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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
211

Snižování vibrací a akustických emisí pohonných jednotek aplikací virtuálního motoru / Vibration and Acoustic Emission Reduction of Powertrains using Virtual Engine

Svída, David January 2011 (has links)
Doctoral thesis deals with combustion engine cranktrain vibrations and vibration analysis methods. The work applies new computational models aimed at powertrain vibration decrease. The computational models can be used in the first stages of powertrain development. Temperature dependences of the rubber shear modulus and loss factor characteristic are found by response analysis of the free damped vibrations in the first part of the thesis. Viscoelastic model parameters of two dampers with different rubber hardness are calculated using optimization methods. Temperature distribution inside the rubber part during the harmonic oscillation is calculated with the knowledge of previous values. Computational models together with a user interface are assembled in Matlab/Simulink software tool. Computational model results of the viscoelastic rubber damper are verified by measurements on a prototype diesel engine in the whole operating engine speed range. Torsional vibrations of the crankshaft with torsional damper are measured by POLYTEC laser rotational tools. The temperature distribution on the damper surface is obtained by Infratec VarioCAM thermographic system. Combustion pressures in the cylinder are measured by SMETEC Combi indication tools. Both the temperature distributions and combustion pressures are used for computational purposes. All the measurement procedures are described also in the thesis.
212

Klopení tenkostěnných ocelových nosníků s otvory ve stěně / Lateral Torsional Buckling of Thin-Walled Steel Beams with Web Holes

Horáček, Martin January 2016 (has links)
The current trend in the design of steel structures leads, due to the saving of the material, to the frequent use of thin-walled cold formed steel sections. Thin cold-formed steel profiles are often manufactured with web holes. A specific example of thin-walled steel profiles are Sigma beams used in additionally installed built-in floors systems in warehouses. The aim of doctoral thesis is the analysis, assessment and experimental verification of the technical solution of thin-walled steel beams with web openings loaded in bending with respect to lateral torsional buckling. The objective is to develop knowledge about the real properties of steel members of considered structural arrangement in order to specify the methods of analysis and design in industrial practice. The theoretical analysis describes the behavior of the beams by means of solving the differential equations of the equilibrium on deformed element of thin walled member under bending. In case of beams with web holes is used the solution in the form of introduction of substitute cross-section properties, which are defined as the weighted average of the properties of full and weakened section. The numerical analysis is focused on the use of commonly available software in order to predict the bending resistance of beams with web opening with respect to lateral torsional buckling. Since the software used in practice solves only the prismatic beams without option to model the web openings, it is in frame of numerical analysis verified the model of beam with reduced thickness of web constantly over the whole beam length in the zone of perforation. The experimental analysis is firstly focusing on the verification of real bending and torsion stiffness of the beams, based on which are being derived the values of basic cross-sectional properties. Subsequently the experimental verification of real bending resistance with respect to the lateral torsional buckling is being performed.
213

Stabilitní problémy prutů z vrstveného konstrukčního skla / Stability problems of laminated structural glass members

Pešek, Ondřej January 2018 (has links)
Transparent and subtle structures are features of modern architecture. Structural glass is constructional material that provides to realize architect's visions and ideas. Glass as a constructional material is more often used as a material for primary load-bearing structures. Realization of safe, reliable and economic glass structure is real challenge for structural engineers because of absence of standards for designing of glass members and elements. Compressed members (columns), bended members (beams) and members loaded by compression and bending (beam-columns) were analysed in the frame of the doctoral thesis whereby the emphasis is being placed on the lack of stability – flexural buckling, lateral-torsional buckling and flexural-lateral-torsional buckling. Measuring of shape and amplitude of initial geometrical imperfections is a part of doctoral thesis. The theoretical analysis describes the behaviour of the member by means of solving the differential equations. The solution according to the second order theory developed for metal members is applied on structural laminated glass members with use of effective cross-sectional characteristics. Numerical analysis is focused on the use of commonly available software based on finite element method in order to predict the load-bearing resistance of laminated glass members. Actual behaviour of laminated and monolithic structural glass members was found within experimental program. The correctness of FEM model and analytical solutions were evaluated by comparing with test results. The goal of the doctoral thesis was determine of buckling curves for calculation of flexural buckling and lateral-torsional buckling resistances by the same calculation procedure as for metal members. Because of small number of experimentally tested specimens the Monte Carlo simulation was performed.
214

