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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Name: ____________________   Date: ____________

1.Easy
2601010014ȳ = ?dimensions in mm

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

bf = 260 mmtf = 10 mmtw = 14 mmhw = 100 mm
ȳ = mm
2.Easy
B = 200H = 325t = 18xdimensions in mm

A hollow rectangular (box) section has outer width B = 200 mm, outer height H = 325 mm and a uniform wall thickness t = 18 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 200 mmH = 325 mmt = 18 mm
Ix = × 10⁶ mm⁴
3.Medium
100 mm150 mm45 mmØ50xIx​ = ?

A 100 mm × 150 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 45 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 150 mmd = 50 mmhole centre: y = 45 mm
Ix = × 10⁶ mm⁴
4.Medium
100 mm200 mm140 mmØ30xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 30 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 = 30 mmhole centre: y = 140 mm
Ix = × 10⁶ mm⁴
5.Hard
1803024016xM = 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 = 180 mmtf = 30 mmtw = 16 mmhw = 240 mmM = 50 kN·m
σtop = MPa
6.Hard
200 mm150 mm52.5 mm50 × 40xIx​ = ?

A 200 mm × 150 mm plate has a rectangular cut-out 50 mm wide and 40 mm high, centred on the 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 mmcut-out: 50 × 40 mmhole centre: y = 52.5 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 85.75 mm
  2. 2. Ix = 242.3 × 10⁶ mm⁴
  3. 3. Ix = 25.78 × 10⁶ mm⁴
  4. 4. Ix = 65.45 × 10⁶ mm⁴
  5. 5. σtop = 59.51 MPa
  6. 6. Ix = 54.9 × 10⁶ mm⁴

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