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
2201510014ȳ = ?dimensions in mm

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

bf = 220 mmtf = 15 mmtw = 14 mmhw = 100 mm
ȳ = mm
2.Easy
b = 160h = 200dimensions in mm

A rectangular section has width b = 160 mm and height h = 200 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 160 mmh = 200 mm
Ibase = × 10⁶ mm⁴
3.Medium
150 mm150 mm105 mmØ30xIx​ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 105 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 = 105 mm
Ix = × 10⁶ mm⁴
4.Medium
1504601610xdimensions in mm

A symmetric I-section has flanges 150 mm wide and 16 mm thick, an overall depth of 460 mm and a web 10 mm thick. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 150 mmH = 460 mmtf = 16 mmtw = 10 mm
Ix = × 10⁶ mm⁴
5.Hard
1203014014xM = 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 bending stress σbottom at the bottom edge.

bf = 120 mmtf = 30 mmtw = 14 mmhw = 140 mmM = 5 kN·m
σbottom = MPa
6.Hard
1804601410xM = 80 kN·mdimensions in mm

A symmetric I-section has flanges 180 mm wide and 14 mm thick, an overall depth of 460 mm and a web 10 mm thick. It carries a bending moment of 80 kN·m about the axis x. Find the size of the bending stress σj at the junction of the web and the top flange.

B = 180 mmH = 460 mmtf = 14 mmtw = 10 mmM = 80 kN·m
σj = MPa

Answer key

  1. 1. ȳ = 90.37 mm
  2. 2. Ibase = 426.7 × 10⁶ mm⁴
  3. 3. Ix = 41.49 × 10⁶ mm⁴
  4. 4. Ix = 302 × 10⁶ mm⁴
  5. 5. σbottom = 49.46 MPa
  6. 6. σj = 54.36 MPa

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