Transcription of Area Moments of Inertia by Integration
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Area Moments of Inertia by Integration
Area Moments of Inertia by Integration Second momentsor Moments of inertiaof an area with respect to the xand yaxes, dAxIdAyIyx22 Evaluation of the integrals is simplified by choosing dAto be a thin strip parallel to one of the coordinate axes1ME101 -Division IIIK austubh DasguptaArea Moments of InertiaProducts of Inertia : for problems involving unsymmetrical cross-sections and in calculation of MI about rotated axes. It may be +ve, -ve, or zero Product of Inertia of area A axes:x andy are the coordinates of the element of area dA=xy dAxyIxy When the xaxis, the yaxis, or both are an axis of symmetry, the product of Inertia is zero. Parallel axis theorem for products of Inertia :AyxIIxyxy + Ixy+ Ixy-Ixy-IxyQuadrants2ME101 -Division IIIK austubh DasguptaArea Moments of InertiaRotation of Axes Product of Inertia is useful in calculating MI @ inclined axes. Determination of axes about which the MI is a maximum and a minimum dAxyIdAxIdAyIxyyx22 Moments and product of Inertia new axes x and y ?
Area Moments of Inertia by Integration • Second moments or moments of inertia of an area with respect to the x and y axes, x ³ yI y …
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