1.Easy
Find the height ȳ of the centroid of the T-section above its bottom edge.
bf = 160 mmtf = 15 mmtw = 8 mmhw = 160 mm
ȳ = mm
Centroid & second moment of area worksheet with answers
2.Easy
A 240 mm × 300 mm plate has a circular hole of diameter 60 mm whose centre is 60 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 240 mmh = 300 mmd = 60 mmhole centre: x = 60 mm
x̄ = mm
3.Medium
A 200 mm × 240 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 144 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 200 mmh = 240 mmd = 40 mmhole centre: y = 144 mm
Ix = × 10⁶ mm⁴
4.Medium
A circular tube has outside diameter D = 80 mm and inside diameter d = 60 mm. Find its radius of gyration r about the horizontal centroidal axis.
D = 80 mmd = 60 mm
r = mm
5.Hard
A welded I-section has a top flange 160 × 20 mm, a web 370 mm high and 14 mm thick, and a bottom flange 290 × 24 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.
top flange: 160 × 20 mmweb: 14 × 370 mmbottom flange: 290 × 24 mm
Ix = × 10⁶ mm⁴
6.Hard
A 150 mm × 300 mm plate has a rectangular cut-out 60 mm wide and 30 mm high, centred on the vertical centre line with its centre 90 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 150 mmh = 300 mmcut-out: 60 × 30 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
Answer key
- 1. ȳ = 137.1 mm
- 2. x̄ = 122.5 mm
- 3. Ix = 229.5 × 10⁶ mm⁴
- 4. r = 25 mm
- 5. Ix = 414.9 × 10⁶ mm⁴
- 6. Ix = 330.6 × 10⁶ mm⁴
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