Determine the location of the horizontal axis y_a 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 y_a 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.

Transcribed Image Text:

Ya = y ly hA