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 = 280dimensions in mm

A solid circular bar has diameter D = 280 mm. Find its second moment of area Ix about a diameter.

D = 280 mm
Ix = × 10⁶ mm⁴
2.Easy
1001010020ȳ = ?dimensions in mm

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

bf = 100 mmtf = 10 mmtw = 20 mmhw = 100 mm
ȳ = mm
3.Medium
100 mm200 mm140 mmØ50xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 140 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 200 mmd = 50 mmhole centre: y = 140 mm
Ix = × 10⁶ mm⁴
4.Medium
3002012020xdimensions in mm

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

bf = 300 mmtf = 20 mmtw = 20 mmhw = 120 mm
Ix = × 10⁶ mm⁴
5.Hard
1603018010xM = 40 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 40 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 160 mmtf = 30 mmtw = 10 mmhw = 180 mmM = 40 kN·m
σbottom = MPa
6.Hard
120210142102210xdimensions in mm

A welded I-section has a top flange 120 × 14 mm, a web 210 mm high and 10 mm thick, and a bottom flange 210 × 22 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 120 × 14 mmweb: 10 × 210 mmbottom flange: 210 × 22 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. Ix = 301.7 × 10⁶ mm⁴
  2. 2. ȳ = 68.33 mm
  3. 3. Ix = 62.88 × 10⁶ mm⁴
  4. 4. Ix = 11.48 × 10⁶ mm⁴
  5. 5. σbottom = 338.6 MPa
  6. 6. Ix = 76.77 × 10⁶ mm⁴

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