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
280251808ȳ = ?dimensions in mm

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

bf = 280 mmtf = 25 mmtw = 8 mmhw = 180 mm
ȳ = mm
2.Easy
18090t = 14x̄ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 180 mm wide and a vertical leg 90 mm high (both measured overall). Both legs are 14 mm thick. Find the distance x̄ of the centroid from the left (outer) edge of the vertical leg.

B = 180 mmH = 90 mmt = 14 mm
x̄ = mm
3.Medium
150 mm150 mm97.5 mmØ30xIx​ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 97.5 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 150 mmd = 30 mmhole centre: y = 97.5 mm
Ix = × 10⁶ mm⁴
4.Medium
120 mm300 mm120 mmØ60xIx​ = ?

A 120 mm × 300 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 120 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 120 mmh = 300 mmd = 60 mmhole centre: y = 120 mm
Ix = × 10⁶ mm⁴
5.Hard
150 mm240 mm168 mm30 × 20xIx​ = ?

A 150 mm × 240 mm plate has a rectangular cut-out 30 mm wide and 20 mm high, centred on the 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 = 150 mmh = 240 mmcut-out: 30 × 20 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
6.Hard
2602518016xsagging 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 120 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 260 mmtf = 25 mmtw = 16 mmhw = 180 mmσt,allow = 60 MPaσc,allow = 120 MPa
Mallow = kN·m

Answer key

  1. 1. ȳ = 175 mm
  2. 2. x̄ = 65.36 mm
  3. 3. Ix = 41.78 × 10⁶ mm⁴
  4. 4. Ix = 266.6 × 10⁶ mm⁴
  5. 5. Ix = 171.4 × 10⁶ mm⁴
  6. 6. Mallow = 10.84 kN·m

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