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
120250t = 22ȳ = ?dimensions in mm

An L-shaped angle section has a horizontal leg 120 mm wide and a vertical leg 250 mm high (both measured overall). Both legs are 22 mm thick. Find the height ȳ of the centroid above the bottom edge.

B = 120 mmH = 250 mmt = 22 mm
ȳ = mm
2.Easy
1601526012ȳ = ?dimensions in mm

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

bf = 160 mmtf = 15 mmtw = 12 mmhw = 260 mm
ȳ = mm
3.Medium
300190t = 8xdimensions in mm

A channel section lies with its open side up: a base plate 300 mm wide with two upright legs, 190 mm high overall. Base and legs are all 8 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 300 mmh = 190 mmt = 8 mm
Ix = × 10⁶ mm⁴
4.Medium
200 mm300 mm195 mmØ30xIx​ = ?

A 200 mm × 300 mm plate has a circular hole of diameter 30 mm on its 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 = 200 mmh = 300 mmd = 30 mmhole centre: y = 195 mm
Ix = × 10⁶ mm⁴
5.Hard
1801030012xM = 40 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 40 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 180 mmtf = 10 mmtw = 12 mmhw = 300 mmM = 40 kN·m
σtop = MPa
6.Hard
2602526016xsagging 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 100 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 260 mmtf = 25 mmtw = 16 mmhw = 260 mmσt,allow = 50 MPaσc,allow = 100 MPa
Mallow = kN·m

Answer key

  1. 1. ȳ = 92.9 mm
  2. 2. ȳ = 189.8 mm
  3. 3. Ix = 19.92 × 10⁶ mm⁴
  4. 4. Ix = 448.5 × 10⁶ mm⁴
  5. 5. σtop = 77.6 MPa
  6. 6. Mallow = 17.35 kN·m

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