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 = 80d = 56dimensions in mm

A circular tube has outside diameter D = 80 mm and inside diameter d = 56 mm. Find its second moment of area Ix about a diameter.

D = 80 mmd = 56 mm
Ix = × 10⁶ mm⁴
2.Easy
2601516014ȳ = ?dimensions in mm

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

bf = 260 mmtf = 15 mmtw = 14 mmhw = 160 mm
ȳ = mm
3.Medium
120 mm200 mm120 mmØ50xIx​ = ?

A 120 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 = 120 mmh = 200 mmd = 50 mmhole centre: y = 120 mm
Ix = × 10⁶ mm⁴
4.Medium
2202512012xdimensions in mm

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

bf = 220 mmtf = 25 mmtw = 12 mmhw = 120 mm
Ix = × 10⁶ mm⁴
5.Hard
2402512020xsagging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 40 MPa in tension and 150 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 240 mmtf = 25 mmtw = 20 mmhw = 120 mmσt,allow = 40 MPaσc,allow = 150 MPa
Mallow = kN·m
6.Hard
150 mm240 mm84 mm30 × 30xIx​ = ?

A 150 mm × 240 mm plate has a rectangular cut-out 30 mm wide and 30 mm high, centred on the vertical centre line with its centre 84 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 240 mmcut-out: 30 × 30 mmhole centre: y = 84 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. Ix = 1.528 × 10⁶ mm⁴
  2. 2. ȳ = 135.6 mm
  3. 3. Ix = 78.84 × 10⁶ mm⁴
  4. 4. Ix = 8.013 × 10⁶ mm⁴
  5. 5. Mallow = 4.367 kN·m
  6. 6. Ix = 171.5 × 10⁶ mm⁴

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