1.Easy
A 200 mm × 240 mm plate has a circular hole of diameter 50 mm whose centre is 150 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 200 mmh = 240 mmd = 50 mmhole centre: x = 150 mm
x̄ = mm
Centroid & second moment of area worksheet with answers
2.Easy
A rectangular section has width b = 260 mm and height h = 275 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.
b = 260 mmh = 275 mm
Sx = × 10³ mm³
3.Medium
A circular tube has outside diameter D = 240 mm and inside diameter d = 220 mm. Find its radius of gyration r about the horizontal centroidal axis.
D = 240 mmd = 220 mm
r = mm
4.Medium
Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.
bf = 120 mmtf = 20 mmtw = 18 mmhw = 220 mm
Ix = × 10⁶ mm⁴
5.Hard
A 150 mm × 300 mm plate has a rectangular cut-out 60 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 = 150 mmh = 300 mmcut-out: 60 × 40 mmhole centre: y = 210 mm
Ix = × 10⁶ mm⁴
6.Hard
A 100 mm × 150 mm plate has a rectangular cut-out 40 mm wide and 50 mm high, centred on the vertical centre line with its centre 97.5 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 100 mmh = 150 mmcut-out: 40 × 50 mmhole centre: y = 97.5 mm
Ix = × 10⁶ mm⁴
Answer key
- 1. x̄ = 97.87 mm
- 2. Sx = 3277 × 10³ mm³
- 3. r = 81.39 mm
- 4. Ix = 37.57 × 10⁶ mm⁴
- 5. Ix = 328.1 × 10⁶ mm⁴
- 6. Ix = 26.54 × 10⁶ mm⁴
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