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
3002512010ȳ = ?dimensions in mm

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

bf = 300 mmtf = 25 mmtw = 10 mmhw = 120 mm
ȳ = mm
2.Easy
b = 60h = 175dimensions in mm

A rectangular section has width b = 60 mm and height h = 175 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 60 mmh = 175 mm
Ibase = × 10⁶ mm⁴
3.Medium
2001524020xdimensions in mm

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

bf = 200 mmtf = 15 mmtw = 20 mmhw = 240 mm
Ix = × 10⁶ mm⁴
4.Medium
200 mm150 mm60 mmØ60xIx​ = ?

A 200 mm × 150 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 60 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 150 mmd = 60 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
5.Hard
120 mm240 mm156 mm80 × 40xIx​ = ?

A 120 mm × 240 mm plate has a rectangular cut-out 80 mm wide and 40 mm high, centred on the vertical centre line with its centre 156 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 120 mmh = 240 mmcut-out: 80 × 40 mmhole centre: y = 156 mm
Ix = × 10⁶ mm⁴
6.Hard
1601020012xM = 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 = 160 mmtf = 10 mmtw = 12 mmhw = 200 mmM = 50 kN·m
σtop = MPa

Answer key

  1. 1. ȳ = 122.5 mm
  2. 2. Ibase = 107.2 × 10⁶ mm⁴
  3. 3. Ix = 53.11 × 10⁶ mm⁴
  4. 4. Ix = 54.91 × 10⁶ mm⁴
  5. 5. Ix = 133.1 × 10⁶ mm⁴
  6. 6. σtop = 182.8 MPa

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