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
240 mm150 mm37.5 mmØ30ȳ = ?

A 240 mm × 150 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 37.5 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 240 mmh = 150 mmd = 30 mmhole centre: y = 37.5 mm
ȳ = mm
2.Easy
b = 300h = 375xdimensions in mm

A rectangular section has width b = 300 mm and height h = 375 mm. Find its elastic section modulus Sx for bending about the horizontal centroidal axis x.

b = 300 mmh = 375 mm
Sx = × 10³ mm³
3.Medium
1201016012xdimensions in mm

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

bf = 120 mmtf = 10 mmtw = 12 mmhw = 160 mm
Ix = × 10⁶ mm⁴
4.Medium
150 mm150 mm52.5 mmØ30xIx​ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 52.5 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 = 52.5 mm
Ix = × 10⁶ mm⁴
5.Hard
100300182101214xdimensions in mm

A welded I-section has a top flange 100 × 18 mm, a web 210 mm high and 14 mm thick, and a bottom flange 300 × 12 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 100 × 18 mmweb: 14 × 210 mmbottom flange: 300 × 12 mm
Ix = × 10⁶ mm⁴
6.Hard
1304402414xM = 50 kN·mdimensions in mm

A symmetric I-section has flanges 130 mm wide and 24 mm thick, an overall depth of 440 mm and a web 14 mm thick. It carries a bending moment of 50 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 = 440 mmtf = 24 mmtw = 14 mmM = 50 kN·m
σj = MPa

Answer key

  1. 1. ȳ = 75.75 mm
  2. 2. Sx = 7031 × 10³ mm³
  3. 3. Ix = 9.441 × 10⁶ mm⁴
  4. 4. Ix = 41.78 × 10⁶ mm⁴
  5. 5. Ix = 74.11 × 10⁶ mm⁴
  6. 6. σj = 28.78 MPa

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