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 = 240d = 204dimensions in mm

A circular tube has outside diameter D = 240 mm and inside diameter d = 204 mm. Find its second moment of area Ix about a diameter.

D = 240 mmd = 204 mm
Ix = × 10⁶ mm⁴
2.Easy
3003012018ȳ = ?dimensions in mm

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

bf = 300 mmtf = 30 mmtw = 18 mmhw = 120 mm
ȳ = mm
3.Medium
200 mm150 mm52.5 mmØ30xIx​ = ?

A 200 mm × 150 mm plate has a circular hole of diameter 30 mm on its 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 = 200 mmh = 150 mmd = 30 mmhole centre: y = 52.5 mm
Ix = × 10⁶ mm⁴
4.Medium
1602010018xdimensions 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 = 18 mmhw = 100 mm
Ix = × 10⁶ mm⁴
5.Hard
1904002210xM = 40 kN·mdimensions in mm

A symmetric I-section has flanges 190 mm wide and 22 mm thick, an overall depth of 400 mm and a web 10 mm thick. It carries a bending moment of 40 kN·m about the axis x. Find the size of the bending stress σj at the junction of the web and the top flange.

B = 190 mmH = 400 mmtf = 22 mmtw = 10 mmM = 40 kN·m
σj = MPa
6.Hard
160190162201416xdimensions in mm

A welded I-section has a top flange 160 × 16 mm, a web 220 mm high and 16 mm thick, and a bottom flange 190 × 14 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 160 × 16 mmweb: 16 × 220 mmbottom flange: 190 × 14 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. Ix = 77.85 × 10⁶ mm⁴
  2. 2. ȳ = 120.5 mm
  3. 3. Ix = 55.84 × 10⁶ mm⁴
  4. 4. Ix = 5.754 × 10⁶ mm⁴
  5. 5. σj = 21.16 MPa
  6. 6. Ix = 86.34 × 10⁶ mm⁴

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