Centroid of an Unequal-Leg Angle
Mediumcentroidscomposite sectionsangles
An unequal-leg angle has a vertical leg 150 mm long and a horizontal leg 100 mm long, both 10 mm thick, meeting at the bottom-left heel. Measured from the outside face of the horizontal leg, the centroid of the section is located most nearly at:
- A23.8 mm
- B40.0 mm
- C48.8 mm
- D75.0 mm
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Answer: C. 48.8 mm
Split the angle into two rectangles that do not overlap: the full vertical leg, 10 × 150 (A₁ = 1,500 mm², centroid 75 mm up), and the remaining part of the horizontal leg, 90 × 10 (A₂ = 900 mm², centroid 5 mm up). ȳ = ΣAy/ΣA = (1,500 × 75 + 900 × 5)/(1,500 + 900) = 117,000/2,400 = 48.8 mm. The heavier vertical leg pulls the centroid well above the simple average of 40 mm, and 75 mm is just the mid-height of the long leg. The horizontal position works the same way: x̄ = (1,500 × 5 + 900 × 55)/2,400 = 23.8 mm from the outside face of the vertical leg, which is the other axis, not the one asked for.
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