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For a rectangular area, The formula for rectangular areas may also be applied to strips parallel to the axes, Dr. Second moments or moments of inertia of an area with respect to the x and y axes, Evaluation of the integrals is simplified by choosing dA to be a thin strip parallel to one of the coordinate axes. Engin AktaşĤ 8.3.Moment of Inertia of an Area by Integration Example: Consider the net hydrostatic force on a submerged circular gate. Consider distributed forces whose magnitudes are proportional to the elemental areas on which they act and also vary linearly with the distance of from a given axis. Internal forces vary linearly with distance from the neutral axis which passes through the section centroid. Engin AktaşĮxample: Consider a beam subjected to pure bending.
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Herein methods for computing the moments and products of inertia for areas and masses will be presented Dr. The point of application of the resultant depends on the second moment of the distribution with respect to the axis.
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the magnitude of the resultant depends on the first moment of the force distribution with respect to the axis. Introduction Forces which are proportional to the area or volume over which they act but also vary linearly with distance from a given axis. 1 8.0 SECOND MOMENT OR MOMENT OF INERTIA OF AN AREAĨ.1 Introduction 8.2 Moment of Inertia of an Area 8.3 Moment of Inertia of an Area by Integration 8.4 Polar Moment of Inertia 8.5 Radius of Gyration 8.6 Parallel Axis Theorem 8.7 Moments of Inertia of Composite Areas 8.8 Product of Inertia 8.9 Principal Axes and Principal Moments of Inertia Dr.