Unformatted text preview: AREA MOMENTS
OF INERTIA See Appendix A of Vol. 1 Statics for a treatment of the theory
and calculation of area moments of inertia. Because this quantity
plays an important role in the design of structures, especially those
dealt with in statics, we present only a brief deﬁnition in this Dy-
namics volume so that the student can appreciate the basic differ-
ences between area and mass moments of inertia. The moments of inertia of a plane areaA about the x- and y-axes in its plane and about the z-axis normal to its plane, Fig. A/ 1, are
deﬁned by H Ix=fy2dA I JdeA Iz=fr2dA Figure A/l where dA is the differential element of area and r2 = x2 + y2.
Clearly, the polar moment of inertia 1, equals the sum Ix + Iy of the
rectangular moments of inertia. For thin ﬂat plates, the area mo-
ment of inertia is useful in the calculation of the mass moment of
inertia, as explained in Appendix B. The area moment of inertia is a measure of the distribution of
area about the axis in question and, for that axis, is a constant prop-
erty of the area. The dimensions of area moment of inertia are (dis-
tance)4 expressed in m4 or mm4 in SI units and ft4 or in.4 in US.
customary units. In contrast, mass moment of inertia is a measure
of the distribution of mass about the axis in question, and its di-
mensions are (mass)(distance)2 which are expressed in kg- m2 in SI
units and in lb-ft-sec2 or lb-in.-sec2 in US. customary units. W ...
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- Spring '08