. The strength of materials; a text-book for engineers and architects. es form conjugate diameters of themomental ellipse. A numerical example on the momental ellipse will be foundon p. 242. Second Moments about any Two Lines throughthe Centroid at Right Angles.—A property of the secondmoments of a figure that is sometimes useful is that the sumof the second moments of an area, about two lines at rightangles through the centroid, is equal to the sum of the secondmoments about any other pair of lines at right angles throughthe centroid. Second Moment or Moment of Inertia of Figureabout an Axis
. The strength of materials; a text-book for engineers and architects. es form conjugate diameters of themomental ellipse. A numerical example on the momental ellipse will be foundon p. 242. Second Moments about any Two Lines throughthe Centroid at Right Angles.—A property of the secondmoments of a figure that is sometimes useful is that the sumof the second moments of an area, about two lines at rightangles through the centroid, is equal to the sum of the secondmoments about any other pair of lines at right angles throughthe centroid. Second Moment or Moment of Inertia of Figureabout an Axis perpendicular to its Plane.—The secondmoment or moment of inertia of an area about an axis operpendicular to its plane is called the polar second momentor moment of inertia, and is equal to 2 a . p o^. Let any two axes x x and y y at right angles be drawnthrough o, and let perpendiculars p x, p m be drawn to theseaxes, Fig. 85. GEOMETRICAL PROPERTIES OF SECTIONS 173 Then p o-^ = p n^ 4- n o^ = PN^ + P M^. •. 2 a . P O^ --= :^ ft . P N^ + ^ a . P M^ = l\x + Ivv. Fig. 85.—Polar Moment of Inertia. Therefore wc have the following rule— The polar second moment, or moment of inertia, about anaxis perpendicular to the plane of any area, is equal to the
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