1.Easy
A 100 mm × 150 mm plate has a circular hole of diameter 30 mm whose centre is 75 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.
b = 100 mmh = 150 mmd = 30 mmhole centre: x = 75 mm
x̄ = mm
Centroid & second moment of area worksheet with answers
2.Easy
Find the height ȳ of the centroid of the T-section above its bottom edge.
bf = 220 mmtf = 20 mmtw = 20 mmhw = 240 mm
ȳ = mm
3.Medium
Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.
bf = 180 mmtf = 30 mmtw = 14 mmhw = 300 mm
Ix = × 10⁶ mm⁴
4.Medium
A symmetric I-section has flanges 130 mm wide and 24 mm thick, an overall depth of 220 mm and a web 6 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.
B = 130 mmH = 220 mmtf = 24 mmtw = 6 mm
Ix = × 10⁶ mm⁴
5.Hard
A symmetric I-section has flanges 170 mm wide and 10 mm thick, an overall depth of 420 mm and a web 8 mm thick. It carries a bending moment of 200 kN·m about the axis x. Find the size of the bending stress σj at the junction of the web and the top flange.
B = 170 mmH = 420 mmtf = 10 mmtw = 8 mmM = 200 kN·m
σj = MPa
6.Hard
A 100 mm × 150 mm plate has a rectangular cut-out 50 mm wide and 20 mm high, centred on the vertical centre line with its centre 60 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.
b = 100 mmh = 150 mmcut-out: 50 × 20 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
Answer key
- 1. x̄ = 48.76 mm
- 2. ȳ = 182.2 mm
- 3. Ix = 96.22 × 10⁶ mm⁴
- 4. Ix = 62.77 × 10⁶ mm⁴
- 5. σj = 215.5 MPa
- 6. Ix = 27.85 × 10⁶ mm⁴
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