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
1602526012ȳ = ?dimensions in mm

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

bf = 160 mmtf = 25 mmtw = 12 mmhw = 260 mm
ȳ = mm
2.Easy
100 mm240 mm84 mmØ40ȳ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 84 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 100 mmh = 240 mmd = 40 mmhole centre: y = 84 mm
ȳ = mm
3.Medium
120100t = 12xdimensions in mm

A channel section lies with its open side up: a base plate 120 mm wide with two upright legs, 100 mm high overall. Base and legs are all 12 mm thick. Find its second moment of area Ix about the horizontal axis x through its centroid.

b = 120 mmh = 100 mmt = 12 mm
Ix = × 10⁶ mm⁴
4.Medium
1402020014xdimensions in mm

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

bf = 140 mmtf = 20 mmtw = 14 mmhw = 200 mm
Ix = × 10⁶ mm⁴
5.Hard
1801528016xM = 40 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 40 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 180 mmtf = 15 mmtw = 16 mmhw = 280 mmM = 40 kN·m
σbottom = MPa
6.Hard
150180181601214xdimensions in mm

A welded I-section has a top flange 150 × 18 mm, a web 160 mm high and 14 mm thick, and a bottom flange 180 × 12 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 150 × 18 mmweb: 14 × 160 mmbottom flange: 180 × 12 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 210.1 mm
  2. 2. ȳ = 122 mm
  3. 3. Ix = 3.521 × 10⁶ mm⁴
  4. 4. Ix = 26.37 × 10⁶ mm⁴
  5. 5. σbottom = 118.5 MPa
  6. 6. Ix = 41.82 × 10⁶ mm⁴

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