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
B = 300H = 350t = 18xdimensions in mm

A hollow rectangular (box) section has outer width B = 300 mm, outer height H = 350 mm and a uniform wall thickness t = 18 mm. Find its second moment of area Ix about the horizontal centroidal axis x.

B = 300 mmH = 350 mmt = 18 mm
Ix = × 10⁶ mm⁴
2.Easy
240 mm240 mm180 mmØ80ȳ = ?

A 240 mm × 240 mm plate has a circular hole of diameter 80 mm on its vertical centre line, with its centre 180 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 240 mmh = 240 mmd = 80 mmhole centre: y = 180 mm
ȳ = mm
3.Medium
280170t = 12ȳ = ?dimensions in mm

A channel section lies with its open side up: a base plate 280 mm wide with two upright legs, 170 mm high overall. Base and legs are all 12 mm thick. Find the height ȳ of the centroid above the bottom edge.

b = 280 mmh = 170 mmt = 12 mm
ȳ = mm
4.Medium
150 mm240 mm168 mmØ30xIx​ = ?

A 150 mm × 240 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 168 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 150 mmh = 240 mmd = 30 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
5.Hard
1601512018xM = 30 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 30 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 160 mmtf = 15 mmtw = 18 mmhw = 120 mmM = 30 kN·m
σtop = MPa
6.Hard
1305001214xM = 80 kN·mdimensions in mm

A symmetric I-section has flanges 130 mm wide and 12 mm thick, an overall depth of 500 mm and a web 14 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 = 130 mmH = 500 mmtf = 12 mmtw = 14 mmM = 80 kN·m
σj = MPa

Answer key

  1. 1. Ix = 390.8 × 10⁶ mm⁴
  2. 2. ȳ = 114.3 mm
  3. 3. ȳ = 51.07 mm
  4. 4. Ix = 171.1 × 10⁶ mm⁴
  5. 5. σtop = 151.5 MPa
  6. 6. σj = 61.1 MPa

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