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Topic: Modulus of rigidity

	Tinius Olsen
		Modulus of rigidity is related to Young's modulus by the equation: E = 2G (1 + r) where E is Young's modulus (psi), G is modulus of rigidity (psi) and r is Poisson's ratio.
		Alternate terms are modulus of elasticity in torsion and modulus of elasticity in shear.
		Apparent modulus of rigidity is a measure of the stiffness of plastics measured in a torsion test (ASTM D-1043).
	www.tiniusolsen.com /resource-center/mechanical-properties-M.html (573 words)

	Shear modulus - Wikipedia, the free encyclopedia
		In materials science, shear modulus, G, or sometimes S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain:
		The shear modulus is one of several quantities for measuring the strength of materials.
		Young's modulus describes the material's response to linear strain (like pulling on the ends of a wire), the bulk modulus describes the material's response to uniform pressure, and the shear modulus describes the material's response to shearing strains.
	en.wikipedia.org /wiki/Shear_modulus (191 words)

	Introduction
		In a torsion test, modulus of rupture in torsion is the maxi-mum shear stress in the extreme fiber of a circular member at failure.
		Alternate terms are modulus of rigidity and modulus of elasticity in shear.
		where E is modulus of elasticity; 1, length of the rod; p, density; f, resonant frequency; k, radius of gyration of the rod about an axis normal to the rod axis and plane of motion (d/4 for cylindrical rods) and j, a constant dependent on the mode of vibration.
	www-rci.rutgers.edu /~craelius/cytomechanics/Biomech_lab.htm (6708 words)

	Temperature coefficient of the modulus of rigidity of aircraft instrument diaphragm and spring materials (Site not responding. Last check: 2007-10-17)
		Temperature coefficient of the modulus of rigidity of aircraft instrument diaphragm and spring materials
		Experimental data are presented on the variation of the modulus of rigidity in the temperature range -20 to +50 degrees C. of a number of metals which are of possible use for elastic elements for aircraft and other instruments.
		The methods of the torsional pendulum was used to determine the modulus of rigidity and its temperature coefficient for aluminum, duralumin, monel metal, brass, phosphor bronze, coin silver, nickel silver, three high carbon steels, and three alloy steels.
	naca.larc.nasa.gov /reports/1931/naca-report-358 (136 words)

	Modulus of Rigidity
		Shear Modulus or Modulus of Rigidity is the coefficient of elasticity for a shearing or torsion force
		Modulus of Rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force.
		Modulus of Rigidity can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material.
	www.engineeringtoolbox.com /modulus-rigidity-d_946.html (224 words)

	Selected Rheological Properties of pH-Adjusted or Succinylated Egg Albumen
		1) was used to measure the apparent viscosity, the yield force, and the modulus of rigidity of the coagulated albumen.
		The apparent rigidity modulus was obtained from the force-distance curves from the capillary extrusion studies.
		The apparent rigidity modulus was taken to be a measure of deformation characteristics of the gels rather than stress-relaxation qualities.
	albumen.stanford.edu /library/c20/gossett1983.html (2943 words)

	Tinius/TechnicalSupport (Site not responding. Last check: 2007-10-17)
		For rigid plastics deformation (which can be flow or flow and shrinkage) is reported as % change in height of specimen after 24 hr under a specified load.
		For substantially elastic isotropic rubbers IRHD is related to Young's modulus by the equation: F/M = 0.00017 R0.65 Pl.35 where F is indenting force in kg; M, Young's modulus in kg/sq cm; R, radius of indentor in cm, and P, penetration in hundredths of mm.
		It is the constant that relates modulus of rigidity to Young's modules in the equation: E = 2G (r + 1) where E is Young's modulus; G, modulus or rigidity and r, Poisson's ratio.
	www.tiniusolsen.com /tmech.html (9481 words)

	Eliminating air pockets under a polished pad - US Patent 6561891 (Site not responding. Last check: 2007-10-17)
		A material of this rigidity is required to provide a flat surface on which polishing pad that generally is not rigid but flexible is positioned.
		The rigidity of the material itself reduces the amount of air that is entrapped between the polishing pad and the rigid material.
		A semi rigid base material was positioned between the pad and the polishing platen such that the grooves in the base material faced the back of the pad.
	www.patentstorm.us /patents/6561891.html (2524 words)

