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Topic: Second moment of area

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Second moment of inertia

Moment of inertia

Parallel axes rule

List of moments of inertia

Centroid

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	Reference.com/Encyclopedia/Second moment of area
		The second moment of area, also known as the area moment of inertia and less precisely as the moment of inertia, is a property of a shape that is used to predict its resistance to bending and deflection.
		It is analogous to the polar moment of inertia, which characterizes an object's ability to resist torsion.
		The second moment of area is not the same thing as the moment of inertia, which is used to calculate angular acceleration.
	www.reference.com /browse/wiki/Second_moment_of_area (423 words)

	Moment of inertia - Wikipedia, the free encyclopedia
		Moment of inertia should not be confused with the second moment of area or area moment of inertia (SI units: m
		For the case where the angular momentum is parallel to the angular velocity, the moment of inertia is simply a scalar.
		However, in the general case of an object being rotated about an arbitrary axis, the moment of inertia becomes a tensor, such that the angular momentum need not be parallel to the angular velocity.
	en.wikipedia.org /wiki/Moment_of_inertia (806 words)

	Radius of gyration - Wikipedia, the free encyclopedia
		The radius of gyration of an area with respect to a particular axis is the square root of the quotient of the area moment of inertia divided by the area.
		It is the distance at which the entire area must be assumed to be concentrated in order that the product of the area and the square of this distance will equal the moment of inertia of the actual area about the given axis.
		The radius of gyration of a mass is similar except that the second moment of inertia of the mass is involved.
	en.wikipedia.org /wiki/Radius_of_gyration (289 words)

	Moment Of Inertia; Definition with examples
		The Area Moment Of Inertia of a beams cross-sectional area measures the beams ability to resist bending.
		The moment of inertia is a geometrical property of a beam and depends on a reference axis.
		The moment of inertia of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis.
	www.efunda.com /math/areas/MomentOfInertia.cfm?Moment=z (230 words)

	Example/Second Moment of Area (Part 2)
		Calculate the second moments of the shaded area shown in Fig.
		For the second moment of area with respect to the y-axis, we need an element of area all of which is at the same distance from the y-axis.
		For the second moment of area with respect to the x-axis, we need an element of area all of which is at the same distance from the x-axis.
	www.iastate.edu /~statics/examples/secmoment/secmomb.html (421 words)

	Resources (Site not responding. Last check: 2007-10-02)
		The second, or area moment of inertia (I) is a measure of how well the cross section of a beam will resist bending.
		We have used second moment calculations to determine the relative flexibility of shark bodies, as well as the flexibility of horn shark and stingray jaws.
		One calculates the second moment of are for a selected skeletal element in a ct scan.
	biomechanics.bio.uci.edu /_html/resources/topics/second_moment.htm (144 words)

	Hydrostatic Curves - Definitions: Details
		=transverse moment of inertia of the waterplane (second moment of area with respect to the x-axis); and V=volume of displacement.
		=longitudinal moment of inertia of the waterplane with respect to the LCF (the principal second moment of area of the waterplane with respect to the y-axis).
		The wetted surface is the total area of the shell of the ship that is wetted by the water in which it floats for a given draft.
	web.nps.navy.mil /~me/tsse/NavArchWeb/1/module5/details.htm (552 words)

	Summary of discussion on the first moment of an area (Site not responding. Last check: 2007-10-02)
		The second moment of an area, >also known as the moment of inertia, is defined as the integral of the >(distance from axis)^2 where the integration is carried out over the area.
		Anders Eriksson wrote: >as a few examples, there are three aspects where the first moment of area >is used: >1) As a definition of the center of gravity; >2) In common engineering expressions for evaluating beam shear stresses; >3) In the calculation of a bending moment for a fully plasticised beam >section.
		The latter is defined as the second moment of >>>a mass<<< (not >an area).
	isb.ri.ccf.org /biomch-l/archives/biomch-l-2002-05/00078.html (965 words)

	[No title] (Site not responding. Last check: 2007-10-02)
		Second Moment of Area About Triangle Base Applying the parallel axis theorem we are considering a translation of the z axis by EMBED Equation.3 .
		The bending moment diagram, in general, is given by the integration of the shear force distribution, hence, the BM for the point load will be a ramp peaking at 200 Nm at the beam centre, and for the uniform load a quadratic.
		For the ‘cross-bar’ of the ‘T’ we have the second moment of area about the centroid as EMBED Equation.3 For the vertical section of the ‘T’ we have the second moment of area about the centroid as EMBED Equation.3 Hence the total second moment of area is EMBED Equation.3 .
	hw.ac.uk /mecWWW/courses/d_towers/23.2ej2/NOTES_SF_AND_BM_STRESS.DOC (3396 words)

