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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
150 mm150 mm52.5 mmØ40ȳ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 52.5 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 150 mmh = 150 mmd = 40 mmhole centre: y = 52.5 mm
ȳ = mm
2.Easy
1601510014ȳ = ?dimensions in mm

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

bf = 160 mmtf = 15 mmtw = 14 mmhw = 100 mm
ȳ = mm
3.Medium
xD = 220d = 192dimensions in mm

A circular tube has outside diameter D = 220 mm and inside diameter d = 192 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 220 mmd = 192 mm
r = mm
4.Medium
2402510016xdimensions in mm

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

bf = 240 mmtf = 25 mmtw = 16 mmhw = 100 mm
Ix = × 10⁶ mm⁴
5.Hard
150 mm200 mm130 mm30 × 20xIx​ = ?

A 150 mm × 200 mm plate has a rectangular cut-out 30 mm wide and 20 mm high, centred on the vertical centre line with its centre 130 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 200 mmcut-out: 30 × 20 mmhole centre: y = 130 mm
Ix = × 10⁶ mm⁴
6.Hard
200 mm300 mm195 mm60 × 30xIx​ = ?

A 200 mm × 300 mm plate has a rectangular cut-out 60 mm wide and 30 mm high, centred on the vertical centre line with its centre 195 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 300 mmcut-out: 60 × 30 mmhole centre: y = 195 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 76.33 mm
  2. 2. ȳ = 86.32 mm
  3. 3. r = 73 mm
  4. 4. Ix = 6.58 × 10⁶ mm⁴
  5. 5. Ix = 99.43 × 10⁶ mm⁴
  6. 6. Ix = 446.1 × 10⁶ mm⁴

Full step-by-step solutions: practise this topic on examproblems.com.