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Topic: Area moments of inertia

	Moment of inertia - Wikipedia, the free encyclopedia
		The moment of inertia can also be called the mass moment of inertia (especially by mechanical engineers) to avoid confusion with the second moment of area, which is sometimes called the moment of inertia (especially by structural engineers) and denoted by the same symbol I.
		In addition, the moment of inertia should not be confused the polar moment of inertia, which is a measure of an object's ability to resist torsion.
		If the moment of inertia tensor has been calculated for rotations about the centroid of the rigid body, there is a useful labor-saving method to compute the tensor for rotations offset from the centroid.
	en.wikipedia.org /wiki/Moment_of_inertia (1428 words)

	List of moments of inertia - Wikipedia, the free encyclopedia
		The following is a list of moments of inertia and area moments of inertia (also known as the second moment of area).
		Moments of inertia have units of dimension mass × length
		, and should not be confused with the mass moment of inertia.
	en.wikipedia.org /wiki/List_of_moments_of_inertia (571 words)

	Area Moment Of Inertia Circle (Site not responding. Last check: 2007-10-25)
		The polar moment of inertia of an area A with respect to the pole O is defined as...
		To measure: The area of the circle, the moment and the moment of inertia in reference to the tangent...
		The planar moment of inertia of a circle with diameter 15 mm is...
	areacircle.micaarea.com /areamomentofinertiacircle (962 words)

	Area Moment of inertia
		The area moment of inertia is the second moment of area around a given axis.
		The polar area moment of inertia, denoted by J
		To calculate the area moment of inertia of the composite body constructed of the three segments shown, one evaluates the moment of inertial of each part about the x-axis and adds the three together.
	em-ntserver.unl.edu /NEGAHBAN/EM223/note18/note18.htm (406 words)

	McGraw-Hill AccessScience: Moment of inertia (Site not responding. Last check: 2007-10-25)
		The analogous positive number quantities, moment of inertia of area and moment of inertia of mass, are involved in the analysis of problems of statics and dynamics respectively.
		The moment of inertia of a figure (area or mass) about a line is the sum of the products formed by multiplying the magnitude of each element (of area or of mass) by the square of its distance from the line.
		The moment of inertia of a figure is the sum of moments of inertia of its parts.
	www.accessscience.com /Encyclopedia/4/43/Est_432000_frameset.html?doi (160 words)

	Areas, Volumes, Centroids, & Moments of Inertia Plane Figures (Site not responding. Last check: 2007-10-25)
		The Second Moment of Area is a geometrical property of a beam and depends on a reference axis (which is in the plane of the area).
		The polar moment of inertia relates to an axis which is perpendicular to the plane of an area.
		When considering solids the Polar Moment of inertia is a measure of the resistance of a mass to angular acceleration.
	www.roymech.co.uk /Useful_Tables/Form/M_of_Inertia_2.html (398 words)

	Accident Reconstruction Network - Linear Momentum
		The mass moment of inertia about an arbitrary axis can be expressed as a quadratic form in the direction cosines of the axis, with coefficients that are the moments and products of inertia.
		The diagonal elements are the principal moments of inertia.
		The corresponding axes are the principal axes of inertia.
	www.accidentreconstruction.com /research/lmomentum/vector_mechanics.asp (4258 words)

	[No title]
		Moments of inertia of areas are used in the study of distributed forces and in calculating deflections of beams.
		Determine the moments of inertia of each part in terms of a parallel coordinate system with its origin at the centroid of the part, and then use the parallel-axis theorem to determine the moment of inertia in terms of the given coordinate system (tabulate the required quantities).
		Sum the moments of inertia of the parts (or subtract in the case of a cutout) to obtain the moment of inertia of the composite area.
	engr.smu.edu /me/2310/8-1_8-2.doc (1088 words)

