1.Easy
A 150 mm × 240 mm plate has a circular hole of diameter 30 mm whose centre is 105 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 150 mmh = 240 mmd = 30 mmhole centre: x = 105 mm
x̄ = mm
Centroid & second moment of area worksheet with answers
2.Easy
A 200 mm × 150 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 105 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.
b = 200 mmh = 150 mmd = 60 mmhole centre: y = 105 mm
ȳ = mm
3.Medium
A symmetric I-section has flanges 170 mm wide and 14 mm thick, an overall depth of 380 mm and a web 12 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.
B = 170 mmH = 380 mmtf = 14 mmtw = 12 mm
Ix = × 10⁶ mm⁴
4.Medium
A hollow rectangular (box) section has outer width B = 220 mm, outer height H = 225 mm and a uniform wall thickness t = 16 mm. Find its radius of gyration r about the horizontal centroidal axis.
B = 220 mmH = 225 mmt = 16 mm
r = mm
5.Hard
A 100 mm × 300 mm plate has a rectangular cut-out 30 mm wide and 40 mm high, centred on the vertical centre line with its centre 210 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 100 mmh = 300 mmcut-out: 30 × 40 mmhole centre: y = 210 mm
Ix = × 10⁶ mm⁴
6.Hard
A welded I-section has a top flange 160 × 10 mm, a web 290 mm high and 10 mm thick, and a bottom flange 280 × 24 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.
top flange: 160 × 10 mmweb: 10 × 290 mmbottom flange: 280 × 24 mm
Ix = × 10⁶ mm⁴
Answer key
- 1. x̄ = 74.4 mm
- 2. ȳ = 71.88 mm
- 3. Ix = 203.1 × 10⁶ mm⁴
- 4. r = 85.32 mm
- 5. Ix = 220.3 × 10⁶ mm⁴
- 6. Ix = 163.1 × 10⁶ mm⁴
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