How to find centroid of an I section | Engineering Mechanics | Elements of civil engineering | Phy

To find the centroid of an I section (also known as an H-beam or a W-beam), you need to follow these steps:

Draw a sketch of the I section with all its dimensions labeled.

Divide the I section into simple geometric shapes such as rectangles, triangles, and semicircles.

Calculate the area and centroid of each of these simple shapes.

Use the parallel axis theorem to find the centroid of the entire I section.

The parallel axis theorem states that the moment of inertia of a shape about an axis parallel to its centroidal axis is equal to the moment of inertia about the centroidal axis plus the product of the area and the square of the distance between the two axes.

Assuming the I section is symmetric about its vertical axis, the centroid will lie on the vertical axis. The centroidal axis of the I section is the line passing through the centers of the two flanges