Second moment of area is also known as area moment of inertia. Consider a small lamina of area A as shown in Figure 11.14. The second moment of area about x-axis and y-axis can be found by integrating the second moment of area of small element of area dA of the lamina, i.e., ∫ x2 dA and ∫ y2 dA, respectively. The product of the area and square of distance of centroid from an axis is known as area moment of inertia. Similarly, the product of area and distance of centre of gravity of a mass from an axis is known as mass moment of inertia.
Figure 11.14 A Plane Area for Analysis of Second Moment of Area
Consider a plane area which is divided into small areas A1, A2,…, An. Let the centroid of the small areas from a given axis be at a distance of r1, r2,…, rn, respectively. The second moment of area can be given as
Leave a Reply