Question

Determine the centroid of the section of the concrete dam shown in Fig.

Answer 1

Let the axis be selected as shown in Fig. Note that it is convenient to take axis in such a way that the centroids of all simple figures are having positive coordinates. If coordinate of any simple figure comes out to be negative, one should be careful in assigning the sign of moment of area of that figure. 

The composite figure can be conveniently divided into two triangles and two rectangles, as shown in Fig. 

Centroids of simple figures are:

y₃ = 1 + \(\frac13\) x 5 = \(\frac83\) m

x₄ = 4 + \(\frac42\) = 6 m

y₄ = 0.5 m

= 2.777 m 

The centroid is at \(\bar x\) = 3.523 m 

and \(\bar y\) = 2.777 m