4. Area Props and Dist Forces

Z z w w2 y y w1 x g o g2 w4 g1 o y g3 x

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Unformatted text preview: wn. z z ∑W W2 y y W1 X G O G2 = W4 G1 O Y G3 x In this case, the moment the composite object makes about the x axis is M M X Y x1W1 x2 W2 xn Wn y1W1 y2 W2 y n Wn And its total area is W W1 W2 Wn If the center of gravity of the composite object is at X , then X W x 1W1 x 2 W2 x n Wn or X G4 x x 1W1 x2 W2 xn Wn W 4‐4 W3 Example Find the area of the plate shown below and calculate the moment that it generates about the x‐ and y‐axes. Calculate the centroid of the plate. 4‐5 4.1.3 Centroids by Integration Suppose that a shape is defined by a function y=y(x). and the lines x= x1 and x=x2.…. Its moment of inertia can be found easily by considering the shape to be made of bars that span from y= 0 to y=y(x). The area of the shape is given by Its moment about the x‐axis is And its moment about the y‐axis is The plate centroid is at x2 x y( x ) x1 x2 x2 2 x dx and y y( x) dx x2 y( x) dx x1 x1 4‐6 1 2 y( x) dx 2 x1 4.2 Distributed Forces Distributed forces often arise in mechanics and it is important to be a...
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