Orientador: Renata Zotin Gomes de Oliveira / Resumo: Este trabalho concentra-se no estudo do comportamento elástico de materiais através da análise das matrizes de rigidez e flexibilidade de estruturas elementares. Baseado em conceitos da disciplina Resistência dos Materiais e nas propriedades elásticas dos materiais são apresentadas e demonstradas relações matemáticas que refletem as associações entre as tensões normais e de cisalhamento atuantes e as deformações e distorções decorrentes. Essas relações são ilustradas computacionalmente, através do software Geogebra. Transformações de coordenadas possibilitam a determinação de tensões em planos diferentes dos originais de forma analítica ou gráfica. Estes conceitos são aplicados a materiais compósitos ortotrópicos sujeitos a carregamento plano, configuração característica de uma lâmina de material compósito empregada em estruturas mais complexas, possibilitando a determinação das propriedades elásticas de uma lâmina em direções diferentes das chamadas direções principais, alinhadas ou ortogonais à direção das fibras. / Abstract: This essay focuses on the study of the elastic behavior of materials through the analysis of the stiffness and flexibility matrices of elementary structures. Based on the concepts of the Material Resistance discipline and the elastic properties of the materials, mathematical relationships are presented and demonstrated that reflect the associations between the acting normal and shear stresses and the resulting deformations and distortions. These relationships are computationally illustrated through Geogebra software. Coordinate transformations allow the determination of stresses in different planes of the originals in an analytical or graphical way. These concepts are applied to orthotropic composites subjected to flat loading, characteristic configuration of a composite material blade used in more complex structures, making it possible to determine the elastic properties of a blade in different directions of the so-called main directions, aligned or orthogonal to the direction of the fibers. / Mestre

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Engineering, 1988. / Mining induced fracturing and associated deformations can commonly be observed around deep gold mining excavations. As the rockmass behaviour and the stability of the excavations are directly influenced by these processes, a proper understanding of this influence would certainly improve current mining practices with respect to blasting, rock breaking, support design and mining lay-outs. The main subject of this thesis is the physics of failure and post failure behaviour of rock and similar materials. Failure is denned here as a state at which the material has been subjected to fracture and/or damage processes. The applicability of commonly used constitutive models in representing such failure and post failure processes has been investigated mainly by means of numerical simulations. Mechanisms which control fundamental fracture and damage processes have been analysed by comparing the results from relevant laboratory experiments with numerical models. Linear elastic fracture mechanics has been applied to explain and simulate the formation of large scale extension fractures which form in response to excessive tensile stresses. Using the flaw concept it is demonstrated that these fractures not only initiate and propagate from the surface of an opening in compressed rock, but that so called secondary fracturing can be initiated from within the solid rock as well. The effect of geological discontinuities such as bedding planes, faults and joints on the formation of (extension) fractures has also been investigated and it has been shown how the presence of such discontinuities can cause the formation o f additional fractures. Micro mechanical models have been, used to investigate the interaction and coalescence processes of micro fractures. It was found that the formation of large scale extension fracturing can be explained from such processes, but so called shear fractures could not directly be reproduced, although such a possibility has been claimed by previous researchers. The formation of shear fractures is of particular- interest as violent failure of rock, which is subjected to compressive stresses only, is often associated with such fractures. In an all compressive stress environment, only shear deformations would allow for the relief of excess stress and thus energy. The formation of shear fractures is associated with complex mechanisms and shear fractures can therefore not directly be represented by tingle cracks. In contrast to the propagation of tensile fractures, which can readily be explained by traditional fracture mechanics in terms of stress concentrations around the crack tip, the propagation of shear fractures requires a different explanation. In this thesis an attempt has nevertheless been made to reproduce shear fractures by direct application of fracture mechanics. This his been done by representing a shear fracture as a single crack and by assuming fracture growth criteria which are either based on critical excess shear stresses, or on a maximum energy release. Both criteria are completely empirical and require a value for the critical shear resistance in the same way as a critical tensile resistance is required to represent the formation of tensile fracture; , The determination of a critical tensile resistance ( Kk ) is relatively straight forward, as the formation of tensile fractures from a pre-existing flaw can be reproduced and observed in standard laboratory tests. The determination of a critical shear resistance is, however, not a common practice, as the formation of a shear fracture from a pre-existing flaw is very infrequently observed. The application of shear fracture growth criteria nevertheless resulted in plausible fracture patterns, which suggests that such criteria are realistic. It is argued here however that the formation of shear fractures cannot be associated with primary fracture growth, but rather with the localisation of failure and damage in an area which is subjected to plastic deformation. The application of fracture mechanics is therefore not correct from a fundamental point of view as these processes are not represented. For this reason plasticity theory has also been applied in order to simulate failure in general, and shear failure localisation in particular. It was in principle possible to reproduce the shear fractures with the use of this theory, but numerical restraints affected the results to such an extent that most of the simulations were not realistic. Plasticity theory can also be extended to include brittle behaviour by the use of so called