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 = 100d = 60dimensions in mm

A circular tube has outside diameter D = 100 mm and inside diameter d = 60 mm. Find its second moment of area Ix about a diameter.

D = 100 mmd = 60 mm
Ix = × 10⁶ mm⁴
2.Easy
xD = 120d = 84dimensions in mm

A circular tube has outside diameter D = 120 mm and inside diameter d = 84 mm. Find its second moment of area Ix about a diameter.

D = 120 mmd = 84 mm
Ix = × 10⁶ mm⁴
3.Medium
150 mm150 mm90 mmØ60xIx​ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 60 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 = 150 mmh = 150 mmd = 60 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
4.Medium
100 mm300 mm180 mmØ40xIx​ = ?

A 100 mm × 300 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 180 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 300 mmd = 40 mmhole centre: y = 180 mm
Ix = × 10⁶ mm⁴
5.Hard
180301008xM = 50 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 50 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 180 mmtf = 30 mmtw = 8 mmhw = 100 mmM = 50 kN·m
σtop = MPa
6.Hard
150 mm200 mm60 mm40 × 30xIx​ = ?

A 150 mm × 200 mm plate has a rectangular cut-out 40 mm wide and 30 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 = 150 mmh = 200 mmcut-out: 40 × 30 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. Ix = 4.273 × 10⁶ mm⁴
  2. 2. Ix = 7.735 × 10⁶ mm⁴
  3. 3. Ix = 40.82 × 10⁶ mm⁴
  4. 4. Ix = 223.7 × 10⁶ mm⁴
  5. 5. σtop = 291.2 MPa
  6. 6. Ix = 97.91 × 10⁶ mm⁴

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