1.Easy
Find the height ȳ of the centroid of the T-section above its bottom edge.
bf = 280 mmtf = 30 mmtw = 20 mmhw = 260 mm
ȳ = mm
Centroid & second moment of area worksheet with answers
2.Easy
A rectangular section has width b = 160 mm and height h = 300 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.
b = 160 mmh = 300 mm
Sx = × 10³ mm³
3.Medium
Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.
bf = 120 mmtf = 10 mmtw = 10 mmhw = 160 mm
Ix = × 10⁶ mm⁴
4.Medium
A symmetric I-section has flanges 100 mm wide and 14 mm thick, an overall depth of 400 mm and a web 8 mm thick. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.
B = 100 mmH = 400 mmtf = 14 mmtw = 8 mm
Sx = × 10³ mm³
5.Hard
A 120 mm × 150 mm plate has a rectangular cut-out 80 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 = 120 mmh = 150 mmcut-out: 80 × 50 mmhole centre: y = 97.5 mm
Ix = × 10⁶ mm⁴
6.Hard
A welded I-section has a top flange 150 × 14 mm, a web 330 mm high and 14 mm thick, and a bottom flange 190 × 24 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.
top flange: 150 × 14 mmweb: 14 × 330 mmbottom flange: 190 × 24 mm
Ix = × 10⁶ mm⁴
Answer key
- 1. ȳ = 219.6 mm
- 2. Sx = 2400 × 10³ mm³
- 3. Ix = 8.378 × 10⁶ mm⁴
- 4. Sx = 693.3 × 10³ mm³
- 5. Ix = 30.31 × 10⁶ mm⁴
- 6. Ix = 229.5 × 10⁶ mm⁴
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