strain softening models. The physical processes which lead to brittle failure are however not directly represented by such models and they may therefore not result in realistic failure patterns. It was in fact found that strain softening models could only produce realistic results if localisation of failure could be prevented. The effect of numerical restraints becomes even more obvious with a strain softening model in the case of failure localisation. While the plasticity models appear inappropriate in representing brittle failure, they demonstrated that plastic deformations can be associated with stress changes which may lead to subsequent brittle fracturing. Although only indirect attempts have been made to reproduce this effect, as appropriate numerical tools are not available, it is clear that many observations of extension fracturing could be explained by plastic deformations preceding the brittle fracturing processes. Many rocks are classified as brittle, but plastic deformation processes often occur during the damage processes as well. The sliding crack for instance, which is thought to represent many micro mechanical deformation processes in rock, directly induces plastic deformations when activated. A pure brittle rock, which may be defined as a rock in which absolutely no plastic deformation processes take place, may therefore only be of academic interest as it is inconceivable that such a rock materiel exists. Only in such an academic case would (linear) elastic fracture mechanics be directly applicable. As plastic deformation processes do play a role in real rock materials it is important to investigate their influence on subsequent brittle failure processes. The elastic stress distribution, which is often used to explain the onset of brittle fracturing, may be misleading as plastic deformations can substantially affect the stress distribution . -recediny fracture initiation. In an attempt to combine both plastic and brittle failure, use has been made of tessellation models, which in effect define potential fracture paths in a random mesh. The advantage of these models is that various failure criteria, with or without strain softening potential, can be used without the numerical restraints which are normally associated with the conventional continuum models. The results of these models are also not free from numerical artefacts, but they appear to be more realistic in general. One o f the m;ij, r conclusions based on these results is that shear failure does not occur in a localised fashion, but is associated with the uniform distribution and extension of damage. Shear failure, which can be related directly to plastic failure, can however induce brittle, tensile, failure due to stress redistribution. While the theories of fracture mechanics and plasticity are well established, their application to rock mechanical problems often leads to unrealistic results. Commonly observed firacture patterns in rock, loaded in compression, are most often not properly reproduced by numerical models for a combination of reasons. Either a model concentrates on the discrete fracturing processes, in which case the plastic deformation processes are ignored, or plasticity is represented, but brittle failure is pooxiy catered for. While theoretically a combination of these models might lead to better representations and simulations, numerical problems do affect all models to a certain extent and a practical solution is not immediately available. The results of numerical models can therefore only be analysed with caution and the underlying assumptions and numerical problems associated with a particular technique need to be appreciated before such results can be interpreted with any sense. Many of the problems are identified here and this may assist researchers in the interpretation of results from numerical simulations. Laboratory experiments, which have been chosen for analyses, involve specimens which have been subjected to compressive stresses and which contain openings from which failure and fracturing is initiated. Such specimens are less subjective to boundary influences and are far more representative of conditions around mining excavations than typical uni- and tri-axial tests. The uniform stress conditions in these latter tests allow boundary effects to dominate the stress concentrations, and thus failure initiation, in the specimens. The large stress gradients, which can be expected to occur around underground excavations, are not reproduced in such specimens. As a consequence failure is not u atained within a particular area, but spreads throughout the complete specimen in the uni- and tri-axial tests. Specimens containing openings are therefore far more likely to reproduce the fracture patterns which can be observed around deep level mining excavations. Numerical simulations of brittle, tensile fracturing around mining excavations resulted in consistent fracture patterns. Fracture patterns could however be strongly influenced by the presence of geological (pre-existing) discontinuities such as bedding planes. Although tensile stresses are often assumed to be absent around deej: <y vel excavations because typical hanging- and foot-walls are subjected to compressive horizontal strain and thus stress, the numerical models identified alternative locations o f Ix 'sile stress and also mechanisms which could induce secondary tensile stresses, A failure criterion has therefore been identified as the most likely cause of large scale fracturing while shear fracturing may only occur in the absence of such tensile stresses .and only as a consequence of failure localisation in damaged rock rather than fracture propagation (in solid rock). Geological discontinuities can easily induce tensile stresses vVher mobilised and may even replace the mining induced fractures by offering a more efficient meat s for energy release. The latter possibility is a true three dimensional issue which has not be en addressed any further in this study, but may be very relevant to jointed rock. Although dynamic failure has not directly been addressed, one of the micliamsms lor brittle, and thus stress relieving, failure under compressive strass conditi ons has been investigated in detail, namely shear fracturing. Shear fractures are effect vely the only discontinuities which allow for stress relief under such conditi ons', in the ibaence of preexisting, geological discontinuities, and are therefore quite rele vant to dynamic rock failure, such as rock bursts, in deep level mining conditions. Potential mechanisms for shear fracture formation and the numerical simulation of these features have been investigated and this may especially assist further research into rock bursts.