	Torsional Analysis
		The stress components are represented in terms of the geometry, the modulus of rigidity of the shaft material, and the applied moment couple.
		By replacing the twist in the displacements, you represent the displacement components in terms of the geometry, the modulus of rigidity of the shaft material, and the applied moment couple.
		Calculate the torsional rigidity of a narrow bar with modulus of rigidity, G, bar width, b, and bar thickness, c.
	documents.wolfram.com /applications/structural/TorsionalAnalysis.html (4306 words)

	C848-88(1999) Standard Test Method for Youngs Modulus, Shear Modulus, and Poissons Ratio For Ceramic Whitewares by ...
		Young's modulus is determined using the resonance frequency in the flexural mode of vibration.
		The shear modulus, or modulus of rigidity, is found using torsional resonance vibrations.
		The actual modulus of each piece need not be determined as long as the limits of the selected frequency range are known to include the resonance frequency that the piece must possess if its geometry and density are within specified tolerances.
	www.astm.org /DATABASE.CART/PAGES/C848.htm (466 words)

	STRENGTH OF MATERIALS - LoveToKnow Article on STRENGTH OF MATERIALS (Site not responding. Last check: 2007-10-17)
		Such observations afforc the most direct means of measuring the modulus of longitudina elasticity of the material, and they serve also to determine the limits within which the material is elastic.
		in., and the modulus of rigidity C from 5000 to 5700 tons per sq.
		The additional slope which shearing stress produces in any originally horizontal layer is q/C, where q is, as before, the intensity of shearing stress and C is the modulus of rigidity.
	www.87.1911encyclopedia.org /S/ST/STRENGTH_OF_MATERIALS.htm (13075 words)

	Elasticity
		To a good approximation, the deformation of a rigid body is proportional to the force, and when the force is removed, the body resumes its original shape.
		Young's modulus (Y or E), the shear modulus (μ or G), the bulk modulus and Poisson's ratio are the most commonly found elastic constants.
		For a given ratio of maximum stress to Young's modulus (about 1/1000 or so for steel), the deflection is proportional to the square of the span, and inversely proportional to the depth of the beam (2c in this case).
	www.du.edu /~jcalvert/tech/elastic.htm (4027 words)

	Screw caps and seals for screw caps - Patent 5756178
		The substance of the middle layer and the substance of the intermediate layers may advantageously have a modulus of rigidity in the same region, preferably a modulus of regidity of between 1300 and 2200 MPa.
		The substance of the outer layers, for its part, may have a modulus of rigidity of between approximately 100 and 300 MPa.
		The intermediate layers 5 joined to the middle layer 4 by layers 6 of polyurethane adhesive may consist of PP films (made of polypropylene) with a thickness of 10 to 50.mu.m, with a high modulus of rigidity (between 1300 and 2200 MPa).
	www.freepatentsonline.com /5756178.html (1749 words)

	Frp Encyclopedia
		Flexural Modulus -A number associated with the flexibility or stiffness of a material.
		Tensile Modulus -A number associated with pulling or stretching a material (tension) and how much it elongates when a certain load is applied to it.
		Foams, Rigid- A thermoset urethane foam which has a higher density, higher modulus, and harder surface than flexible urethane foams.
	www.kemlite.com /frp_encyclopedia.cfm (2564 words)

	The Complete Polyurethane Glossary of Terms
		Modulus in polyurethane may be either static or dynamic; static moduli are subdivided into tangent, chord, and compounder's.
		Compounder's modulus is always in tension, but all the others may be in shear, compression or tension.
		Other terms used in connection with "modulus" are elasticity, rigidity, Young's tangent, and elongation.
	www.polyurethane-1.com /open-cast-terms.htm (4087 words)

	Transports Québec : Research & Development Projects (Site not responding. Last check: 2007-10-17)
		Knowledge of the rigidity modulus of bituminous mixtures allows appropriate choices that increase this resistance.
		Design methods for bituminous mixtures, on which the modulus value depends, are evolving rapidly, requiring development of a new method for determining the modulus.
		A methodology was developed for characterizing the complex modulus of a mixture using a frequency sweep test and for characterizing the fatigue resistance under constant strain of a mixture.
	www.mtq.gouv.qc.ca /en/ministere/recherche/projets/description.asp?NO_PROJ=R275.1P1 (267 words)

