Determine the location of the horizontal axis y a at which a vertical gate in a dam

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Determine the location of the horizontal axis ya at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure). The model for ya is

where Y̅ is the y-coordinate of the centroid of the gate, IY̅ is the moment of inertia of the gate about the line y = Y̅, h is the depth of the centroid below the surface, and A is the area of the gate.

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Calculus

ISBN: 9781285057095

10th Edition

Authors: Ron Larson, Bruce H. Edwards

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