A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfilment of the requir tents for the degree of Master of Science in Engineering. Johannesburg 1996. / The design of bord and pillar working in South African collieries is based on the pillar strength formula developed by Salamon and Munro1967 and which has been used widely since then for designing pillars. This formula is based on the statistical analysis of 27 collapsed and 98 intact coal pillar cases from collieries located in the Transvaal and the Free state. The main objective of this study is to establish the difference in the strength of the coal material in ditferent seams by means of laboratory testing. In this manner, some 753 coal samples from 10 collieries from 4 seams were tested. The size and width to height ratio effects on strength were analysed. The size effect showed that the difference between the seams was obvious, with a difference of 59,4 per cent between the strongest and weakest coal. The statistical re-analysis showed that the strength of the six blocks from the No 2 seam, Witbank Coalfield occurred in a fairly tight strength range; and that laboratory coal strengths from individual seams or mines could deviate to a significant although relatively small extent from the overall average. / AC2017

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, September 2016 / The aim of this research was to investigate the bord and pillar design procedure in use at the time on chrome and platinum mines and subject it to a critical appraisal and, if necessary, propose an improved methodology. An analysis of the current method and some of the alternatives proposed in the literature has shown that the methodologies suffer from drawbacks that can be detrimental to the mining industry due to overdesign or rendering an excavation unsafe. The conclusion was that improvement is essential. The influence of the variability of the rock mass properties input parameters on the factor of safety in the current equation was calculated and the findings were that the value of the factor of safety can vary by up to 30 percent due to these variation. The proposed process adopted FLAC2D Hoek-Brown simulations to develop full stress deformation curves for typical pillars. The mine stiffness concept was introduced to determine the pillar load which automatically included the influence of the pillar and strata stiffness, excavation spans, pillar yield and failure. The factor of safety was obtained by dividing the pillar strength by the stress value of the intersection point of the two linear equations for the stiffness of the system and the pillar respectively. The proposed methodology was calibrated by applying it to two mines in the Bushveld. The conclusion was that the methodology is a significant improvement over the one in use. It was shown that a combination of the FLAC2D Hoek Brown and the System Pillar Equilibrium Concept can predict the extent of the fracture zones and, to certain extent, the pillar stresses. The stage has been reached where the methodology can be used to predict the most likely commencement of failure of pillars at greater depth and alternative pillar mining methods can be modelled. / MT2017

In an effort to obtain an improved mode III fracture toughness test suitable for a testing standard, mechanics analysis, experimental testing, and finite element analysis (FEA) have been conducted. Of particular concern are the merits of one-point and two-point edge crack torsion (ECT) test methods, the influence of specimen geometry that overhangs beyond load/support points, and the influence of crack length on the compliance and energy release rate. Shear stress distributions at the crack front are determined to examine the uniformity of mode III loading and mode II influence. The shear stress distributions in the one-point and two-point tests are virtually identical, indicating that either of the two tests could be used interchangeably. Based on the uniformity of the mode III shear stress distribution along the crack front, it was found that the ECT specimen should have minimum overhang. Longer crack lengths tend to produce nonuniform shear stress distributions. A modified two-point ECT test fixture was developed to allow testing of specimens with a range of dimensions. This development enabled experimental verification of the results from the FEA overhang series. The specimens with a minimum overhang produced consistant mode III toughness data. The most reliable way to reduce data is through the original compliance calibration method. A modified ECT specimen was developed with a staggered crack front to produce uniform mode III crack growth. Finite element analysis of the modified ECT specimen shows a uniform mode III stress distribution along the crack front with little mode II interaction. / by Grant Browning. / Thesis (M.S.C.S.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

