A luggage transport system for a new airport is having some problems.
The railway track bends when the luggage carrier passes over it and
will probably
break. To analyze this bending, engineers must determine the neutral
axis of the beam, which for a homogeneous beam passes through the centroid
of the cross section. (The area moment of inertia of the cross
section will be found in a
latter
section).

What is known:

The dimensions of the cross section are as shown.

Question

Rail Cross Section

Where is the centroid of the cross section?

Approach

Break the beam cross section into simpler, component parts.

Determine the centroid and area of each component part.

Use the method of composite parts to calculate the x and y locations
of the centroid of the cross section.