	List of moments of inertia - Encyclopedia, History, Geography and Biography
		The following is a list of moments of inertia.
		The following moments of inertia are derived from the fact that the moment of inertia of a point object is $mr^2 \,$ .
		List of moments of inertia, Moments of inertia, Area moments of inertia, Mechanics, Physics lists and Introductory physics.
	www.arikah.com /encyclopedia/List_of_moments_of_inertia (677 words)

	EM 274 - Objectives/Mass Moments of Inertia (Site not responding. Last check: 2007-10-25)
		Be able to calculate the mass moment of inertia of a thin uniform slab from the second moment of area for an area of the same shape as the slab.
		Be able to calculate (from memory) the mass moment of inertia of a rectangular body with respect to an axis along one edge or an axis through the center of gravity of the rectangular body and parallel to one edge.
		Be able to calculate (from memory) the mass moment of inertia of a uniform cylinder with respect to an axis through the center of mass of the cylinder and along the axis of the cylinder.
	www.public.iastate.edu /~statics/objectives/ch105.html (293 words)

	Autodesk - AutoCAD - Calculate area moments of inertia for 3D solid object (Site not responding. Last check: 2007-10-25)
		The moment of inertia as known by civil and structural engineers, also referred to as the second moment of area, section moduli, or area moment, can be calculated only from a two-dimensional (2D) cross section.
		The Area moments of inertia for the region is displayed adjacent to the Moments of Inertia field in the Text window.
		Note: The area moments of inertia is calculated using the UCS Z axis as the axis of rotation.
	usa.autodesk.com /adsk/servlet/ps/item?siteID=123112&id=2896668&linkID=2475323 (401 words)

	centroid
		Once these area moments of inertia are determined, principal values of them and the axes to which they refer, can be found.
		The mass moment of inertia about a vertical line through the mass center would be the mass at the left times (L/3)^2 + 1/12 (2m) L^2 + (2m) [2/3 L -1/2 L]^2.
		Once these area moments of inertia are determined, principal values of them and the axes to which they refer, can be found (see pps.
	www.eng.auburn.edu /users/drmac/centroid.html (766 words)

	[No title]
		An object's moment of inertia is the sum of the masses that make up the rigid body multiplied by the distance the mass is from the body.
		When this body is a collection of finite elements, the moment of inertia is a simple summation of each element's mass multiplied by it's distance from the axis of rotation.
		The theory of moments of inertia dates back to Newton, but their application to pattern recognition was not recognized until the 1970's.
	www.cs.mcgill.ca /~ramadan/projects/644/theory.html (475 words)

	Spring and Compliance Characteristics - SDP/SI Tech Library D220-T200
		MOMENT OF INERTIA - The moment of inertia of a rigid body about a given axis in the body is the sum of the product of the mass of each volume element and the square of its distance from the axis.
		Moments of inertia of the standard shapes are tabulated in handbooks (see Par.
		PRODUCT OF INERTIA - The product of inertia of a rigid body about two intersecting, perpendicular axes in the body is the sum of the product of the mass (volumes, areas) of a constituent element and the product of the distances of the element from the two perpendicular axes.
	www.sdp-si.com /D220/HTML/D220T200.htm (622 words)

	Areas, Volumes, Centroids, & Moments of Inertia of Solids (Site not responding. Last check: 2007-10-25)
		The principal moments of inertia are miminum values with axes through the centroid.
		The radius with reference to an axis is that distance form the axis at which the entire mass of a body may be considered as concentrating keeping the moment of inertia unchanged.
		To determine the Moment of Inertia about an axis which is parallel to a centroid axis and at a distance d.
	www.roymech.co.uk /Useful_Tables/Form/M_of_Inertia.html (290 words)

	Topic 4.7a - Centroids/Inertia
		The Moment of Inertia is obtained by breaking the object into very small bits of mass dM, multiplying these bits of mass by the square of the distance to the x (and y) axis and summing over the entire object.
		This Area Moment of Inertia is obtained by breaking the object into very small bits of area dA, multiplying these bits of area by the square of the distance to the x (and y) axis and summing over the entire object.
		The polar moment of inertia is the sum of the produce of each bit of area dA and the radial distance to an origin squared.
	physics.uwstout.edu /StatStr/Strength/Beams/bdsn51a.htm (764 words)