With the need to improve corrosion resistance in columns and piles, the innovative idea of Centrally Prestressed Fiber Reinforced Concrete (CPFRC) columns is a promising solution. The first step is to compare if the compressive strength of any mix is affected by the size, geometry, or even the inclusion of polyolefin fibers in a specimen. The results showed that the cylinder size of 4 in. x 8 in., which is the most common size used by the testing labs, has the highest compressive strength. There was no sign on compressive strength improvement with the use of polyolefin fibers, except for reduction in cracking size and concrete spalling. The second step compared the ultimate strength, ductility characteristics and failure mode of CPFRC columns to conventional columns. CPFRC showed adequate axial and flexural resistance, in addition to ductile behavior similar to regular reinforced concrete columns. / by Daniel A. Grijalba. / Thesis (M.S.C.S.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Orientador: Francisco Antonio Bertoz / Coorientador: Maria Cristina Rosifini Alves Rezende / Banca: Marcelo Coelho Goiato / Banca: Kurt Faltin Júnior / Resumo: A ação dos produtos desinfetantes sobre as propriedades físico-químicas da resina acrílica norteia sua seleção para a higienização de aparelhos ortodônticos removíveis. Avaliou-se a resistência à fratura de resina acrílica ativada quimicamente após ciclagem em diferentes soluções desinfetantes. Foram confeccionados quarenta corpos de prova com resina acrílica autopolimerizável incolor (Clássico,Ind.&Com.Ltda./Brasil) utilizando-se matriz metálica retangular e circular, seguindo-se às técnicas de polimerização sob pressão úmida (imersão em água/n=20) e sob pressão seca (sem água/n=20) foram subdivididos em 4 grupos (n=5), conforme a solução utilizada para ciclagem: água destilada (Controle), bicarbonato de sódio, hipoclorito de sódio 1% e Corega®Tabs. A ciclagem consistiu em imersão em 100 ml da solução por 10 minutos três vezes ao dia e, em seguida, manutenção em recipiente fechado contendo saliva artificial a 37ºC. Este ciclo foi realizado durante 30 dias, trocando-se as soluções e a saliva a cada procedimento executado. Na sequência os espécimes foram submetidos ao ensaio de resistência flexural a três pontos foi utilizada máquina EMIC DL3000, à velocidade de 5mm/min, dispondo-se as amostras em suporte contendo dois apoios de sustentação, sendo aplicada força axial e equidistante aos dois outro pontos até a ruptura do corpo-de-prova. Os espécimes circulares foram levados para leitura em Microscópio de Força Atômica (AFM - V Nanoscope Veeco). Os resultados, submetidos à análise de variância (P<0,001 ) e o Teste de Tuckey (P<0,05) não apontaram diferenças significantes para a resistência flexural. Conclui-se que os métodos de polimerização e as soluções testadas não modificaram a resistência flexural... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The disinfectant products action on the physicochemical properties of acrylic resin guides its selection to the cleaning of removable orthodontic appliances. The fracture resistance of acrylic resin after cycling in different disinfectant solutions was evaluated. Forty specimens were made with colorless acrylic resin (Clássico, Ind. & Com.Ltda. / Brazil), using matrix, followed by the techniques of polymerization under wet pressure (immersion in water / n = 20) and dry pressure (no water / n = 20). The samples were divided into 4 groups (n = 5) as the solution used for cycling: distilled water (Control), sodium bicarbonate, sodium hypochlorite 1% and Corega®Tabs. The cycling consisted of immersion in 100 ml of solution for 10 minutes three times a day and then maintained in a closed container containing artificial saliva at 37 º C. These cycles were conducted during 30 days, changing the solutions and artificial saliva for each procedure performed. Latter, the specimens were submitted to surface analysis with Atomic Force Microscope (AFM - Veeco Nanoscope V). A machine, EMIC DL3000, was used for the three-point flexural strength test, speed of 5mm/min, providing the sample in medium containing two restraints support. After that axial force was applied and equidistant to the two other points to the body to break the specimens. The results were submitted to analysis of variace(P<0,001) and Tuckey Test (P<0,05) showed no significant differences in flexural strength test. The Atomic Force Microscopy analysis revealed less topographical roughness for the group Corega®Tabs. We conclude that the polymerization methods and solutions tested did not alter the flexural strength of the material studied except the comparation between... (Complete abstract click electronic access below) / Mestre

Thesis (Nav. E.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004. / Includes bibliographical references (leaves 44-46). / Although there has been interest in the behavior of metal plates under blast and projectile loading for many years, definitive open-source analysis has only been recently forthcoming. This analysis is most often in the form of scaled recreations of the dynamic blast event, or "live fire" tests. New developments in methods of recreating blast and projectile induced plate failure using a quasi-static approach provide possible, accurate, alternatives to the cumbersome and expensive live fire test. This research endeavors to develop an accurate, quasi-static method of recreating the petalling phase of blast and projectile failure in metal sheets, based on a modified trousers- type test. By using the trousers-type fracture test the overall plastic bending kinematics of the fractured petal is preserved, as well as the mixed mode (mode one and mode three) fracture. Through analytical and qualitative analysis, a testing apparatus to generate this trousers-type, plastic bending and mixed mode fracture was designed and machined. The apparatus was then used to test thin steel sheets of varying thickness (0.419 and 0.724mm) in order to validate the quasi-static method of recreating the petalling phase through a comparison with analytically derived results. / by Michael L. Roach. / S.M. / Nav.E.