Modelling and Mechanical Analysis of Continuously Transposed Conductor / Modellering och mekanisk analys av CTC

Hu, Haicheng January 2020 (has links)
As the CTC (transposed continuously conductor) is widely accepted as the cable used in transformers, mechanical analysis of CTC under different load cases is in need. This paper introduces a new method of creating detailed CTC models automatically in Comsol Multiphysics and the models are applied for conducting FEA (Finite Element Analysis) for different load cases of practical importance. The numerical analysis is verified by comparing the FEA results and the analytical results for the response of the CTC. The difference between the FEA of simplified models (bare straight strands conductor models) and detailed models (transposed strand conductor models), is also evaluated. Finally, the detailed model with an epoxy coating is evaluated. The detailed CTC model is found to be more compliant when subjected to radial bending compared to the simplified model, but it is stiffer than the simplified model when subjected to an axial bending load. In torsion, the detailed CTC models have much lower torsional rigidity than the simplified models. The epoxy coating makes the whole structure much more compliant and largely decreases the torsional rigidity of the CTC structure. The research shows that the difference between the simplified model and the detailed model is not negligible in many load cases. However, for an analysis that does not strictly require accuracy when doing axial loading analysis, the simplified model is a good option since it is easier to model, computationally cheaper, and the result is close to the detailed model result. In other cases, the detailed model is to be preferred. / CTC-kablar som används i högspänningstransformatorer utsätts under drift för olika typer av mekaniska laster och det finns ett behov att kunna analysera mekaniska egenskaper vid olika typer av lastfall. I denna rapport introduceras en ny metod för att automatiskt skapa detaljerade modeller av CTC i Comsol Multiphysics. Dessa modeller används sedan för analys med finita element-metoden (FEM) av några praktiskt viktiga belastningsfall. Den numeriska analysen verifieras genom att jämföra FE-resultaten med analytiska resultat för enkla idealiserade balkgeometrier. Vidare analyseras skillnaden mellan FEA för de förenklade modellerna och geometriskt detaljerade modeller CTC både med och utan isolerande epoxiskikt kring ledarna. Den detaljerade CTC-modellen visade sig vara mindre styv, jämfört med den förenklade modellen, när den utsätts för radiell böjning, men styvare när den utsattes för en axiell böjning, där radiell och axiell avser riktningarna CTC har i en högspänningstransformator. I torsion har de detaljerade CTC-modellerna mycket lägre vridstyvhet än de förenklade modellerna. Epoxibeläggningen gör hela strukturen mycket mer kompliant och minskar till stor del torsionsstyvheten hos CTC strukturerna. Vidare visar resultaten att skillnaden mellan den förenklade modellen och den detaljerade modellen inte är försumbar i många belastningsfall. Men för en analys som inte strikt kräver noggrannhet när man utför axiell belastningsanalys, är den förenklade modellen ett bra alternativ eftersom den är avsevärt lättare att modellera, beräkningarna är mycket snabbare och resultaten ligger nära de för den detaljerade modellen. I andra fall är den detaljerade modellen att föredra.
215

[en] DRILL STRING VIBRATIONS IN SOLIMÕES BASIN OPERATIONS / [pt] VIBRAÇÕES EM COLUNAS DE PERFURAÇÃO EM OPERAÇÕES NA BACIA DO SOLIMÕES

