Centroid & second moment of area worksheet with answers

Free printable Centroid & second moment of area worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
2401516016ȳ = ?dimensions in mm

Find the height ȳ of the centroid of the T-section above its bottom edge.

bf = 240 mmtf = 15 mmtw = 16 mmhw = 160 mm
ȳ = mm
2.Easy
b = 100h = 100xdimensions in mm

A rectangular section has width b = 100 mm and height h = 100 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 100 mmh = 100 mm
Sx = × 10³ mm³
3.Medium
160200t = 12xdimensions in mm

A channel section lies with its open side up: a base plate 160 mm wide with two upright legs, 200 mm high overall. Base and legs are all 12 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 160 mmh = 200 mmt = 12 mm
Ix = × 10⁶ mm⁴
4.Medium
1202510012xdimensions in mm

Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.

bf = 120 mmtf = 25 mmtw = 12 mmhw = 100 mm
Ix = × 10⁶ mm⁴
5.Hard
120 mm200 mm140 mm50 × 50xIx​ = ?

A 120 mm × 200 mm plate has a rectangular cut-out 50 mm wide and 50 mm high, centred on the vertical centre line with its centre 140 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 120 mmh = 200 mmcut-out: 50 × 50 mmhole centre: y = 140 mm
Ix = × 10⁶ mm⁴
6.Hard
100 mm200 mm60 mm50 × 40xIx​ = ?

A 100 mm × 200 mm plate has a rectangular cut-out 50 mm wide and 40 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 = 200 mmcut-out: 50 × 40 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 131.1 mm
  2. 2. Sx = 166.7 × 10³ mm³
  3. 3. Ix = 26.78 × 10⁶ mm⁴
  4. 4. Ix = 4.504 × 10⁶ mm⁴
  5. 5. Ix = 75.01 × 10⁶ mm⁴
  6. 6. Ix = 62.84 × 10⁶ mm⁴

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