Question

Calculate the moment of interia of the following diagram about horizontal axis

Answer 1

Answer:

The moment of inertia of a tee section can be found if the total area is divided into two, smaller ones, A, B, as shown in figure below. Sub-area A consists of the entire web plus the part of the flange just above it, while sub-area B consists of the remaining flange part, having a width equal to b-tw. The final area, may be considered as the additive combination of A+B. Therefore, the moment of inertia Ix of the tee section, relative to non-centroidal x1-x1 axis, passing through the top edge, is determined like this:where h the tee height, b the width of the flange, tf the thickness of the flange (parallel to x-x) and tw the thickness of the web (perpendicular to x-x).

Knowing Ix1, the moment of inertia Ix relative to centroidal x-x axis, can be determined using the Parallel Axes Theorem (see below). For this purpose, the distance between parallel axes x and x1 is needed. In other words, the location of the centroid must be determined. Its distance from the bottom edge of the tee is named yc in the figure below, however for this calculation we need its distance from the top edge, which should be h-yc. Using the first moments of area, of the sub-areas A,B, relative to axis x1, we find that:

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