PAULO ALBERTO DA COSTA MATTOS 28 January 2016 (has links)
[pt] Os custos de uma campanha exploratória, incluindo a perfuração de poços de petróleo estão cada vez mais elevados. As vibrações nas colunas de perfuração estão presentes a todo momento nas operações de perfuração, o que podem ocasionar a quebra destas colunas e do BHA (Bottom Hole Assembly), danos em brocas e demais equipamentos. Além do custo do possível dano e/ou perda destes equipamentos, existem os custos da sonda parada e a despesas operacionais das companhias contratadas, o chamado custo de Stand by, e o mais indesejável, a perda do poço. Fenômenos como Bit Bounce, Stick-Slip e Forward/Backward Whril, que advém das vibrações axiais, torcionais e laterais respectivamente, são motivos de vários estudos. Esta dissertação pretende fazer a validação do modelo matemático de dinâmica torcional utilizado na dissertação de mestrado de CAYRES (2013) para gerar mapas de estabilidade para vibrações torcionais. Nesta dissertação parâmetros reais de uma coluna de perfuração foram inseridos no modelo com objetivo de obter mapas de estabilidade de vibrações torcionais para a perfuração de um poço na Bacia de Solimões. Tais mapas de estabilidade foram gerados a partir deste modelo matemático, que na tese de CAYRES (2013), é baseado em procedimento experimental, com um atrito não linear induzindo o fenômeno stick-slip que está associado às vibrações torcionais. Este fenômeno tem relação entre torque e velocidade angular na broca provocando vibrações indesejáveis na coluna de perfuração. A geração destes mapas permitiu que a análise de sensibilidade e a averiguação da ocorrência ou não de vibrações torcionais fossem feitas, bem como a inserção de valores de WOB (peso sobre a broca) e RPM (velocidade de rotação) de um caso real de perfuração de um poço na Bacia do Solimões. Nesta análise de sensibilidade foram considerados, além dos aspectos acima citados, o tipo de broca e formação geológica, permitindo assim a validação do modelo de CAYRES (2013) e contribuindo para a otimização dos processos operacionais da perfuração de poços de petróleo. / [en] The costs of an exploration campaign, including the drilling of oil wells are increasingly high. The vibrations in the drill strings are present at all times in drilling operations that can cause damage of these drill pipe and BHA (Bottom Hole Assembly), as drill bits and other equipment. Besides the cost of a possible damage or loss of such equipment, there are the costs when the rig is not operating and the expenses of all companies involved in the operations, called the cost of stand by, and the worst case scenario of the undesirable loss of the well. The Phenomena like Bit Bounce, Stick-Slip and Forward/Backward Whril, that arises from axial, torsional and lateral vibrations respectively are the motivation of several studies. This dissertation aims to show the validation of the mathematical modeling of the torsional dynamics used in CAYRES (2013) that generate stability maps for torsional vibrations. In this dissertation real parameters from a drill string were inserted in this mathematical modeling, aiming to obtain stability maps for torsional vibrations during a drilling operation of a well in Solimões Basin. Such stability maps were generated from a dynamic model that in CAYRES (2013) thesis is based on an experimental procedure with a nonlinear friction inducing stick-slip phenomenon associated to torsional vibrations. This phenomenon is related to torque and angular velocity on the bit generating undesirable vibrations. Build stability maps and checking when torsional vibrations happen, and then comparing with a real case of WOB (weight on bit) and RPM (rotary speed) in Solimões Basin. In this sensitivity analysis were considered, besides the aspects mentioned above, the kind of bit and geological formation in order to contribute to the optimization of the oil well drilling operational process.
216

Fabrication and Characterization of Torsional Micro-Hinge Structures

Marrujo, Mike Madrid 01 June 2012 (has links) (PDF)
ABSTRACT Fabrication and Characterization of Torsional Micro-Hinge Structures Mike Marrujo There are many electronic devices that operate on the micrometer-scale such as Digital Micro-Mirror Devices (DMD). Micro actuators are a common type of DMD that employ a diaphragm supported by torsional hinges, which deform during actuation and are critical for the devices to have high stability and reliability. The stress developed within the hinge during actuation controls how the actuator will respond to the actuating force. Electrostatically driven micro actuators observe to have a fully recoverable non-linear viscoelastic response. The device consists of a micro-hinge which is suspended by two hinges that sits inside a micro machined well. To achieve a specific angle of rotation when actuated, the mechanical forces need to be characterized with a range of different forces applied to the edge of the micro-hinge. This research investigates the mechanical properties and the amount of force needed to rotate to specific angles by comparing theoretical performance to experimentally measured values. Characterizing the mechanical forces on the micro-hinge will further the understanding of how the device operates under a specific applied force. The material response to the amount of stress within the hinges will control the amount of actuation that is achieved by that force. The test devices were fabricated using common semiconductor fabrication techniques. The micro-hinge device was created on a 500µm, double-sided polished, single crystal (100) silicon wafer. In order to create this device, both wet etching and dry etching techniques were employed to produce an 8µm thick plate structure. The bulk etching of 480µm was achieved by wet etching down into the silicon (Si) to create the wells. Dry etching was used for its high precision to release the micro-hinge structure. Once fabricated, the micro-hinge actuators were tested using a Technics turntable arm with a built in micrometer that applied a constant force while measuring the displacement of the actuator. The rotation of the hinge was measured by reflecting a Helium-Neon (HeNe) laser beam off a mirror, which is attached to the pivot of the arm that’s applying the force, and any type of displacement was recorded with a Photo Sensitive Device (PSD). The test stand applied a small force which replicated the amount of electrostatic forces needed to achieve a specific degree of rotation. Results indicate that the micro-hinge achieved a repeatable amount of rotation when forces were applied to it. The micro-hinge would endure deformation when too much force would be applied and yield a maximum amount of force allowed.
217