	Areas, Volumes, Centroids, & Moments of Inertia Plane Figures (Site not responding. Last check: 2007-10-02)
		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.
		To determine the Second Moment of Area about an axis which is parallel to a centroid axis and at a distance k.
	www.roymech.co.uk /Useful_Tables/Form/M_of_Inertia_2.html (397 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)

	CEE 340: Structural Analysis I
		P:EMA 304 or 303 and Mech Engr 307 or con reg.
		Properties of Areas - Centroid, First Moment of Area, Second Moment of Area (Moment of Inertia)
		To identify determinate, indeterminate, stable and unstable structures.
	www.engr.wisc.edu /cee/courses/cee340.html (582 words)

	Lecture 28: Centroids and Moment of Inertia
		The Moment of Inertia (I) is a term used to describe the capacity of a cross-section to resist bending.
		The Moment of Inertia is an important value which is used to determine the state of stress in a section, to calculate the resistance to buckling, and to determine the amount of deflection in a beam.
		The easiest way to determine the moment of inertia of such a section is to find the moment of inertia of the component parts about their own centroidal axis and then apply the transfer formula.
	darkwing.uoregon.edu /~struct/courseware/461/461_lectures/461_lecture28/461_lecture28.html (1380 words)

	Guitar necks as beams
		The geometric property of the section's shape and area is known as the Second Moment of Area, I, and represents the way in which the area of the section is distributed about the neutral axis.
		What is most significant is that the second moment, though proportional to the width, is also proportional to the cube of the depth.
		The area of the section on the graph is found by calculating the area of each strip, and adding them all together.
	www.btinternet.com /~paul.everard/equa/beam.htm (1241 words)

	Hydrostatic Curves - Definitions: Basics
		This property of the waterplane is its second moment of area about a transverse axis passing through the center of flotation.
		This is the second moment of area of the waterplane about its centerline.
		The cross-sectional area of each station shown in the body plan up to the waterline in question is determined for input into the calculation of the volume of displacement, this set of curves is also known as the Bonjean curves.
	web.nps.navy.mil /~me/tsse/NavArchWeb/1/module5/basics.htm (575 words)

	[No title]
		It is expressed in cm4 or mm4 NOTE The second moment of area is also referred to as the moment of inertia.
		3.5 section modulus for a homogeneous material, it is second moment of area divided by the distance to any point from the neutral axis at which the stress is to be calculated.
		The general stiffener requirement for both minimum section modulus and second moment of area may be 50 % of that required for stiffener members of integral tanks.
	www.nmma.org /certification/local/downloads/documents/DIS_12215-5.2_with_fig-2004-03-25.doc (3654 words)

	Climate (Site not responding. Last check: 2007-10-02)
		A stochastic dynamical model of rainfall based on a fractional diffusion type kinetic equation introduced earlier by the authors describes fairly well how the second moment statistics of area-averaged rain rate depends on the averaging length L and predicts a power law scaling behavior as L -> 0.
		In particular, a scaling regime is identified in which the various second moment statistics of area- and/or time-averaged rain field exhibit invariance under a combined rescaling of the space and time variables Ð a property known as dynamic scaling, the scaling exponent being identified with the Lvy index.
		Although the space and time scales resolved in the radar data used to establish the model turn out to be too coarse for the dynamic scaling behavior to be experimentally demonstrated, we predict that it should be observable in high frequency rain gauge data from dense gauge networks.
	climate.gsfc.nasa.gov /viewPaperAbstract.php?id=719 (252 words)

	The Bending moment, M (Site not responding. Last check: 2007-10-02)
		is the stress (compression or tension), y is the bone radius, M the moment of bending, I the second moment of area, E the elastic modulus, and R the radius of bending.
		I, the second moment of area, describes the way that material is distributed about a given axis--in this case about the neutral axis.
		M, the bending moment, is a property of the situation and cannot be modified.
	musr.physics.ubc.ca /~jess/sci1/biol/beamtheory/node1.html (420 words)

