an existing bridge. Ulla River Viaduct is presented as a case study, allowing to analyse some aspects of its design and what their alteration entails. To this end, 6 different 3D FE models are compared, 5 of which show a modification from the original configuration. In addition, several positions of the train are considered to contrast the effects when the torsional modes are excited. The performed dynamic calculations are based on the implicit direct integration procedure. The analysis of the case study demonstrates the benefit of closing the torsional circuit of the deck. The results also evidence the need of including torsional effects in its dynamic assessment when low values of torsional rigidity are considered. All this is not easy when simplified 2D or 3D beam models are used. As a final remark, the original design of the Ulla River Viaduct is found highly efficient from a dynamical point of view.

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AASHTO LRFD requires the use of longitudinal stiffeners in plate girder webs when the web slenderness D/tw is greater than 150. This practice is intended to limit the lateral flexing of the web plate during construction and at service conditions. AASHTO accounts for an increase in the web bend buckling resistance due to the presence of a longitudinal stiffener. However, when the theoretical bend buckling capacity of the stiffened web is exceeded under strength load conditions, the Specifications do not consider any contribution from the longitudinal stiffener to the girder resistance. That is, the AASHTO LRFD web bend buckling strength reduction factor Rb applied in these cases is based on an idealization of the web neglecting the longitudinal stiffener. This deficiency can have significant impact on girder resistance in regions of negative flexure. This research is aimed at evaluating the improvements that may be achieved by fully considering the contribution of web longitudinal stiffeners to the girder flexural resistance. Based on refined FE test simulations, this research establishes that minimum size longitudinal stiffeners, per current AASHTO LRFD requirements, contribute significantly to the post buckling flexural resistance of plate girders, and can bring as much as a 60% increase in the flexural strength of the girder. A simple cross-section Rb model is proposed that can be used to calculate the girder flexural resistance at the yield limit state. This model is developed based on test simulations of straight homogenous girders subjected to pure bending, and is tested extensively and validated for hybrid girders and other limit states. It is found that there is a substantial deviation between the AISC/AASHTO LTB resistance equations and common FE test simulations. Research is conducted to determine the appropriate parameters to use in FE test simulations. Recommended parameters are identified that provide a best fit to the mean of experimental data. Based on FE simulations on unstiffened girders using these recommended parameters, a modified LTB resistance equation is proposed. This equation, used in conjunction with the proposed Rb model also provides an improved handling of combined web buckling and LTB of longitudinally stiffened plate girders. It is observed that the noncompact web slenderness limit in the Specifications, which is an approximation based on nearly rigid edge conditions for the buckling of the web plate in flexure is optimistic for certain cross-sections with narrow flanges. This research establishes that the degree of restraint at the edges of the web depend largely on the relative areas of the adjoining flanges and the area of the web. An improved equation for the noncompact web slenderness limit is proposed which leads to a better understanding and representation of the behavior of these types of members.

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Lateral-torsional buckling (LTB) is an important failure mode that needs to be taken into account during the design of steel beams. The fundamental equation for determining the elastic critical moment of a beam was derived with the assumption that the beam is subjected to a uniform bending moment distribution. Loads on steel structures generate a great variety of bending moment distributions. The effect of the bending moment distribution is taken into account by a parameter known as the equivalent moment factor. The procedure outlined in the South African National Standard for limit-states design of hot-rolled steel work, SANS 10162-1:2011, for determining the equivalent moment factor was originally developed for a bending moment that is uniformly or linearly distributed, however it is currently used for all bending moment distributions. A Finite Element (FE) model was developed in this investigation for determining the equivalent moment factor. The numerical model included residual stresses and initial geometric imperfections commonly found in hot-rolled steel beams. To validate the assumptions made during the development of the FE model an in-depth experimental investigation was conducted on simply supported beams. Three different load configurations were considered in the experimental study in order to simulate various bending moment distributions. A comparison of the equivalent moment factor between the numerical results and the results obtained from various steel specifications, including SANS 10162-1:2011, was carried out in an attempt to quantify the positive and negative attributes of the various methods employed by steel design specifications. The experimental investigation concluded that the FE model is able to successfully represent a simply