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The Relativistic Elasticity of Rigid Bodies  [PDF]
A. Brotas,J. C. Fernandes
Physics , 2003,
Abstract: In 1909 Born studied the "relativistic undeformable body" but made the mistake of calling it "rigid". The "rigid body" as one can find in Relativity books is, in fact, this Born "undeformable body". In Relativity it is necessary to distinguish between "rigid" and "undeformable". The "undeformable" body (in the sense of the most rigid possible) must be the "deformable" body where schock waves propagate with maximum speed c. We present in this text the elastic laws for rigid bodies. We think that these laws, which are ignored by the majority of relativists, should be taught in the elementary relativistic courses. With the approach of 2005, the centenary year of Relativity, we should like to appeal to all those who have some influence on these matters to avoid this mistake of repeatedly calling "rigid" to the "undeformable body".
Local elasticity map and plasticity in a model Lennard-Jones glass  [PDF]
Michel Tsamados,Anne Tanguy,Chay Goldenberg,Jean-Louis Barrat
Physics , 2009, DOI: 10.1103/PhysRevE.80.026112
Abstract: In this work we calculate the local elastic moduli in a weakly polydisperse 2DLennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse grained microscopic expressions for the strain, displacement and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale the glass appears as a composite material composed of a rigid scaffoldingand of soft zones. Only recently calculated in non homogeneous materials, the local elastic structure plays a crucial role in the elasto-plastic response of the amorphous material. For a small macroscopic shear strain the structures associated with the non-affine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in form of plastic rearrangements. The spatio-temporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.
Evaluation of Modulus of Elasticity and Modulus of Subgrade Reaction of Soils Using CBR Test
Journal of Civil Engineering Research , 2012, DOI: 10.5923/j.jce.20120201.05
Abstract: This paper presents the procedure of evaluation of the modulus of elasticity (E) and the modulus of subgrade reaction (ks) value based on the California Bearing Ratio (CBR) tests and FEM analysis. The pressure-displacement response of the soil in the CBR mould is simulated using Cosmosworks FEM model where the soil, the load plunger, and the steel mould of CBR are represented. The correlation of Modulus of Elasticity (E) with California Bearing Ratio (CBR) is developed based on the elastic properties of the soil sample. Furthermore, the correlation between E and CBR is proposed. Using the E values, modulus of subgrade reaction can be calculated and vice versa as well. Thus CBR test is expected to simplify the effort in determination of the modulus of subgrade reaction which is used in Foundation design, soil structure interaction, design of highway formations etc.
Comparison of Some Methods to Determine the Modulus of Elasticity of Some Onion Varieties  [PDF]
Journal of Biological Sciences , 2001,
Abstract: Banko and Yalova-12, varieties of onion were studied for some physical parameters such as size, shape, and density. An instron test machine was used to perform a compression test on both varieties. Modulus of elasticity was found from force-deformation curve(experimental method) and Hertz equation. The effects of the loading direction (polar or equatorial), loading speed, onion varieties, and the calculation methods were examined on the modulus of elasticity. The effects of loading speed and varieties on the modulus of elasticity were found to be significant. Modulus of elasticity was decreased with increasing loading speed. No significant differences were found in values of modulus of elasticity for experimental method and Hertz equation and the loading direction (polar or equatorial load).
Relation between Static and Dynamic Modulus of Elasticity of Wood
DIVóS, Ferenc,TANAKA, Toshinari
Acta Silvatica & Lignaria Hungarica , 2005,
Abstract: Static and dynamic modulus of elasticity (MOE) of spruce lumber were determined under different conditions like cross head speed, bending and longitudinal vibration, and mode numbers. The characteristic time of MOE determination is introduced. Characteristic time is defined as the typical MOE determination time. Shorter characteristic times are shown to result in higher MOE values. An order of magnitude change in characteristic time resulted in a 1.7% change in MOE. We found clear evidence that creep exists on a short time scale.
Maderas. Ciencia y tecnología , 2003, DOI: 10.4067/S0718-221X2003000200002
Abstract: the present paper reports the results of an investigation regarding the relationship between the global and the local modulus of elasticity in sawn timber of argentinean eucalyptus grandis. for this purpose an empirical research project with 50 beams in structural sizes subjected to bending was carried out. the results obtained according to european standards show the values of both types of modulus of elasticity and the influence of the more important strength and stiffness reducing growth characteristics on their variation, as well as give evidence of the effectiveness of the criterion established in the american standard astm d 198 (1999) for correcting the influence of shear on the global modulus of elasticity
The position effect of structural Eucalyptus round timber on the flexural modulus of elasticity
Christoforo, André L;Panzera, Túlio H;Batista, Fabiano B;Borges, Paulo H. R;Lahr, Francisco A. R;Franco, Claudenir F;
Engenharia Agrícola , 2011, DOI: 10.1590/S0100-69162011000600019
Abstract: round timber has great use in civil construction, performing the function of beams, columns, foundations, poles for power distribution among others, with the advantage of not being processed, such as lumber. the structural design of round timber requires determining the elastic properties, mainly the modulus of elasticity. the brazilian standards responsible for the stiffness and strength determination of round timber are in effect for over twenty years with no technical review. round timber, for generally present an axis with non-zero curvature according to the position of the element in the bending test, may exhibit different values of modulus of elasticity. this study aims to analyze the position effect of eucalyptus grandis round timber on the flexural modulus of elasticity. the three-point bending test was evaluated in two different positions based on the longitudinal rotation of the round timber element. the results revealed that at least two different positions of the round timber element are desired to obtain significant modulus of elasticity.