	Dr Derek Bray, DAPS - Guided Weapons Technology Short Course Information (Site not responding. Last check: 2007-10-02)
		The second moment of area of a section is equivalent to its moment of inertia so that any tables of moment of inertia data may be used to produce equivalent second moment of area data.
		The second moment of area of a plane area about any axis is equal to the second moment of area about a parallel axis through the centroid of the area plus the product of the area and the square of the distance between the two axes.
		It is therefore clear that the minimum value of second moment of area relates to an axis passing through the centroid.
	www.rmcs.cranfield.ac.uk /aeroxtra/gwtcfund2moa.htm (340 words)

	[No title] (Site not responding. Last check: 2007-10-02)
		For a rectangular cross-section, the second moment of area is
		Since the bending moment per unit width is inversely proportional to the square of the thickness of the plate, the minimum number of plies required would be 135 which gives the thickness of the all Glass/epoxy laminate as
		In a plate under a bending moment, the magnitude of ply stresses is maximum on the top and bottom face.
	www.eng.usf.edu /~kaw/promal/Promal_Design.html (635 words)

	Untitled
		In the diagram, the large area has been broken down into smaller areas, such that the position of the centroid of each is known, as is its area.
		We can calculate its second moment of area by subtracting the second moment of area of the small rectangle from that of the large one.
		which says that the second moment of area about an arbitrary axis XX parallel to the neutral axis is equal to the second moment of area about the neutral axis plus the product of the square of distance between the two axes and the total area of the shape.
	www.hull.ac.uk /engineering/teaching/57034/centroid.shtml (736 words)

	DoITPoMS TLP - Beam Stiffness - Second moment of area
		The second moment of area, I, can be used as a measure of how stiff a particular geometry of a beam is, or how well the geometry resists bending.
		For regular cross-sectional shapes, the second moments of area are often tabulated in books.
		In the case of a hollow beam, the second moment of area is found by subtracting that of the removed area from the appropriate solid section equation, eg.
	www.doitpoms.ac.uk /tlplib/BD1/secondmoment.php (192 words)

	Second Moment: Do Burglars Calculate ROI? A Logistic Regression Analysis
		Interestingly, however, once a burglar locks in on the target, it appears little can be done to stop him or her from actually penetrating the premises.
		Houses that had one or more of the following attributes: that they were adjacent to a wooded area, that they were detached family homes, or that they were far from schools had a greater probability of being burglarized.
		On the other hand, the greater the number of children in the household, the greater the probability that the premises would be occupied, and therefore the lower the chance of burglary.
	www.2ndmoment.com /articles/burglars.php (2186 words)

	Understanding Second Moment Of Area (Site not responding. Last check: 2007-10-02)
		The second moment of area (or moment of inertia) of a shape is a property which measures the efficiency of that shape in respect of its resistance to bending.
		Most beams have two axes of symmetry, X-X and Y-Y, termed the priciple axes, which intersect at the centroid (or centre of gravity) of the section.
		The larger the second moment of area the better the resistance to bending.
	www2.umist.ac.uk /construction/intranet/teaching/ul222/exp/2maex.htm (215 words)

	Rigging - Full
		In the second half of the 19th century yacht racing was borne as a sport.
		During the industrial revolution vast areas of woodland were destroyed, for various reasons such as building of ships and for firewood.
		This is because the strength on the mast is largely dependant on the second moment of area of the mast section.
	www.marinearchitecture.com /articles/rigging (5246 words)

	Position of centroid of weld (Site not responding. Last check: 2007-10-02)
		For weld on one side, first moment of area about the centroid is 100 t x
		Second moment of area of area of the weld about a horizontal centroidal axis is
		Second moment of area about a vertical axis through the weld centroid is
	www.mech.uq.edu.au /courses/mech2100/question_3.html (175 words)

	[No title]
		Determine the centroid of an arbitrary area, line, or composite area or line through integration or the aid of standard tables for known geometric shapes.
		Determine the second moment of area for an arbitrary area or composite area through integration or the use of standard tables for geometric shapes.
		Apply the parallel axis theorem to determine the second moment of area for arbitrary and composite areas about a specified axis.
	engr.oregonstate.edu /about/accreditation/syllabi/ENGR211_syllabus.doc (268 words)

	[No title] (Site not responding. Last check: 2007-10-02)
		Calculate the moment about the pivot point (H on Figure 2) of the balance arm with the aid of this diagram, i.e.
		Construct a table showing the measured height (h), wetted area (A = bh), Ic, yc, yp and the associated theoretical and experimental hydrostatic forces.
		Plot the theoretical hydrostatic force and the measured hydrostatic force as functions of the height of the water on one diagram.
	www.eng.auburn.edu /~xshi/WordFile/lab1.doc (823 words)

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