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chapter5 (centroids &amp; centres of gravity)

# chapter5 (centroids &amp; centres of gravity) - (3...

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CHAPTER FIVE CENTROIDS AND CENTRES OF GRAVITY

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5.2. Centroids of Areas For the homogenous plate: weight of element of plate w = density x g x volume = ρ g t A Where: is density (kg/m 3 ); g = m/s 2 ; t = thickness of plate (m); and A is the area of the element, m 2 . Also: The weight of the whole plate, W = g t A where A is the area of the plate. Substituting for W and W in moment equations (1) and dividing by g t,

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We write moment equations for area: The co-ordinates x and y define the co-ordinates of a homogenous plate. The point (x,y) defines the centroid of the area A of the plate. See Figure 5.3. y x C y x Fig. 5.3 Σ Σ M x A x A x A x A M y A y A y A y A U g Limits xA x dA yA y dA y n n x n n : .... : .... sin : , ........... ( ) = + + = + + = = z z 1 1 2 2 1 1 2 2 3
5.1 First Moments of Areas The integral xdA in equation (3) is defined as the first moment of the area A wrt the y axis and is denoted as Qy: i.e. Qy = xdA . Likewise: along x-axis: Qx = ydA . i.e. Qy = xdA . And : Qx = ydA . ………………. (4) Comparing Equations

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Unformatted text preview: (3) and (4): Qy = x A and Qx = y A i.e. x = Qy/A and y = Qx/A x x dA A y y dA A = = z z Examples Solve Examples Using the method of integration to locate Centroids. Centroids of Composite Objects Centroids of Composite Objects Contd. Examples Solve Examples to Illustrate the centroid of Composite Objects. Examples Solve Examples to illustrate the centroids of beams with distributed Loads. Assignment-1 1. The column is used to support the floor which exerts a force of 3000 N on top of the column. The effect of soil pressure along its side is distributed as shown. Replace this loading by an equivalent resultant force and specify where it acts along the column, measured from the base A. Assignment-2 2. The wall footing is used to support the column load of 12,000 N. Determine the intensities w 1 and w 2 of the distributed loading acting on the base of the footing for equilibrium....
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chapter5 (centroids &amp; centres of gravity) - (3...

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