Static modulus of elasticity of concrete measured by the ultrasonic method  [cached]
Sena Rodrigues, S.,Pazini Figueiredo, E.
Materiales de Construccion , 2003,
Abstract: Lately, a huge number of accidents caused by problems found in the durability of concrete structures due to inappropriate project design, lack of control of quality during the project s execution, inadequate maintenance practices and an aggressive environment has been reported. This finding has required from the professionals constant inspections and evaluations of the real conditions of all concrete structures. In order to perform those inspections, one should know not only the elastic modulus to analyze the concrete structural behaviour but also to investigate its performance, since the strains may yield cracks able to compromise the durability- of structures. Non-destructive testing techniques, particularly the ultrasonic testing, are performed to evaluate and determine the quality of a concrete structure or element. Currently, such essays have been widely researched and analyzed all over the world because they enable the examination of structures without damaging them. The purpose of the present study was to correlate the ultrasonic pulse velocity and the elastic modulus of several concrete specimens molded with a range of water-cement ratios, different kinds of aggregates and curing methods. All the concrete specimens were tested in different ages to determine the pulse velocity and the static modulus of elasticity standardized according to KBR 8522, through mechanical extensometers, electrical strain gauge and LVTD inductive transducer. Recientemente se ha registrado un gran número de accidentes causados por problemas relacionados con la durabilidad de las estructuras de hormigón y debidos a un inadecuado proyecto de dise o, ausencia de control de calidad durante la ejecución del proyecto, prácticas inadecuadas de construcción y un ambiente agresivo. Este hallazgo ha dado lugar a que los ingenieros realicen constantes inspecciones y evaluaciones de la condición real de todas las estructuras de hormigón. Para llevar a cabo estas inspecciones, se debe conocer no sólo el módulo de elasticidad, para analizar el comportamiento estructural del hormigón, sino, también, investigar su desarrollo, ya que los esfuerzos pueden originar grietas que comprometan la durabilidad de las estructuras. Varias técnicas no-destructivas, particularmente ensayos ultrasónicos, se han desarrollado para evaluar y determinar la calidad de una estructura o un elemento de hormigón. Actualmente, este tipo de pruebas ha sido ampliamente investigado y analizado, ya que permiten el examen de las estructuras sin afectarlas. El propósito del presente estudio fue correlacionar la velo
The Effect of Wood Knot as a Defect on Modulus of Elasticity (MOE) and Damping Correlation  [cached]
Notulae Scientia Biologicae , 2011,
Abstract: This research was carried out to investigate the influence of knots on modulus of elasticity and on damping factor of vibration. Rectangular bars from Cupressus arizonica wood were used. Five individual trees were selected, and samples of 2*2*36 cm were cut and conditioned at 21°C and 65% relative humidity. Experiments based on free vibration and free-free bar method were performed and controlled in static bending test due to their modulus of elasticity. As expected, this kind of defect showed significant effects on modulus of elasticity, damping factor of vibration and FFT diagrams. A significant relation was observed between modulus of elasticity and damping factor between the two dynamic and static methods, but this relation decrease about 60% in knot-containing specimens. Modes of FFT spectrums of defect-free specimens were pick-like, symmetric specimens without any breaks, but the spectra of knot-containing samples spectrums were entirely asymmetric. Applying these diagrams in order to recognize the suitability or unsuitability of a piece of wood for specific applications, especially due to internal defects that are not visible, could be very important, and must be considered in future research.
Influence of the type of measuring device in determining the static modulus of elasticity of concrete
Araújo, S. S.;Guimar?es, G. N.;Geyer, A. L. B.;
Revista IBRACON de Estruturas e Materiais , 2012, DOI: 10.1590/S1983-41952012000500001
Abstract: this paper presents a comparative analysis of the results obtained in static modulus of elasticity tests of plain concrete cylindrical specimens. the purpose of this study is to identify and evaluate the influence of several factors involved in modulus of elasticity tests such as the strain measurement device used (dial indicators, electrical surface bonded strain gages, externally fixed strain gages and linear variation displacement transducer - lvdt), the type of concrete (class c30 and class c60) and cylindrical specimen size (100 mm x 200 mm and 150 mm x 300 mm). the modulus tests were done in two different laboratories in the goiania, go region and were performed according to code abnt nbr 8522:2008, which describes the initial tangent modulus test, characterized by strains measured at tension values of 0.5 mpa and 30% of the ultimate load. one hundred and sixty specimens were tested with statistically satisfactory results. it was concluded that the type of strain measurement device greatly influenced the modulus of elasticity results. tests in specimens 100 mm x 200 mm showed highest statistical variation.
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