Centroid of Arbitrary Cross-Section for an axial member

Centroid of an Arbitrary Cross-Section

Recall from statics that the centroid, C, of an area may be calculated by integration.

To do so let the element of area be dA = dy dz located at the arbitrary coordinates (y,z). Also let the coordinates of the centroid be (y_c, z_c) measured from the global

y-z axes.

Let A be the total area of the cross-section. Then the y-coordinate of the centroid is calculated as follows:

Ay_c = ∫ y dA or y_c = ∫ y dA / A (result)

Likewise the z-coordinate of the centroid is z_c = ∫ z dA / A (result)

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