	Section Properties
		Calculated section property values are area, moments of inertia, center of gravity location, extreme fiber distances, section moduli, and radius of gyration.
		The appropriate X-X or Y-Y moment of inertia is then divided by this distance (fiber distance) to get the section modulus for each of the four sides.
		To specify a section t be used either type in the section name in the entry area and press the [Tab] key -or- use the [Section] button to use the built in steel section database.
	www.enercalc.com /sel_help/sectprop.htm (1142 words)

	Centroid, Area, and Moments of Inertia for Laminas
		This particular set of axes is called the principal axes, and the corresponding moments of inertia with respect to these axes are called the principal moments of inertia.
		It is seen that computation of an area and moments is actually a requirement of computing the integration of the type:
		Due to the additive property of areas and moments, we can obtain the total area and moments of lamina by simply add individuals together.
	www.infogoaround.org /JBook/Inertia.html (892 words)

	Moments of inertia...so many? Text - Physics Forums Library
		Moments of inertia are typically used when you need to analyze rotation and it's usually about some specific axis.
		Special shapes have "principle moments of inertia" based on their symmetry and you can use that to find the moments about an arbitrary axis using the translation rules for moments.
		these are all done except inertia, i figure it would be of more use to provide the user with the moments about the origin than the centroid.
	www.physicsforums.com /archive/index.php/t-47092.html (488 words)

	List of moments of inertia . Cartesian coordinate system (Site not responding. Last check: 2007-10-25)
		Moments of inertia have physical unit units of dimension mass × length2.
		Moment of inertia#Area moment of inertia Area moments of inertia have physical unit units of dimension Length4.
		The following is a list of moment of inertia moments of inertia.
	www.uk.fraquisanto.net /List_of_moments_of_inertia (338 words)

	Section Properties
		Instantaneously compute properties ranging from basic area and moments of inertia to advanced properties for complex sections, such as torsional constants, shear areas, and plastic section modulii.
		• Principal moments of inertia and corresponding Principal angles
		These include moment of inertia and first moment of areas.
	www.csiberkeley.com /SEC_BLDR_features/Section_Properties.htm (95 words)

	abstracts
		In the chimpanzees, the cross-sectional area of compact bone and the area moments of inertia (Ix, Iy, Imax, Imin, Ip) increased toward the most proximal diaphysis, whereas in the humans, the area moments of inertia increased toward both the most proximal and most distal diaphysis.
		The cross-sectional area of compact bone in the humans marked a peak value around mid diaphysis and showed a reverse pattern for the area moments of inertia.
		Bipedal locomotion may correspond to a changing pattern in the comparative area moments of inertia and comparative diameter along the femur shaft.
	www.saga-jp.org /sympo/Saga5/lastest/abstract/poster6/akiyoshi.html (391 words)

	Mass and Area Moments of InertiaDefine the mass moment of inertia of a particle with mass m about an axis a (Site not responding. Last check: 2007-10-25)
		Mass and Area Moments of InertiaDefine the mass moment of inertia of a particle with mass m about an axis a
		Define the mass moment of inertia of a particle with mass m about an axis a-a' located a perpendicular distance r from the mass.
		Know how to use the parallel axis theorem (given) to find the moment of inertia about another axis which is parallel to the original axis.
	www.vuse.vanderbilt.edu:8888 /be101s01/study_aid/sa15.htm (137 words)