supported beam with realistic characteristics that include residual stresses and imperfections. The comparative study illustrated that for a bending moment distribution with a constant moment gradient, SANS 10162-1:2011 provides excellent results. However, for the other distributions considered in this investigation highly conservative results were obtained for the equivalent moment factor. The relevance of these findings were made clear by considering three design cases found in steel structures. The resistance moment of the beams in each of these cases was calculated according to each of the steel specifications. It was found that the use of a highly conservative procedure for determining the equivalent moment factor can lead to the uneconomical design of a structure. / AFRIKAANSE OPSOMMING: Laterale-torsie knik is ’n belangrike falings modus wat in ag geneem moet word tydens die ontwerp van staal balke. Die fundamentele vergelyking vir die bepaling van die elastiese kritieke moment van ’n balk is afgelei met die aanname dat die balk onderworpe is aan ’n eenvormige buigmoment verdeling. Belastings op staalstrukture genereer ’n groot verskeidenheid van buigmoment verdelings. Die effek van hierdie buigmoment verdelings word in ag geneem deur ’n parameter wat bekend staan as die ekwivalente moment faktor. Die prosedure uiteengesit in die Suid-Afrikaanse Nasionale Standaard vir die ontwerp van warm-gewalste staalwerk, SANS 10162-1:2011, vir die bepaling van hierdie faktor is oorspronklik ontwikkel vir ’n buigmoment wat uniform of linieêr verdeel is oor die lengte van die balk, maar dit word tans gebruik vir alle buigmoment verdelings. ’n Eindige Element (FE) model is ontwikkel in hierdie ondersoek vir die bepaling van die ekwivalente moment faktor. Die numeriese model sluit die residuele spannings en aanvanklike geometriese imperfeksies wat in die algemeen teenwoordig is in warm-gewalste profiele in. Die aannames wat gemaak is tydens die ontwikkeling van die FE model is bevestig met ’n in diepte eksperimentele ondersoek oor die gedrag van eenvoudig opgelegde balke. Drie verskillende las konfigurasies is oorweeg in die eksperimentele studie om verskeie buigmoment verspreidings na te boots. ’n Vergelyking van die ekwivalente moment faktor tussen die numeriese resultate en die resultate verkry van verskeie staal spesifikasies, insluitend SANS 10162-1:2011, is uitgevoer in ’n poging om die positiewe en negatiewe eienskappe van die verskillende metodes wat gebruik word in verskillende staal ontwerp spesifikasies, te kwantifiseer. Die eksperimentele ondersoek het tot die gevolgtrekking gelei dat die FE model in staat is om ’n eenvoudige opgelegte balk te verteenwoordig, met realistiese eienskappe wat residuele spannings en imperfekies insluit. Die vergelykende studie toon dat SANS 10162-1:2011 uitstekende resultate bied vir ’n buigmoment verdeling met ’n konstante moment gradiënt. Dit was egter gevind dat vir ander verdelings wat in hierdie ondersoek oorweeg is, SANS 10162-1:2011 hoogs konserwatiewe resultate bied. Die toepaslikheid van hierdie bevindinge is duidelik gemaak deur drie ontwerp gevalle wat algemeen in staalstrukture gevind word te bestudeer. Die weerstandsmoment is in elk van die gevalle bereken volgens elke staal spesifikasies. Daar is gevind dat die gebruik van ’n hoogs konserwatiewe prosedure vir die bepaling van die ekwivalente moment faktor kan lei tot die ontwerp van ’n onekonomiese struktuur.

O objetivo deste trabalho é estudar a influência da rigidez do quadro na dirigibilidade de um veículo de competição fórmula SAE (protótipo E2-M, da equipe EESC-USP) em ambiente multicorpos com o software Adams/Car. Um modelo contendo os subsistemas de suspensão, direção, pneumático, powertrain, barra estabilizadora e quadro foi construído em ambiente multicorpos com componentes modelados como corpos rígidos. Posteriormente foram elaborados três modelos de quadros flexíveis com diferentes valores de rigidez torcional para substituir o quadro rígido. Estes foram obtidos através da análise modal com o auxílio do método dos elementos finitos. Para comparação da dinâmica lateral dos modelos, típicas manobras do estudo de dirigibilidade foram consideradas tais como rampsteer, step-steer e single lane change. Os resultados obtidos foram de aceleração lateral e velocidade de guinada. Pelas condições avaliadas, pode-se concluir que a rigidez torcional de um quadro para o protótipo E2-M pode estar entre 700 e 1500 N.m/o. Essa variação de rigidez representou 5 kg de massa no quadro. Porém deve-se fazer uma avaliação modal com a massa suspensa calibrada para verificar se não existe acoplamento de modos e freqüências com outros subsistemas. / This dissertation is intended to study the influence of frame stiffness in handling of a Formula SAE vehicle (E2-M prototype from EESC-USP Formula SAE team) in multibody with Adams/Car software. A model containing the subsystems of suspension, steering, tires, powertrain, frame and stabilizing bar was built considering rigid bodies. Subsequently, three models of flexible frames were developed with different values of torsional stiffness to replace the rigid frame. They were obtained through modal analysis with the aid of finite element method. For the handling investigation, maneuvers such as ramp-steer, step-steer and single lane change were considered. The results evaluated were lateral acceleration and yaw velocity. According to results, the torsional stiffness for the E2-M prototype can be between 700 and 1500 Nm/o. But an eigenvalue analyses is also necessary to verify if there is no coupling of modes of the calibrated sprung mass with other subsystems.

