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
1602022010ȳ = ?dimensions in mm

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

bf = 160 mmtf = 20 mmtw = 10 mmhw = 220 mm
ȳ = mm
2.Easy
200 mm240 mm120 mm50 mmØ40x̄ = ?

A 200 mm × 240 mm plate has a circular hole of diameter 40 mm whose centre is 50 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 200 mmh = 240 mmd = 40 mmhole centre: x = 50 mm
x̄ = mm
3.Medium
100 mm150 mm90 mmØ30xIx​ = ?

A 100 mm × 150 mm plate has a circular hole of diameter 30 mm on its 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 = 100 mmh = 150 mmd = 30 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
4.Medium
300252608xdimensions in mm

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

bf = 300 mmtf = 25 mmtw = 8 mmhw = 260 mm
Ix = × 10⁶ mm⁴
5.Hard
100 mm300 mm180 mm50 × 30xIx​ = ?

A 100 mm × 300 mm plate has a rectangular cut-out 50 mm wide and 30 mm high, centred on the vertical centre line with its centre 180 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 300 mmcut-out: 50 × 30 mmhole centre: y = 180 mm
Ix = × 10⁶ mm⁴
6.Hard
1002012016xM = 20 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 20 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 100 mmtf = 20 mmtw = 16 mmhw = 120 mmM = 20 kN·m
σtop = MPa

Answer key

  1. 1. ȳ = 181.1 mm
  2. 2. x̄ = 101.3 mm
  3. 3. Ix = 27.92 × 10⁶ mm⁴
  4. 4. Ix = 45.17 × 10⁶ mm⁴
  5. 5. Ix = 223.5 × 10⁶ mm⁴
  6. 6. σtop = 123.5 MPa

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