Mechanochromic Donor-Acceptor Torsional Springs Based on ortho-Substituted Diphenyldiketopyrrolopyrrole

Raisch, Maximilian 24 January 2023 (has links)
Mechanochromic polymers are force-sensitive materials that change their color as a response to mechanical stimuli. This visualization of forces can be used to further optimize polymer-based materials by understanding microscopic force transduction or to display fatigue of material. Most mechanochromic systems rely on bond cleavage, so they can only distinguish between “on” and “off” state without any further correlation of the applied force with the optical signal. Although reversibility to the initial state is possible for most of these systems, it often demands time or input of energy making them rather unsuitable for sensing forces in real-time. In this work, the development and application of mechanochromic donor (D)-acceptor (A) torsional springs is presented as a new concept for mechanochromic materials. The mechanically induced planarization of D and A leads to a continuous red-shift of both absorption and emission color. A suitable DA-system is found in ortho-substituted diphenyldiketopyrrolopyrrole (o-DPP) having the large torsional angle required for the equilibrium geometry and therefore showing blue-shifted optical spectra compared to reference compounds with a smaller torsional angle. The covalent incorporation into tough poly(meta,meta,para-phenylene) (PmmpP) by Suzuki polycondensation enables sufficient force transduction to the DA spring during uniaxial elongation of thin-film specimens. The detected mechanochromic response correlates with the applied stress and shows full reversibility upon stress release. Theoretical experiments based on density functional theory (DFT) confirm the experimental results and offer a detailed explanation of the molecular deformations responsible for the optical shift. In addition, the application as stress sensor was tested investigating the molecular force transduction in glassy PmmpP as a function of the number average molecular weight (Mn) by blending o-DPP-PmmpP probe chains of varying Mn with pristine PmmpP. The distinct mechanochromic response for entangled and non-entangled probe chains, respectively, allows the extraction of the critical molar mass (Mc) that is required for entanglements to become effective. The resulting value for the entanglement molar mass Me ≈ 1/2 Mc is in excellent agreement with the value determined by rheology.
218

I-girder Composite Bridges with Lateral Bracing : Improved load distribution

Vestman, Victor January 2023 (has links)
This thesis deals with the subject of lateral bracing between the bottom flanges of I-girder composite bridges. The focus is on the impact of adding lateral bracing on existing bridges, as well as on new bridges. Experience and knowledge from bridge projects around the world are investigated and implemented in the evaluation of the research subject. Many existing bridges are in need of being strengthened or replaced, due to the increased traffic volume and heavier traffic loads. Different approaches can be used to prolong the lifetime of existing bridges. The approach is different depending on the cause, but for increasing the lifetime regarding fatigue some of the most suitable options are described in this thesis. A proposed concept is presented, in this thesis, along with some research questions to be answered. The use of lateral bracings in composite bridges varies between different parts of the world. In one country it can be a requirement/common praxis for long span composite bridges with two I-girders, in other countries there are no requirements of using them. Some parts of these regulations and requirements can be traced back to the tradition in both manufacturing and construction of this type of bridges. This thesis investigates how lateral bracing is used around the world to distribute eccentric loads between primary longitudinal structural members, provide resistance to lateral loads, and to permit an existing two-girder structural system to be retrofitted to behave similarly to an often more expensive closed steel box girder. Furthermore, several case studies have been conducted to investigate the impact on the structural behavior of composite bridges where a lateral bracing is implemented in the structure. The results from these case studies are presented in the thesis and show the advantages of the quasi-box section for which the lateral bracing is closing the composite cross section. By making the I-girder composite cross section acting more like a box-section, the distribution of eccentric loads between the girders is improved. The impact on longitudinal stresses from traffic loads and the additional effects on internal sectional parts are also evaluated and discussed. Furthermore, proposals of the connection design for lateral bracings in existing bridges are suggested. Finally, conclusions from the results are stated.
219