	4.54 BEAM54 2-D Elastic Tapered Unsymmetric Beam (UP19980821 ) (Site not responding. Last check: 2007-10-25)
		The element real constants describe the beam in terms of the cross-sectional areas, the area moments of inertia, the extreme fiber distances from the centroid, the offset distances, and the shear deflection constant.
		The moments of inertia (IZ_) are about the principal axis of the beam.
		The element may be used in axisymmetric analyses if hoop effects are negligible, such as for bolts, slotted cylinders, etc. The areas and moments of inertia must be input on a full 360° basis for an axisymmetric analysis.
	www.uic.edu /depts/accc/software/ansys/html/elem_55/chapter4/ES4-54.htm (1565 words)

	statics STATICS is Easy with Streaming Video!
		STATICS: Statics Analysis of forces on structures in statics equilibrium, properties of forces, moments, couples and resultant, conditions for statics equilibrium, friction, centroids, and area moments of inertia.
		The sections on beams are especially useful when the course in statics is immediately followed by a course in mechanics of materials, while statics, mechanics of materials sections on the inertia properties of three-dimensional bodies are primarily intended for the students who will later study in dynamics the three-dimensional motion of rigid bodies.
		In this connection, it should be mentioned that statics, mechanics of materials determination of the centroids of composite areas precedes the calculation of centroids by integration, thus making it possible to establish the concept of moment of area firmly before introducing the use of integration.
	www.yourotherteacher.com /statics-content.html (5248 words)

	IronCAD Community -> Moments Of Inertia Debate
		I have some colleagues that feel the units of measurement on the Moments of Inertia Compute Dialog Box are not right.
		The moment of inertia of a mass taken about a given axis of rotation is equal to its total mass multiplied by the square of the orthogonal distance from said axis to the center of gravity (geometric centroid, in the case of a homgeneous mass) of said mass.
		In many engineering problems (such as the analysis of beam cross-sections), a different kind of moment of inertia is used.
	www.ironcad.com /support/community/index.php?showtopic=3509 (420 words)

	GSI: GTWorks - Geometric and Volume Analysis
		The area can be evaluated in its entirety, or designated islands or voids within the area can be excluded.
		Once a bounded area has been defined and voids identified, GTWorks provides information on perimeter, center of gravity, first and second moments of inertia, radius of gyration and polar moment of inertia.
		In either case, the system will provide information on surface area, volume, mass, weight, center of gravity, moments of inertia, products of inertia and first, second, and third principal moments of inertia.
	www.graytechsoftware.com /products/gtworks/prod01-2e.asp (278 words)

	Beams (Site not responding. Last check: 2007-10-25)
		A beam is a slender structure which is assumed to be fully described by the properties—area, moments of inertia, density—of a thin cross section.
		Cross section moment, normal and shear force along the beams can be displayed both as x-y diagrams and line plots on the geometry.
		Cross section bending moment, torsion moment, normal force, and shear forces along the beams can be displayed both as x-y diagrams and line plots on the geometry.
	www-math.cudenver.edu /~jmandel/doc/sme/intro19.htm (1079 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		The eigenvalues (l1, l2, l3) represent the moments of inertia about the principal axis and the eigenvectors, and represent the direction cosines of the three orthogonal planes containing the principal axis (it should be noted that these three planes also represent the best, intermediate and worst least squares planes).
		We wish to extend the earlier study of Argos (1988) and investigate if there is a correlation between the solvent accessible area of individual domains and their molecular weights and if this behaviour is similar to that of single domain monomeric proteins.
		Solvent accessible areas were calculated for each domain (i) as an isolated unit (Ai) and in the presence of all the polypeptide chain (Api).
	www.bmm.icnet.uk /~domains/PAPER/method-c.html (501 words)

	Elastic beam deflection calculator example
		The first step is to determine the value of Young's Modulus to be used; since the beam is made of steel, we go with the given steel value: 206,850 MPa, which is 206,850,000,000 Pa (remember, since everything else is in metric and using N/m/s, we use single Pascals).
		Next, determine the moment of inertia for the beam; this usually is a value given in most textbook problems, or if it needs to be calculated, a listing of formulas for determining moment of inertias for many common geometries is provided here.
		This is a good time to choose the loading case, so looking over the list, it looks like loading case #13 is our best bet; its beam is cantilevered on one end, and it has the single point load that is not a set distance from either end.
	www.aps.anl.gov /asd/me/Calculators/example.html (314 words)

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