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
3001026018ȳ = ?dimensions in mm

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

bf = 300 mmtf = 10 mmtw = 18 mmhw = 260 mm
ȳ = mm
2.Easy
xD = 160dimensions in mm

A solid circular bar has diameter D = 160 mm. Find its second moment of area Ix about a diameter.

D = 160 mm
Ix = × 10⁶ mm⁴
3.Medium
100 mm200 mm120 mmØ60xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 60 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 = 60 mmhole centre: y = 120 mm
Ix = × 10⁶ mm⁴
4.Medium
1803020012xdimensions in mm

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

bf = 180 mmtf = 30 mmtw = 12 mmhw = 200 mm
Ix = × 10⁶ mm⁴
5.Hard
1201020020xM = 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 bending stress σbottom at the bottom edge.

bf = 120 mmtf = 10 mmtw = 20 mmhw = 200 mmM = 50 kN·m
σbottom = MPa
6.Hard
120 mm150 mm52.5 mm30 × 30xIx​ = ?

A 120 mm × 150 mm plate has a rectangular cut-out 30 mm wide and 30 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 = 120 mmh = 150 mmcut-out: 30 × 30 mmhole centre: y = 52.5 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 182.7 mm
  2. 2. Ix = 32.17 × 10⁶ mm⁴
  3. 3. Ix = 64.71 × 10⁶ mm⁴
  4. 4. Ix = 30.38 × 10⁶ mm⁴
  5. 5. σbottom = 264.1 MPa
  6. 6. Ix = 33.2 × 10⁶ mm⁴

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