Integrating curvatures over beam length, the deflection, at some point along x-axis, should also be reversely proportional to I. 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. Thus their combined moment of inertia is: The higher this number, the stronger the section. These triangles, have common base equal to h, and heights b1 and b2 respectively. Moment of Inertia (Iz, Iy) also known as second moment of area, is a calculation used to determine the strength of a member and it’s resistance against deflection. In this video we introduce the second moment of area / inertia and its significance in the behaviour of a structure, learning how to determine the second mom. The method is demonstrated in the following examples. Moment of inertia of a rigid body about a fixed axis is defined as the sum. Moments of inertia are always calculated relative to a specific axis, so the moments of inertia of all the sub shapes must be calculated with respect to this same axis, which will usually involve applying the parallel axis theorem. The moment of inertia of a triangle with respect to an axis perpendicular to its base, can be found, considering that axis y'-y' in the figure below, divides the original triangle into two right ones, A and B. B) Calculate its rotational speed when it reaches the bottom. This can be proved by application of the Parallel Axes Theorem (see below) considering that triangle centroid is located at a distance equal to h/3 from base. The moment of inertia of a triangle with respect to an axis passing through its base, is given by the following expression: Where b is the base width, and specifically the triangle side parallel to the axis, and h is the triangle height (perpendicular to the axis and the base). The moment of inertia of a triangle with respect to an axis passing through its centroid, parallel to its base, is given by the following expression:
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