	Quantitative treatment of the creep of metals by dislocation and rate-process theories (Site not responding. Last check: 2007-10-17)
		The theory was also used to predict the dependence of steady-state rate of creep on physical constants of the material and good agreement was obtained with data in the literature for pure annealed metals.
		The rate of creep was found to decrease with increasing modulus of rigidity.
		This relation suggest that one of the requirements for a heat-resisting alloy is that its matrix be a metal that has a high modulus of rigidity and therefore a high modulus of elasticity.
	naca.larc.nasa.gov /reports/1946/naca-report-845 (152 words)

	Choosing Materials
		Basically, that's just the modulus of rigidity times the moment of inertia for the section.
		Aluminium has almost exactly 1/3 the modulus rigidity of steel (~30000KPSI steel/~10000KPSI ally), so for an equivalent tube stiffness, you would need the moment of inertia to be 3 times as high.
		It's modulus is nearly that of steel, but it's weight is nearly half.
	www.ihpva.org /people/tstrike/building/materials.htm (505 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		Also used in torsion equations is the torsional analogy of Young’s Modulus called the Modulus of Rigidity, denoted G. These two constants, one geometric property and one material property, will be used in this section.
		The angle of twist experienced by a rod under a torsional load is given by:
		Where Q is the angle of twist given in radians, T is the amount of torque causing the twisting, J is the Polar Moment of Inertia, L is the length of the specimen, and G is the Modulus of Rigidity.
	www.egr.msu.edu /classes/msm211lab/polar_moment_of_inertia/lab3.htm (571 words)

	rigidity modulus of polyurethane rubber (Site not responding. Last check: 2007-10-17)
		Since the material is non-linear, rigidity modulus is not a constant value.
		The problem we are facing is that consistent angle of twist values are not obtained for the same torsional load and hence the torional rigidity modulus values are also inconsistent.
		Re: rigidity modulus of polyurethane rubber -- antony
	www.engineersedge.com /wwwboard/posts/2393.html (279 words)

	Determination of the rigidity modulus of thin soft coatings by indentation measurements
		The effect of layer thickness on the elastic response of thin layers loaded with a relatively large ball indentor was determined with a Wallace Indentation Tester.
		Thin coatings of gelatin gel on a rigid support were used and the identation results compared with absolute determinations of rigidity modulus.
		The empirical equation obtained relates rigidity modulus to the load, indentation, layer thickness and ball radius.
	stacks.iop.org /0022-3727/3/29 (246 words)

	AETHELWEARD - LoveToKnow Article on AETHELWEARD (Site not responding. Last check: 2007-10-17)
		It must be very different from ordinary matter as we know it, for waves travelling in matter constitute sound, which is propagated hundreds of thousands of times slower than light.
		It follows that the density of the aether must exceed io~18, and its elastic modulus must exceed io3, which is only about io~8 of the modulus of rigidity of glass.
		It thus appears that if the amplitude of vibration could be as much as icT2 of the wave-length, the aether would be an excessively rare medium with very slight elasticity; and yet it would be capable of transmitting the supply of solar energy on which all terrestrial activity depends.
	66.1911encyclopedia.org /A/AE/AETHELWEARD.htm (2352 words)

	[No title]
		Define section modulus and what is its value for a circular section of diameter D. Sketch (qualitative) the shear stress distribution in a symmetrical ‘I’ section.
		The bulk modulus of the material of the bar is 67 Gpa.
		Density of spring material is 78.5 kN/m3. Modulus of rigidity EMBED Equation.3 GPa.
	www.annauniv.edu /academic/ugqp/D207.DOC (769 words)