The aim of this study was to evaluate the mechanical properties of engine-driven Nickel-Titanium instruments manufactured by different thermal treatments. In the first part of this study, 60 reciprocating instruments were used (n=20): Reciproc R25 (REC 25.08), Unicone L25 (UNC 25.06) e Prodesign R 25 (PDR 25.06). The cyclic flexural fatigue resistance was performed measuring the time to failure in an artificial stainless steel canal with a 60º angle and a 5 mm radius of curvature (n=10). The torsional test was performed according to ISO 3630-1, measuring the torque and angle of rotation at failure in the 3 mm from the tip portion (n=10). Additionally, the fractured surface of each instrument was examined by scanning electron microscopy (SEM) to assess the topographic features of the fractured surface. Data were analyzed using one was analysis of variance ANOVA and Tukey test, the level of significance was set at 5%. The results of the cyclic flexural fatigue showed that PDR 25.06 presented significantly higher values than the other groups (P<0.05). REC 25.08 showed higher fatigue resistance than UNC 25.06 (P<0.05). In relation to the torsional test, the PDR 25.06 presented the lowest torque load than REC 25.08 and UNC 25.06 (P<0.05). In addition, there was no significant difference between REC 25.08 and UNC 25.06 (P>0.05). The PDR 25.06 and UNC 25.06 showed higher angular rotation until fracture than REC 25.08 (P<0.05). No difference was found between PDR 25.06 and UNC 25.06. All the instruments showed typical topographic features of cyclic flexural and torsional fatigue. The second part of this study evaluated the cyclic flexural and torsional fatigue resistance of reciprocating instruments Reciproc Blue (RB 25.08), WaveOne Gold Primary (WOG 25.07) and Prodesign R 25 (PDR 25.06) (n=20). The cyclic flexural fatigue test was performed with the same previsoly described device, using a root curvature with 60º and a 5 mm radius (n=10) and the torsional test was performed according to ISO 3630-1 (n=10). The fractured surface of each instrument was examined by scanning electron microscopy (SEM). Data were analyzed using one was analysis of variance ANOVA and Tukey test, the level of significance was set at 5%. The results of the cyclic flexural fatigue test showed that PDR 25.06 presented significantly higher values than the other groups (P<0.05). RB 25.08 showed higher fatigue resistance than WOG 25.07 (P<0.05). The torsional test showed that PDR 25.06 had lowed torsional load (P<0.05). No difference was found between RB 25.08 and WOG 25.07 (P>0.05). In relation the angular rotation, the PDR 25.06 showed higher angular rotation values than RB 25.08 and WOG 25.07 (P<0.05). RB 25.08 presented higher angular values than WOG 25.07 (P<0.05). All the instruments showed typical topographic features of cyclic flexural and torsional fatigue. The third part of this study was to evaluate the torsional fatigue resistance of NiTi rotary glide path instruments. The torsional test was performed according to ISO 3630-1, measuring the torque and angle of rotation at failure in the 3 mm from the tip portion. A total of 56 glide path instruments were used (n=8): Logic 25.01 (LOG 25.01), Logic CM 25.01(LOG CM 25.01), Proglider 16.02 (PGD 16.02), Hyflex GPF 15.01, 15.02, 20.02 (HGPF) and Mtwo 10.04. The fractured surface of each instrument was examined by scanning electron microscopy (SEM). Data were analyzed using one was analysis of variance ANOVA and Tukey test, the level of significance was set at 5%. The results showed that LOG 25.01 had a significantly higher torsional load than the other groups (P<0.05). The PGD 16.02 had significantly difference in comparison with HGPF 15.01 and 15.02 (P<0.05). LOG CM 25.01 had higher torsional load than HGPF 15.01 and 15.02 (P<0.05). No difference was found among Mtwo 10.04, HGPG 15.01, 15.02 and 20.02. In relation the angular rotation, LOG CM 25.01 and HGPF 15.01 presented the highest values (P<0.05). PGD 16.02 had the lowest values (P<0.05) followed by Mtwo 10.04. LOG 25.01 had higher angle of rotation than PGD 16.02 and Mtwo 10.04 (P<0.05). All the instruments showed typical topographic features of torsional fatigue. / O objetivo deste estudo foi avaliar o comportamento mecânico de instrumentos mecanizados de Níquel-Titânio (NiTi) fabricados com diferentes tratamentos