[en] ANALYSIS AND MODELING OF TORSIONAL VIBRATIONS AND STICK-SLIP PHENOMENON IN SLENDER STRUCTURE SYSTEMS: EXPERIMENTAL INVESTIGATIONS AND NONLINEAR IDENTIFICATION / [pt] ANÁLISE E MODELAGEM DE VIBRAÇÃO TORCIONAL E STICK-SLIP EM SISTEMAS DE ESTRUTURAS ESBELTAS: INVESTIGAÇÕES EXPERIMENTAIS E IDENTIFICAÇÃO NÃO LINEAR

INGRID PIRES MACEDO OLIVEIRA DOS SANTOS 31 October 2023 (has links)
[pt] Durante a perfuração de poços de petróleo, a coluna de perfuração apresenta um comportamento dinâmico complexo, esta tese foca no estudo experimental e na modelagem matemática deste comportamento. Neste trabalho, destaca-se as vibrações autoexcitadas axiais, laterais e torcionais, que podem levar a efeitos como o bit bouncing, o whirling e stick-slip torcional. A primeira contribuição desta tese é a análise experimental de um bancada de testes, que fornece informações sobre a dinâmica de sistemas torcionais. A influência dos parâmetros de controle não lineares na resposta do sistema é investigada, identificando as condições sob as quais o fenômeno stick-slip ocorre. Em segundo lugar, a tese propõe estratégias de identificação de sistemas para sistemas não lineares, utilizando a mesma bancada de testes supracitada. Uma abordagem híbrida para a identificação é proposta, onde técnicas de modelagem de caixa cinza e caixa preta são combinadas para calibrar os parâmetros do sistema, particularmente aqueles associados ao atrito. Essa abordagem aumenta a precisão das estimativas em comparação com os métodos tradicionais de caixa cinza, mantendo a interpretabilidade. Além disso, a pesquisa emprega physics-informed deep learning para estimar os parâmetros mecânicos e de atrito do modelo de dois graus de liberdade. A calibração usando dados experimentais obtidos de uma bancada de testes fornece informações sobre o comportamento de sistemas de perfuração. Finalmente, a tese apresenta investigações experimentais sobre o acoplamento entre oscilações torcionais e axiais utilizando uma bancada experimental de perfuração em escala de laboratório modificada e adaptada equipada com brocas e amostras de rocha reais. Em resumo, esta tese aumenta a compreensão da dinâmica de colunas de perfuração e apresenta aplicações úteis para técnicas de identificação de sistemas na análise de oscilações torcionais e axiais. / [en] During drilling for oil extraction purposes, the drill string experiences complex dynamic behavior, and this work delves into the experimental study and the mathematical modeling of such behavior. Self-excited vibrations, such as axial, lateral, and torsional vibrations, which can lead to detrimental effects such as bit bouncing, whirling, and torsional stick-slip are highlighted in this thesis. Distinct aspects of drilling dynamics are considered in this investigation to enhance the understanding of various phenomena. Initially, an experimental analysis of a lab-scale rig is conducted, providing valuable insights into the dynamics of such systems. And the influence of control parameters on the system’s response is examined, particularly in identifying the conditions under which the stick-slip phenomenon is likely to occur. Secondly, the thesis proposes system identification strategies for nonlinear systems, specifically focusing on the same laboratory test rig. An innovative ensemble approach is proposed, which combines gray and black-box modeling techniques to effectively calibrate the parameters of a dynamical system, particularly those associated with friction. This approach improves prediction accuracy compared to traditional gray-box methods while maintaining interpretability in the dynamic responses. Furthermore, the research employs physics-informed deep learning to estimate the low-dimensional model mechanical and friction parameters. Calibration using experimental data obtained from a specialized setup provides insights into the drill-string system s behavior. Finally, the thesis involves experimental investigations on the coupling between torsional and axial oscillations using a modified and adapted lab-scale drilling rig equipped with real drill bits and rock samples. In summary, this thesis advances our understanding of drill-string dynamics and presents helpful applications for system identification techniques.
220