	Steel Dictionary - M
		Those properties of a material that reveal the elastic and inelastic reaction when force is applied, or that involve the relationship between stress and strain; for example, the modulus of elasticity, tensile strength and fatigue limit.
		The tangent modulus and secant modulus are not restricted within the proportional limit; the former is the slope of the stress-strain curve at a specified point; the latter is the slope of a line from the origin to a specified point on the stress-strain curve.
		Force which would be required to stretch a substance to double its normal length, on the assumption that it would remain perfectly elastic, i.e., obey Hooke's Law throughout the twist.
	www.mesteel.com /dictionary/m.htm (2065 words)

	Combining the Biot-Geertsma-Gassmann equation with the Batzle-Wang formulation to produce a modeling solution for ... (Site not responding. Last check: 2007-10-17)
		Two of the needed input parameters for predicting velocities in porous, fluid-filled rocks, the bulk modulus of the empty, porous rock and the shear modulus of the rock, are very difficult to obtain in situ.
		In the past, these values were typically chosen a priori and input into the BGG and shear-wave equations in a forward modeling mode.
		Thus, a novel modeling approach is developed by inverting the BGG and shear-wave equations to generate values for the bulk and shear moduli, respectively, by using available velocity and porosity data obtained from well logs and/or cores from water/brine-saturated rocks.
	flux.aps.org /meetings/YR98/BAPS4CF98/abs/S1000005.html (185 words)

	Carbon fiber reinforced compounds are more rigid: News from Premix Thermoplastics
		Based on chopped carbon fiber, milled carbon fiber and carbon nanotubes, the new compounds provide the increased rigidity of carbon fiber as well as the electrical conductivity.
		The addition of carbon fibers not only increases the flexural modulus (rigidity) of the compound, but also increases the tensile strength, lowers the shrinkage and increases the electrical conductivity.
		Compounds that are based on milled carbon fiber are less prone to warpage while compounds that are based on carbon nanotubes can be electrically conductive with as little as 3% fiber reinforcement.
	www.manufacturingtalk.com /news/pix/pix101.html (382 words)

	IHS ESDU: Data Item 67022
		67022: Modulus of rigidity of sandwich panels with hexagonal cell cores.
		ESDU 67022 provides the modulus of rigidity of matrixes of square, rectangular and hexagonal cells.
		The variation of modulus with both the angle between and the length of the attached and unattached walls which form the cells is given together with the effect of cell size/ height ratio.
	www.esdu.com /graphics/dataitem/67022.htm (120 words)

	C1259-98 Standard Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio for Advanced Ceramics by ... (Site not responding. Last check: 2007-10-17)
		Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen.
		Dynamic Young's modulus is determined using the resonant frequency in the flexural mode of vibration.
		The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations.
	amaec.kicet.re.kr /cd_astm/PAGES/C1259.htm (331 words)

	JEPTER, Volume 74, Number 4, 2001 EXPERIMENTAL INVESTIGATION OF MECHANICAL VIBRATIONS OF THE ELEMENTS OF COMBUSTIBLE ... (Site not responding. Last check: 2007-10-17)
		Grishin and A. Golovanov UDC 533.6.011.6 Vibrations of elements of combustible forest materials (CFMs) in a laminar air flow are studied experimentally using optical-fiber facilities.
		The elastic properties of combustible forest materials - the Young modulus and the rigidity, whose values in the limiting cases are in satisfactory agreement with the known data - are determined.
		It is stated that vibrations of combustible forest materials can affect their heat and mass exchange with the environment.
	www.itmo.by /jepter/742001e/740929.html (138 words)

	Forest Products Journal: EDGEWISE FLEXURAL PROPERTIES AND MODULUS OF RIGIDITY OF DIFFERENT SIZES OF SOUTHERN PINE LVL ... (Site not responding. Last check: 2007-10-17)
		EVANGELOS J. The results of this study confirm that modulus of rupture (MOR) values of southern pine plywood and laminated veneer lumber members are influenced by the beam depth when tested at the same span-to-depth ratio.
		As the depth increased, the MOR values decreased significantly among the tested groups.
		Edgewise moduli of rigidity (G) values (average of 36 ksi) for different grades and constructions of plywood members were obtained by a method that requires flexure tests at different span-to-depth ratios.
	static.elibrary.com /f/forestproductsjournal/january012001/edgewiseflexuralpropertiesandmodulusofrigidityofdi/index.html (233 words)

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