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
150 mm200 mm100 mm45 mmØ60x̄ = ?

A 150 mm × 200 mm plate has a circular hole of diameter 60 mm whose centre is 45 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 150 mmh = 200 mmd = 60 mmhole centre: x = 45 mm
x̄ = mm
2.Easy
120 mm300 mm150 mm84 mmØ30x̄ = ?

A 120 mm × 300 mm plate has a circular hole of diameter 30 mm whose centre is 84 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 120 mmh = 300 mmd = 30 mmhole centre: x = 84 mm
x̄ = mm
3.Medium
2603016020xdimensions in mm

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

bf = 260 mmtf = 30 mmtw = 20 mmhw = 160 mm
Ix = × 10⁶ mm⁴
4.Medium
120 mm150 mm60 mmØ60xIx​ = ?

A 120 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 = 120 mmh = 150 mmd = 60 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
5.Hard
1601022020xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 60 MPa in tension and 90 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 160 mmtf = 10 mmtw = 20 mmhw = 220 mmσt,allow = 60 MPaσc,allow = 90 MPa
Mallow = kN·m
6.Hard
100 mm300 mm195 mm50 × 50xIx​ = ?

A 100 mm × 300 mm plate has a rectangular cut-out 50 mm wide and 50 mm high, centred on the vertical centre line with its centre 195 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 × 50 mmhole centre: y = 195 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. x̄ = 78.12 mm
  2. 2. x̄ = 59.52 mm
  3. 3. Ix = 27.89 × 10⁶ mm⁴
  4. 4. Ix = 32.36 × 10⁶ mm⁴
  5. 5. Mallow = 21.29 kN·m
  6. 6. Ix = 219 × 10⁶ mm⁴

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