Statics

Centroid

The geometric centre of an area: the point where its first moments about any axis balance.

The centroid of an area is located by x̄ = ΣAᵢxᵢ/ΣAᵢ and ȳ = ΣAᵢyᵢ/ΣAᵢ, breaking a composite shape into simple parts whose own centroids are known. Holes are included as negative areas. For a rectangle it is the middle; for a triangle, one third of the height from the base.

The centroid is where the resultant of a uniformly distributed load acts, where the neutral axis of a beam passes in elastic bending, and where the hydrostatic depth is measured when finding the force on a submerged gate.

How much of the FE Civil exam is Statics?