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
200 mm300 mm210 mmØ40ȳ = ?

A 200 mm × 300 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 210 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 200 mmh = 300 mmd = 40 mmhole centre: y = 210 mm
ȳ = mm
2.Easy
3001514012ȳ = ?dimensions in mm

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

bf = 300 mmtf = 15 mmtw = 12 mmhw = 140 mm
ȳ = mm
3.Medium
260180t = 8xdimensions in mm

A channel section lies with its open side up: a base plate 260 mm wide with two upright legs, 180 mm high overall. Base and legs are all 8 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 260 mmh = 180 mmt = 8 mm
Ix = × 10⁶ mm⁴
4.Medium
1403020014xdimensions in mm

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

bf = 140 mmtf = 30 mmtw = 14 mmhw = 200 mm
Ix = × 10⁶ mm⁴
5.Hard
200 mm200 mm130 mm80 × 40xIx​ = ?

A 200 mm × 200 mm plate has a rectangular cut-out 80 mm wide and 40 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 = 200 mmh = 200 mmcut-out: 80 × 40 mmhole centre: y = 130 mm
Ix = × 10⁶ mm⁴
6.Hard
2002026012xM = 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 = 200 mmtf = 20 mmtw = 12 mmhw = 260 mmM = 50 kN·m
σtop = MPa

Answer key

  1. 1. ȳ = 148.7 mm
  2. 2. ȳ = 126.4 mm
  3. 3. Ix = 16.39 × 10⁶ mm⁴
  4. 4. Ix = 31.87 × 10⁶ mm⁴
  5. 5. Ix = 129.8 × 10⁶ mm⁴
  6. 6. σtop = 68.52 MPa

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