térmicos. Na primeira parte do estudo foram utilizados 60 instrumentos reciprocantes para a realização dos teste de fadiga cíclica flexural e torcional (n=20): Reciproc R25 (REC 25.08), Unicone L25 (UNC 25.06) e Prodesign R 25 (PDR 25.06). O teste de fadiga cíclica flexural foi realizado com o objetivo de mensurar o tempo para a fratura dos instrumentos em um canal artificial de aço inoxidável com curvatura com 60º de angulação e 5 mm de raio (n=10). Para o teste de torção, os 3 mm inicias das pontas dos instrumentos foram fixadas em um aparelho de torção (n=10), de acordo com a norma ISO 3630-1. Este teste foi realizado com o objetivo de mensurar o torque máximo e o ângulo de rotação suportado pelos instrumentos até sua fratura. Adicionalmente, todos os fragmentos dos instrumentos fraturados foram examinados em microscopia eletrônica de varredura (MEV) para avaliar as características topográficas da superfície da área da fratura. A análise-estatística foi realizada utilizando o teste de análise de variância com um fator ANOVA e teste de Tukey, o nível de significância foi de 5%. Os resultados de fadiga cíclica flexural demonstraram que o PDR 25.06 apresentou maior tempo para a fratura do que os outros grupos (P<0.05). O instrumento REC 25.08 apresentou maior resistência a fadiga cíclica flexural do que o UNC 25.06 (P<0.05). O teste de torção demonstrou que o PDR 25.06 apresentou significantemente menor resistência torcional do que o REC 25.08 e UNC 25.06 (P<0.05). Além disso, não houve diferença entre REC 25.08 e UNC 25.06. Com relação ao ângulo de rotação, o PDR 25.06 e UNC 25.06 apresentaram diferença significante quando comparado ao REC 25.08. Não houve diferença entre PDR 25.06 e UNC 25.06 (P>0.05). Todos os instrumentos apresentaram característica topográficas típicas de fadiga cíclica flexural e torcional. Na segunda parte deste estudo avaliou-se a fadiga cíclica flexural e torcional dos instrumentos reciprocantes Reciproc Blue R25 (RB 25.08), WaveOne Gold Primary (WOG 25.07) e Prodesign R 25 (PDR 25.06) (n=20). O teste de fadiga cíclica flexural foi realizado com dispositivo descrito anteriormente, utilizando curvaturas de 60º e 5 mm de raio (n=10). O teste de torção foi realizado de acordo com a norma ISO 3630-1 (n=10). Todos os fragmentos dos instrumentos fraturados foram examinados em microscopia eletrônica de varredura (MEV) para avaliar as características topográficas da superfície da área da fratura. A análise-estatística foi realizada utilizando o teste de análise de variância com um fator (ANOVA) e teste de Tukey, o nível de significância foi de 5%. Os resultados de fadiga cíclica flexural demonstraram que o PDR 25.06 apresentou a maior resistência a fadiga cíclica flexural do que dos outros grupos (P<0.05). O RB 25.08 apresentou maior tempo para à fratura do que o WOG 25.07 (P<0.05). O teste de torção, o PDR 25.06 apresentou a menor resistência à torção do que os outros grupos (P<0.05). Não houve diferença significante entre RB 25.08 e WOG 25.07 (P>0.05). Em relação ao ângulo de rotação, o PDR 25.06 apresentou maiores valores quando comparados com RB 25.08 e WOG 25.07. O RB 25.08 apresentou diferença significante quando comparado com WOG 25.07. Todos os instrumentos apresentaram características topográficas típicas de fadiga cíclica flexural e torcional. Na terceira parte deste estudo avaliou-se a resistência torcional de instrumentos empregados para patência do canal radicular, de acordo com a norma ISO 3630-1. Foram utilizados 56 instrumentos rotatórios (n=8): Logic 25.01 (LOG 25.01), Logic CM 25.01 (LOG CM 25.01), Proglider 16.02 (PGD 16.02), Hyflex GPF 15.01, 15.02, 20.02 (HGPF) e Mtwo 10.04. Os fragmentos dos instrumentos fraturados foram examinados em microscopia eletrônica de varredura (MEV) para avaliar as características topográficas da superfície da área da fratura. A análise-estatística foi realizada utilizando o teste de análise de variância com um fator ANOVA e teste de Tukey, o nível de significância foi de 5%. Os resultados demonstraram que o LOG 25.01 apresentou significantemente maior resistência torcional do que os demais grupos (P<0.05). O grupo da PGD 16.02 apresentou diferença significante quando comparado com HGPF 15.01 e 15.02 (P<0.05). O LOG CM 25.01 apresentou maior resistência torcional do que o grupo do HGPF 15.01 e 15.02 (P<0.05). Não houve