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
200 mm200 mm100 mm150 mmØ50x̄ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 50 mm whose centre is 150 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 200 mmh = 200 mmd = 50 mmhole centre: x = 150 mm
x̄ = mm
2.Easy
150 mm200 mm100 mm45 mmØ40x̄ = ?

A 150 mm × 200 mm plate has a circular hole of diameter 40 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 = 40 mmhole centre: x = 45 mm
x̄ = mm
3.Medium
1201528010xdimensions in mm

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

bf = 120 mmtf = 15 mmtw = 10 mmhw = 280 mm
Ix = × 10⁶ mm⁴
4.Medium
100 mm240 mm168 mmØ60xIx​ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 168 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 = 168 mm
Ix = × 10⁶ mm⁴
5.Hard
200201408xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 35 MPa in tension and 100 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 200 mmtf = 20 mmtw = 8 mmhw = 140 mmσt,allow = 35 MPaσc,allow = 100 MPa
Mallow = kN·m
6.Hard
100 mm200 mm60 mm50 × 20xIx​ = ?

A 100 mm × 200 mm plate has a rectangular cut-out 50 mm wide and 20 mm high, centred on the 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 = 100 mmh = 200 mmcut-out: 50 × 20 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. x̄ = 97.42 mm
  2. 2. x̄ = 76.31 mm
  3. 3. Ix = 42.16 × 10⁶ mm⁴
  4. 4. Ix = 107.2 × 10⁶ mm⁴
  5. 5. Mallow = 5.708 kN·m
  6. 6. Ix = 64.95 × 10⁶ mm⁴

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