Rail Subparts

Rail Dimensions

The beam cross section can be broken into 4 composite parts consisting of 3 rectangles and a triangle as shown. Orient an axis system as shown, so that the cross section lies entirely in the x-y plane. Since the thickness is constant for all the parts, the centroid can be found using the area equations,

Part 1

Part 1 is a rectangle with an area of

     A₁ = (2)(3) = 6 cm²

The centroid of a rectangle lies at half its width and half its height, so for part 1

Part 2 is a rectangle with an area of

     A₂ = (16)(2) = 32 cm²

Its centroid is located at

Part 3 is a rectangle with an area of

     A₃ = (2)(10) = 20 cm²

Its centroid is located at

Part 4 is a triangle with an area of

     A₄ = (0.5)(4)(4) = 8 cm²

The centroid of a right triangle is located two-thirds of the distance from the vertex to the other end; therefore, for part 4

With these results, find the total area of the system is

Substituting the areas and centroid locations for each of the individual parts into the first two equations gives