Therefore, it can be seen from the former equation, that when a certain bending moment M is applied to a beam cross-section, the developed curvature is reversely proportional to the moment of inertia I. In Physics the term moment of inertia has a different meaning. When a body starts to move in rotational motion about a constant axis, every element in the. Since the distance from centroid is squared, it affects the moment of inertia much more than the area A. It can be inferred that inertia is related to the mass of a body. CENTROID AND MOMENT OF INERTIA 85 Width of element dx Area of the element kx2 dx Total area of spandrel kx dx a 2 0 z kx ka a3 0 3 3 3 L NM O QP Moment of area about y axis kx dx x a 2 0 ×z kx dx a 3 0 z kx a4 0 4 L NM O QP ka4 4 Moment of area about x axis dAy 2 0 z kx dx kx k x dx k xa aa 2 2 2 4 0 2 5 00 2 2 2 5 × L NM O QPzz k a2 5 10 x ka ka.
It is also called the geometrical centre or the centre of gravity. The centre of area of such figure is known as centroid. Making similar considerations, the moment of inertia of the angle, relative to axis y0 is: It turns out that the new moment of inertia is drastically increased compared to the centroidal one. The plane figures (like triangle, quadrilateral, circle, trapezoid, etc.) have only areas but no mass.