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
xD = 280d = 272dimensions in mm

A circular tube has outside diameter D = 280 mm and inside diameter d = 272 mm. Find its second moment of area Ix about a diameter.

D = 280 mmd = 272 mm
Ix = × 10⁶ mm⁴
2.Easy
xD = 110dimensions in mm

A solid circular bar has diameter D = 110 mm. Find its second moment of area Ix about a diameter.

D = 110 mm
Ix = × 10⁶ mm⁴
3.Medium
2001528010xdimensions in mm

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

bf = 200 mmtf = 15 mmtw = 10 mmhw = 280 mm
Ix = × 10⁶ mm⁴
4.Medium
150 mm200 mm80 mmØ60xIx​ = ?

A 150 mm × 200 mm plate has a circular hole of diameter 60 mm on its vertical centre line, with its centre 80 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 200 mmd = 60 mmhole centre: y = 80 mm
Ix = × 10⁶ mm⁴
5.Hard
1001028012xM = 15 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 15 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 100 mmtf = 10 mmtw = 12 mmhw = 280 mmM = 15 kN·m
σtop = MPa
6.Hard
2602530020xsagging 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 120 MPa in compression. Find the largest sagging bending moment Mallow the beam can carry.

bf = 260 mmtf = 25 mmtw = 20 mmhw = 300 mmσt,allow = 35 MPaσc,allow = 120 MPa
Mallow = kN·m

Answer key

  1. 1. Ix = 33.03 × 10⁶ mm⁴
  2. 2. Ix = 7.187 × 10⁶ mm⁴
  3. 3. Ix = 49.86 × 10⁶ mm⁴
  4. 4. Ix = 98.12 × 10⁶ mm⁴
  5. 5. σtop = 45.89 MPa
  6. 6. Mallow = 19.06 kN·m

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