diferença significante entre os intrumentos Mtwo 10.04 e HGPF 15.01, 15.02 e 20.02. Com relação ao ângulo de rotação, o LOG CM 25.01 e HGPF 15.01 apresentaram os maiores valores (P<0.05). O PGD 16.02 apresentou o menor valor de todos os grupos (P<0.05) seguido pelo Mtwo 10.04. O LOG 25.01 apresentou maiores ângulos de rotação do que o PGD 16.02 e Mtwo 10.04 (P<0.05). Todos os instrumentos apresentaram característica topográficas típicas de fadiga torcional. As características da secção transversal, tipo de núcleo, taper e o tratamento térmico possuem forte influência sobre as propriedades mecânicas dos instrumentos de NiTi. No entanto, o tratamento térmico é um dos fatores primordiais para maior flexibilidade dos instrumentos. O instrumento PDR 25.06 apresentou maior resistência à fadiga cíclica flexural e maior ângulo de rotação no teste de torção do que todos os outros instrumentos reciprocantes avaliados. No entanto, menor resistência torcional. Os intrumentos LOG 25.01 apresentaram maior resistência torcional e o LOG CM 25.01 maiores ângulos de rotação.

As vigas de rolamento são estruturas destinadas ao suporte de pontes rolantes, estas amplamente utilizadas para movimentação de cargas em galpões industriais. O presente trabalho apresenta um estudo sobre as vigas de rolamento de aço sem contenção lateral entre apoios, em geral projetadas com vão inferior a 7 metros, portanto destinadas ao suporte de pontes rolantes leves (capacidade nominal até 250 kN). A ausência de contenções laterais intermediárias aliada ao desalinhamento e à imprecisão na locação dos trilhos, bem como à presença de forças horizontais transversais ao eixo da viga (aceleração/frenagem do trole), impõem flexão lateral e torção, esforços que são equilibrados apenas pelas contenções nos apoios. A análise foi realizada utilizando o Método dos Elementos Finitos (MEF), considerando a análise não linear física e geométrica do problema, ou seja, um modelo mais próximo da viga real. Os resultados numéricos, quando comparados aos obtidos por meio da teoria de flexo-torção, mostraram uma inversão na distribuição esperada de tensões na mesa superior do perfil, ou seja, nos pontos onde deveria ocorrer aumento da tensão longitudinal de compressão, ocorreu redução. Esta inversão pode ou não ocorrer, dependendo da espessura da mesa superior, intensidade e posição da força vertical da roda da ponte. Além disso, os resultados determinados via MEF foram comparados com os obtidos via modelo tradicional de barra (momento de torção substituído por um binário de forças horizontais nas mesas). A comparação indicou divergência entre os resultados, podendo o dimensionamento pelo modelo de barra levar tanto a situações a favor da segurança como contra a segurança. / The runway girders are structures intended for support cranes, these broadly used to movement of loads in industrial buildings. This research presents a study about the runway girders without lateral bracing between support points, generally designed with span lower than 7 meters, therefore intended for support of light cranes (rated capacity until 250 kN). The absence of intermediate lateral bracing allied to misalignment and imprecision location of the rail, also the presence of the side thrust on the girder (acceleration/ braking of the trolley), causes lateral flexural and torsion, which are balanced only by the lateral containment on support points. The analysis was made using the Finite Element Method (FEM), which includes a nonlinear physical and geometric analysis of the structural problem, in other words, a model closest to the real girder. The numerical results, when compared to the results of the flexural-torsional theory, showed an inversion in the expected distribution of stress on the top flange of the shape, in other words, at the points where must occur increase of the longitudinal stress, reduction occurred. This inversion may or may not occur, depending on the thickness of the top flange, modulus and position of the load of the crane wheel. Besides, the numerical results were compared with the results of classical bar model for beams (torque is replaced by a couple of horizontal forces applied on the flanges). The comparison showed a divergence between the results, where the design by bar classical model can lead to situations of high safety or against safety.