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
2403018010ȳ = ?dimensions in mm

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

bf = 240 mmtf = 30 mmtw = 10 mmhw = 180 mm
ȳ = mm
2.Easy
xD = 250dimensions in mm

A solid circular bar has diameter D = 250 mm. Find its second moment of area Ix about a diameter.

D = 250 mm
Ix = × 10⁶ mm⁴
3.Medium
100180t = 10xdimensions in mm

A channel section lies with its open side up: a base plate 100 mm wide with two upright legs, 180 mm high overall. Base and legs are all 10 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 100 mmh = 180 mmt = 10 mm
Ix = × 10⁶ mm⁴
4.Medium
160202808xdimensions in mm

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

bf = 160 mmtf = 20 mmtw = 8 mmhw = 280 mm
Ix = × 10⁶ mm⁴
5.Hard
240103008xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 60 MPa in tension and 120 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 240 mmtf = 10 mmtw = 8 mmhw = 300 mmσt,allow = 60 MPaσc,allow = 120 MPa
Mallow = kN·m
6.Hard
150 mm150 mm97.5 mm50 × 30xIx​ = ?

A 150 mm × 150 mm plate has a rectangular cut-out 50 mm wide and 30 mm high, centred on the vertical centre line with its centre 97.5 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 150 mmcut-out: 50 × 30 mmhole centre: y = 97.5 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 174 mm
  2. 2. Ix = 191.7 × 10⁶ mm⁴
  3. 3. Ix = 14.46 × 10⁶ mm⁴
  4. 4. Ix = 44.39 × 10⁶ mm⁴
  5. 5. Mallow = 24.71 kN·m
  6. 6. Ix = 41.26 × 10⁶ mm⁴

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