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
120 mm200 mm140 mmØ40ȳ = ?

A 120 mm × 200 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 140 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 120 mmh = 200 mmd = 40 mmhole centre: y = 140 mm
ȳ = mm
2.Easy
1801518016ȳ = ?dimensions in mm

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

bf = 180 mmtf = 15 mmtw = 16 mmhw = 180 mm
ȳ = mm
3.Medium
2602526012xdimensions in mm

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

bf = 260 mmtf = 25 mmtw = 12 mmhw = 260 mm
Ix = × 10⁶ mm⁴
4.Medium
120 mm150 mm97.5 mmØ30xIx​ = ?

A 120 mm × 150 mm plate has a circular hole of diameter 30 mm on its 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 = 120 mmh = 150 mmd = 30 mmhole centre: y = 97.5 mm
Ix = × 10⁶ mm⁴
5.Hard
180280146xM = 150 kN·mdimensions in mm

A symmetric I-section has flanges 180 mm wide and 14 mm thick, an overall depth of 280 mm and a web 6 mm thick. It carries a bending moment of 150 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 = 180 mmH = 280 mmtf = 14 mmtw = 6 mmM = 150 kN·m
σj = MPa
6.Hard
2401030010xM = 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 = 240 mmtf = 10 mmtw = 10 mmhw = 300 mmM = 40 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 97.79 mm
  2. 2. ȳ = 137.2 mm
  3. 3. Ix = 60.72 × 10⁶ mm⁴
  4. 4. Ix = 33.34 × 10⁶ mm⁴
  5. 5. σj = 194.4 MPa
  6. 6. σbottom = 160.5 MPa

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