Transcription of Centroids - Mercer University
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Centroids - Mercer University
Centroids Introduction The earth exerts a gravitational force on each of the particles forming a body. These forces can be replace by a single equivalent force equal to the weight of the body and applied at the center of gravity for the body. The centroid of an area is analogous to the center of gravity of a body. The concept of the first moment of an area is used to locate the centroid. 5-2. Centroids Centroid of mass ( Center of mass). ( Center of weight). ( Center of gravity). For a solid, the point where the distributed mass is centered Centroid of volume, Centroid of area x M x m x dm yM y m y dm Center of Gravity of a 2D Body Center of gravity of a plate Center of gravity of a wire M y x W x W. x dW. M y yW y W. y dW. 5-7. Centroids &First Moments of Areas & Lines Centroid of an area Centroid of a line x W x dW. x gM g x dM x W x dW. M V tA). dM dV tdA. x La x a dL. x At x t dA x L x dL. x A x dA Q y yL y dL. first moment with respect to y yA y dA Qx first moment with respect to x 5-8.
13.828 10 mm 757.7 10 mm u u ¦ ¦ A x A X X 54.8 mm 3 2 3 3 13.828 10 mm 506.2 10 mm u u ¦ ¦ A y A Y Y 36.6 mm •Compute the coordinates of the area centroid by dividing the first moments by the total area.
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