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 = 180d = 152dimensions in mm

A circular tube has outside diameter D = 180 mm and inside diameter d = 152 mm. Find its second moment of area Ix about a diameter.

D = 180 mmd = 152 mm
Ix = × 10⁶ mm⁴
2.Easy
120202008ȳ = ?dimensions in mm

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

bf = 120 mmtf = 20 mmtw = 8 mmhw = 200 mm
ȳ = mm
3.Medium
2402016014xdimensions in mm

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

bf = 240 mmtf = 20 mmtw = 14 mmhw = 160 mm
Ix = × 10⁶ mm⁴
4.Medium
150 mm240 mm168 mmØ30xIx​ = ?

A 150 mm × 240 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 168 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 240 mmd = 30 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
5.Hard
100 mm200 mm70 mm40 × 50xIx​ = ?

A 100 mm × 200 mm plate has a rectangular cut-out 40 mm wide and 50 mm high, centred on the vertical centre line with its centre 70 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 200 mmcut-out: 40 × 50 mmhole centre: y = 70 mm
Ix = × 10⁶ mm⁴
6.Hard
200152408xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 30 MPa in tension and 120 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 200 mmtf = 15 mmtw = 8 mmhw = 240 mmσt,allow = 30 MPaσc,allow = 120 MPa
Mallow = kN·m

Answer key

  1. 1. Ix = 25.33 × 10⁶ mm⁴
  2. 2. ȳ = 166 mm
  3. 3. Ix = 17.31 × 10⁶ mm⁴
  4. 4. Ix = 171.1 × 10⁶ mm⁴
  5. 5. Ix = 64.25 × 10⁶ mm⁴
  6. 6. Mallow = 14.83 kN·m

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