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
120 mm240 mm84 mmØ60ȳ = ?

A 120 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 edge. Find the height ȳ of the centroid above the bottom edge.

b = 120 mmh = 240 mmd = 60 mmhole centre: y = 84 mm
ȳ = mm
2.Easy
2603018018ȳ = ?dimensions in mm

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

bf = 260 mmtf = 30 mmtw = 18 mmhw = 180 mm
ȳ = mm
3.Medium
200 mm150 mm90 mmØ40xIx​ = ?

A 200 mm × 150 mm plate has a circular hole of diameter 40 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 = 200 mmh = 150 mmd = 40 mmhole centre: y = 90 mm
Ix = × 10⁶ mm⁴
4.Medium
2401016020xdimensions in mm

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

bf = 240 mmtf = 10 mmtw = 20 mmhw = 160 mm
Ix = × 10⁶ mm⁴
5.Hard
1401022016xM = 5 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 5 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 140 mmtf = 10 mmtw = 16 mmhw = 220 mmM = 5 kN·m
σtop = MPa
6.Hard
2201024020xhogging Mdimensions in mm

A cast-iron beam has the T-section shown, with the flange on top. The allowable stresses are 50 MPa in tension and 90 MPa in compression. Find the largest hogging bending moment Mallow the beam can carry (give its size).

bf = 220 mmtf = 10 mmtw = 20 mmhw = 240 mmσt,allow = 50 MPaσc,allow = 90 MPa
Mallow = kN·m

Answer key

  1. 1. ȳ = 123.9 mm
  2. 2. ȳ = 164.2 mm
  3. 3. Ix = 55.83 × 10⁶ mm⁴
  4. 4. Ix = 16.76 × 10⁶ mm⁴
  5. 5. σtop = 15.89 MPa
  6. 6. Mallow = 25.7 kN·m

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