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
xD = 240d = 232dimensions in mm

A circular tube has outside diameter D = 240 mm and inside diameter d = 232 mm. Find its second moment of area Ix about a diameter.

D = 240 mmd = 232 mm
Ix = × 10⁶ mm⁴
2.Easy
xD = 280d = 272dimensions in mm

A circular tube has outside diameter D = 280 mm and inside diameter d = 272 mm. Find its second moment of area Ix about a diameter.

D = 280 mmd = 272 mm
Ix = × 10⁶ mm⁴
3.Medium
100 mm300 mm90 mmØ30xIx​ = ?

A 100 mm × 300 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 90 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 300 mmd = 30 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
4.Medium
2002524020xdimensions in mm

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

bf = 200 mmtf = 25 mmtw = 20 mmhw = 240 mm
Ix = × 10⁶ mm⁴
5.Hard
1202016016xM = 25 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 25 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 120 mmtf = 20 mmtw = 16 mmhw = 160 mmM = 25 kN·m
σbottom = MPa
6.Hard
1104401412xM = 40 kN·mdimensions in mm

A symmetric I-section has flanges 110 mm wide and 14 mm thick, an overall depth of 440 mm and a web 12 mm thick. It carries a bending moment of 40 kN·m about the axis x. Find the size of the maximum bending stress σmax in the section.

B = 110 mmH = 440 mmtf = 14 mmtw = 12 mmM = 40 kN·m
σmax = MPa

Answer key

  1. 1. Ix = 20.65 × 10⁶ mm⁴
  2. 2. Ix = 33.03 × 10⁶ mm⁴
  3. 3. Ix = 222.4 × 10⁶ mm⁴
  4. 4. Ix = 66.3 × 10⁶ mm⁴
  5. 5. σbottom = 198.3 MPa
  6. 6. σmax = 41.96 MPa

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