1.Easy
A 200 mm × 300 mm plate has a circular hole of diameter 40 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 = 200 mmh = 300 mmd = 40 mmhole centre: x = 60 mm
x̄ = mm
Centroid & second moment of area worksheet with answers
2.Easy
A 150 mm × 240 mm plate has a circular hole of diameter 50 mm whose centre is 45 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 150 mmh = 240 mmd = 50 mmhole centre: x = 45 mm
x̄ = mm
3.Medium
A symmetric I-section has flanges 150 mm wide and 22 mm thick, an overall depth of 360 mm and a web 8 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.
B = 150 mmH = 360 mmtf = 22 mmtw = 8 mm
Ix = × 10⁶ mm⁴
4.Medium
Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.
bf = 280 mmtf = 25 mmtw = 10 mmhw = 120 mm
Ix = × 10⁶ mm⁴
5.Hard
A 120 mm × 300 mm plate has a rectangular cut-out 40 mm wide and 30 mm high, centred on the vertical centre line with its centre 105 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 120 mmh = 300 mmcut-out: 40 × 30 mmhole centre: y = 105 mm
Ix = × 10⁶ mm⁴
6.Hard
The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the size of the bending stress σtop at the top edge.
bf = 120 mmtf = 10 mmtw = 10 mmhw = 280 mmM = 10 kN·m
σtop = MPa
Answer key
- 1. x̄ = 100.9 mm
- 2. x̄ = 76.73 mm
- 3. Ix = 209.8 × 10⁶ mm⁴
- 4. Ix = 7.189 × 10⁶ mm⁴
- 5. Ix = 267.4 × 10⁶ mm⁴
- 6. σtop = 29.61 MPa
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