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International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
ISBN: 9781305501607

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BuyFindarrow_forward

International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
ISBN: 9781305501607
Textbook Problem

Using the method of composite surfaces, locate the centroid of the surface.

To determine

Centroidal coordinates of composite surface.

Explanation

Given Information:

The following composite surface in given,

  

Calculation:

For the calculation of x¯i, axis x is to be considered and similarly for y¯i ,y axis is considered. For calculating z¯i, z axis is considered.

The above figure has been divided into simple geometrical shapes and these shapes have been numbered to find the individual area and centroidal distances from the reference axes.

The area of the simple geometrical shapes can be calculated as follows

  1. Rectangle = A=b×d
  2. Triangle = A=12×b×h

The centroidal distance of the geometries lies at

  1. Rectangle (marked as 1, 2 and 4) = Centroid lies at the midpoint of the dimension in consideration. If the centroid lies on the axis considered, the centroidal distance is considered zero. There are total 3 rectangles in the above figure.
  2. For the rectangle marked as 2, the area can be calculated by calculating the length AC,

      AC2=AE2+EC2AC2=9002+(360150)2AC2=854100AC=854100AC=924.175

  3. Triangle (marked as 3) = Centroid lies at the distance of h3 of the dimension in consideration. There are 2 triangular plates.

Consider the following figure,

  

Let us prepare the table for area and centroidal distances.

    iPartAix¯iy¯iz¯i
    1Rectangular Plate2×(900×100)=1800000.009002=4500.00
    2Rectangular Plate2×(924.175×150)=277252.590.009002=4501502=75
    3Triangular Plate2×12×(900×(360150))=1890000.0023×900=600150+( 360150)3 =220
    4Rectangular Plate(300×900)=2700000

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