4. Area Props and Dist Forces

# 4. Area Props and Dist Forces - 4 AREA PROPERTIES AND...

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4 1 4. A REA P ROPERTIES AND D ISTRIBUTED F ORCES 4.1 Centroids 4.1.1 Basic Shapes The centroid or “center of gravity” of a 2D object is defined as that location where the total weight of the object could be considered to be acting. It can be found easily by taking moments. x y z G W x y = x y dW O x y z

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4 2 The weight of the plate is given by dW W The moment M x of the planar shape about the y axis is given by dW x M x If the entire weight were focused at a location x bar, and it generated the same moment, then we would have dW x W x or W dW x x A similar analysis for rotation about the x axis yields W dW y y
4 3 Centroids of some common shapes are shown in the table below. y x 3 4 r 2 2 r A r C h b bh A y x C h 3 1 C h b bh A 2 1 x C h h b a b a 2 3 1 a b  b a h A 2 1 r x y C 2 r A C b a 5 2 b 8 3 ab A 3 2 Zero slope a C b Zero slope b 10 3 3 ab A a a 4 3

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4. Area Props and Dist Forces - 4 AREA PROPERTIES AND...

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