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
200 mm300 mm105 mmØ40ȳ = ?

A 200 mm × 300 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 105 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 200 mmh = 300 mmd = 40 mmhole centre: y = 105 mm
ȳ = mm
2.Easy
B = 100H = 150t = 10xdimensions in mm

A hollow rectangular (box) section has outer width B = 100 mm, outer height H = 150 mm and a uniform wall thickness t = 10 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 100 mmH = 150 mmt = 10 mm
Ix = × 10⁶ mm⁴
3.Medium
100 mm200 mm120 mmØ50xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 120 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 200 mmd = 50 mmhole centre: y = 120 mm
Ix = × 10⁶ mm⁴
4.Medium
3003014016xdimensions in mm

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

bf = 300 mmtf = 30 mmtw = 16 mmhw = 140 mm
Ix = × 10⁶ mm⁴
5.Hard
2401012018xM = 20 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 20 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 240 mmtf = 10 mmtw = 18 mmhw = 120 mmM = 20 kN·m
σtop = MPa
6.Hard
100 mm150 mm52.5 mm40 × 50xIx​ = ?

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 52.5 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 = 52.5 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 151 mm
  2. 2. Ix = 13.48 × 10⁶ mm⁴
  3. 3. Ix = 65.49 × 10⁶ mm⁴
  4. 4. Ix = 17.29 × 10⁶ mm⁴
  5. 5. σtop = 96.53 MPa
  6. 6. Ix = 26.54 × 10⁶ mm⁴

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