![]() ![]() 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. Where Ixy is the product of inertia, relative to centroidal axes x,y (=0 for the I/H section, due to symmetry), and Ixy' is the product of inertia, relative to axes that are parallel to centroidal x,y ones, having offsets from them d_. Where I' is the moment of inertia in respect to an arbitrary axis, I the moment of inertia in respect to a centroidal axis, parallel to the first one, d the distance between the two parallel axes and A the area of the shape, equal to 2b t_f + (h-2t_f)t_w, in the case of a I/H section with equal flanges.įor the product of inertia Ixy, the parallel axes theorem takes a similar form: The so-called Parallel Axes Theorem is given by the following equation: ![]() An axis is fixed and then the second moment of area of each shape is calculated and summed to the area multiplied by the distance between the fixed axis and the shape centroid squared.The moment of inertia of any shape, in respect to an arbitrary, non centroidal axis, can be found if its moment of inertia in respect to a centroidal axis, parallel to the first one, is known. The parallel axis thereom is used to seperate the shape into a number of simpler shapes.
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