Elastic Lateral Torsional Buckling of Beams Strengthened with Cover Plates while under Loading

Iranpour, Amin 18 January 2024 (has links)
The aging infrastructure worldwide and the typical increase in service loads relative to original design loads make it essential to develop effective techniques for strengthening and rehabilitating existing structures, to enhance their resistance. An effective method for strengthening existing steel I-beams is to weld either one or two cover plates to the flange(s). In many cases, it is not feasible to completely unload the beam before carrying out the strengthening procedure. In these conditions, operators resort to strengthen beams while under loading. In such scenarios, it becomes a challenging task to assess the lateral torsional buckling (LTB) capacity of the member under present steel design standards (e.g., CAN/CSA-S16 2019 and ANSI/AISC360 2022) which do not consider the effect of pre-strengthening loads on LTB resistance. Within this context, the present study investigates the effects of pre-strengthening loads on the critical moment capacity by developing a series of solutions, ranging from elaborate and accurate to simplified but approximate, to predict the elastic LTB capacity of beams strengthened with cover plate(s) while under load. In this respect, the study contributes to the existing body of knowledge through four aspects: In the first contribution, a shell-based finite element (FE) study is developed to analyze the effect of various geometric and loading parameters on the LTB capacity of doubly symmetric beams strengthened symmetrically with two cover plates. The study carefully simulates the entire history, including the application of pre-existing loads, clamping forces to align the initially straight steel cover plates with the bent beam configuration, the rebound effect arising after clamping force removal, the contact at the interfaces between cover plates and flanges induced by welding, and the application of post-strengthening loads up to the point of elastic LTB initiation for the strengthened system, as determined by eigenvalue analysis. A simplified design equation is then proposed to quantify the post-strengthening critical moment capacity. The validity of the equation is assessed against FE results and its merits and limitations are discussed. The study shows that web distortional effects play a crucial role in reducing the elastic critical moment capacity. Practical recommendations are provided to mitigate such distortional effects and hence maximize the elastic critical moment capacity of the strengthened beams. The second contribution formulates a variational principle for the LTB analysis of doubly symmetric beams strengthened symmetrically with identical steel cover plates. The formulation considers the full sequence of loading and strengthening and captures the effects of pre-strengthening loads and the beneficial effects of pre-buckling deformation (PBD). The study examines the effect of geometry, partial strengthening schemes, presence of different pre- and post-strengthening load patterns, and load height effects. The variational principle is subsequently used to develop a FE formulation, culminating in a quadratic eigenvalue problem. The validity of the FE formulation is assessed through comparisons with other numerical techniques predictions as well as experimental results by others, and subsequently used to conduct a parametric study to characterize the gain in elastic critical moment capacity attained by cover plate strengthening. For beams partly strengthened with cover plates along their spans, the study identifies the optimum locations for cover plates that maximize the critical moments. The third contribution builds upon the variational principle developed by formulating a simple and approximate energy-based design-oriented solution to quantify the LTB resistance of simply supported I-beams strengthened with cover plates. The solution captures the detrimental effect of loads acting on the beam before strengthening and the beneficial effects resulting from PBD, pre- and post-strengthening load heights, as well as moment gradient effects. The potential use of the equations developed in practical applications involving beam strengthening is illustrated through design examples. The fourth contribution expands the variational formulation to include beams with monosymmetric cross-sections and/or symmetric beams with unsymmetric cover plate geometries. The modified variational principle is used to develop a thin-walled beam FE formulation, which is subsequently employed to predict the non-distortional LTB capacity of monosymmetric strengthened beams. Comparative analyses with shell models confirm the validity of the proposed solutions, and practical design recommendations for suppressing web distortion are provided. The effects of various design parameters on the total elastic critical moment capacity are evaluated in a systematic parametric study. The study identifies the loading conditions under which the magnitude of pre-strengthening loads significantly influences the predicted total critical moments. The solutions developed in the present study equip structural designers and analysts with novel techniques that reliably quantify the LTB strength of steel beams strengthened with cover plates, thus enabling them to optimize strengthening strategies for beams whose strengths are governed by LTB modes of failure.

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