Centroid of a Composite Area
Centroid of a Composite Area
The centroid of a built-up section is the area-weighted average of its parts’ centroids — the reference axis for bending calculations.
It is ȳ = (A_1·y_1 + A_2·y_2)/(A_1 + A_2). where A_1, y_1 and A_2, y_2 are the areas and centroid heights of the two parts.
Inputs
A_1 := 2000 mm^2=2e-03 m^2
y_1 := 25 mm=25 mm
A_2 := 1500 mm^2=1.5e-03 m^2
y_2 := 120 mm=120 mm
Take the area-weighted average height.
y_c := (A_1·y_1 + A_2·y_2)/(A_1 + A_2)=65.71 mm
Results
The centroid lies nearer the larger area. It locates the neutral axis, about which the section’s second moment of area is then computed.
Assumptions & limitations
- Composite of simple parts.
- Heights to a common reference.
- Non-overlapping areas.