The first moment of area as defined in Art. 4.1 will be used to determine the centroid of the following sections by the method of integration:
- Rectangular section,
- Circular section, and
- Triangular section
Centroid of a Rectangular Section by Integration.
Fig. 4.2 shows a rectangular section ABCD having width = b and depth = d. Consider a rectangular elementary strip of thickness ‘dy’ at a distance y from the axis OX.
Fig. 4.2 (a)
Centroid of Circular Section by Integration.
Centroid of a Triangular Section by Integration.
Problems of Finding Centre of Gravity of Areas by Integrations Method
Problem 4.1. Determine the co-ordinates of the C.G. of the area OAB shown in Fig. 4.5, if the curve OB represents the equation of a parabola, given by
in which OA = 6 units.
and AB = 4 units.
Sol. The equation of parabola is y = kx2 … (i)
First determine the value of constant k. The point B is lying on the curve and having co-ordinates
x = 6 and y = 4