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
120101808ȳ = ?dimensions in mm

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

bf = 120 mmtf = 10 mmtw = 8 mmhw = 180 mm
ȳ = mm
2.Easy
xD = 190d = 182dimensions in mm

A circular tube has outside diameter D = 190 mm and inside diameter d = 182 mm. Find its second moment of area Ix about a diameter.

D = 190 mmd = 182 mm
Ix = × 10⁶ mm⁴
3.Medium
xD = 210d = 198dimensions in mm

A circular tube has outside diameter D = 210 mm and inside diameter d = 198 mm. Find its radius of gyration r about the horizontal centroidal axis.

D = 210 mmd = 198 mm
r = mm
4.Medium
200 mm200 mm80 mmØ50xIx​ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 50 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 = 200 mmh = 200 mmd = 50 mmhole centre: y = 80 mm
Ix = × 10⁶ mm⁴
5.Hard
1401022018xM = 10 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 10 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 140 mmtf = 10 mmtw = 18 mmhw = 220 mmM = 10 kN·m
σtop = MPa
6.Hard
110160162201414xdimensions in mm

A welded I-section has a top flange 110 × 16 mm, a web 220 mm high and 14 mm thick, and a bottom flange 160 × 14 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 110 × 16 mmweb: 14 × 220 mmbottom flange: 160 × 14 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 133.2 mm
  2. 2. Ix = 10.11 × 10⁶ mm⁴
  3. 3. r = 72.16 mm
  4. 4. Ix = 132.2 × 10⁶ mm⁴
  5. 5. σtop = 30.33 MPa
  6. 6. Ix = 67.25 × 10⁶ mm⁴

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