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
1403010014ȳ = ?dimensions in mm

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

bf = 140 mmtf = 30 mmtw = 14 mmhw = 100 mm
ȳ = mm
2.Easy
b = 300h = 325dimensions in mm

A rectangular section has width b = 300 mm and height h = 325 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 300 mmh = 325 mm
Ibase = × 10⁶ mm⁴
3.Medium
100 mm240 mm84 mmØ60xIx​ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 84 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmd = 60 mmhole centre: y = 84 mm
Ix = × 10⁶ mm⁴
4.Medium
120 mm150 mm60 mmØ40xIx​ = ?

A 120 mm × 150 mm plate has a circular hole of diameter 40 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 = 120 mmh = 150 mmd = 40 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
5.Hard
200 mm150 mm90 mm30 × 30xIx​ = ?

A 200 mm × 150 mm plate has a rectangular cut-out 30 mm wide and 30 mm high, centred on the vertical centre line with its centre 90 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 150 mmcut-out: 30 × 30 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
6.Hard
2602026010xM = 15 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 15 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 260 mmtf = 20 mmtw = 10 mmhw = 260 mmM = 15 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 98.75 mm
  2. 2. Ibase = 3433 × 10⁶ mm⁴
  3. 3. Ix = 110.4 × 10⁶ mm⁴
  4. 4. Ix = 33.32 × 10⁶ mm⁴
  5. 5. Ix = 55.97 × 10⁶ mm⁴
  6. 6. σbottom = 68.66 MPa

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