Fiber-reinforced concrete (FRC) is nowadays extensively used in civil engineering throughout the world due to the composites of FRC can improve the toughness, flexural strength, tensile strength, and impact strength as well as the failure mode of the concrete. It is an easy crazed material compared to others materials in civil engineering. Concrete, like glass, is brittle, and hence has a low tensile strength and shear capacity. At present, there are different materials that have been employed to reinforce concrete. In our experiment, nanostructures iron oxide was prepared by electrodepostion in an electrolyte containing 0.2 mol/L sodium acetate (CH3COONa), 0.01 mol/L sodium sulfate (Na2SO4) and 0.01 mol/L ammonium ferrous sulfate (NH4)2Fe(SO4)2.6H2O under magnetic stirring. The resulted showed that pristine Fe2O3 particles, Fe2O3 nanorods and nanosheets were synthesized under current intensity of 1, 3, 5 mA, respectively. And the pull-out tests were performed by Autograph AGS-X Series. It is discovering that the load force potential of nanostructure fibers is almost 2 times as strong as the control sample.

A research report submitted to the Faculty of Engineering and Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering, Johannesburg 2017 / Depletion of mineral resources is a reality of mining. It is critical that as resources get depleted, new reserves are subsequently opened up continuously if a mine is to continue operating. Failure to open up new reserves will result in a mining operation running out of reserves and ultimately ceasing operations. Besides the economic considerations of an ore reserve such as the grade and tonnage, stability of the mining operation is of equal importance. A mine should remain stable for the entire period that it remains operational. Pillars play a critical role in ensuring the stability of an excavation; actually, regional pillars ensure the overall stability of a mine. It therefore goes without saying, pillar design is an integral component of any successful mine design. This project was undertaken with the objective of ensuring that the new reserves being opened up in the Khuseleka Ore Replacement Project (KORP) section are not only profitable, but also stable. This was done through a) maximisation of extraction ratio, thereby maximising the mines’ profitability. b) designing the regional pillar layout for the KORP section using current empirical and numerical pillar design methods and comparing the results to come up with the most optimal design. c) ensuring the stability of the on and off reef mine infrastructure by determining the Rockwall Condition Factor (RCF) values on the footwall infrastructure due to pillars left above and thus prevent damage to these excavations through stress induced failures. Consideration was given to the standard Khuseleka footwall infrastructure layouts for the design based on the planning department’s layout of haulages and crosscuts for the KORP section. The layout of the footwall excavations indicated that the pillars would be differently sized thereby having an influence on the APS, pillar strength and factors of safety of the regional pillars. d) numerical modelling analysis of the effects of leaving stabilizing pillars on the 27 raise line where the haulages intersect the reef horizon. The methodology employed for this undertaking involved a critical literature review of existing pillar design methods, applying and comparing them, and coming up with an economic and safe design. To be able to design a pillar layout that met the objectives listed above, engineering design principles had to be applied. It involved gathering the relevant geological and geotechnical information required as input parameters for the different empirical and numerical analyses methods. What came out from this project was that each method employed yielded its own set of results. This highlighted the need to understand the context under which a design is carried out and the shortcomings of each method employed. It showed how important it is to have all the relevant information of not only the characteristics of the rock mass in which an excavation will be made, but also on the strengths and limitations of the tools available to design a structure. It highlighted the fact that to minimize uncertainty and have a more robust design, it was necessary to spend time and effort in gathering as much relevant data as possible. In the end engineering judgment was used to decide on the best method or system to employ in the design of the pillars. / XL2018