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
3001012018ȳ = ?dimensions in mm

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

bf = 300 mmtf = 10 mmtw = 18 mmhw = 120 mm
ȳ = mm
2.Easy
240 mm200 mm100 mm180 mmØ80x̄ = ?

A 240 mm × 200 mm plate has a circular hole of diameter 80 mm whose centre is 180 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 240 mmh = 200 mmd = 80 mmhole centre: x = 180 mm
x̄ = mm
3.Medium
100 mm240 mm168 mmØ40xIx​ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 40 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 = 100 mmh = 240 mmd = 40 mmhole centre: y = 168 mm
Ix = × 10⁶ mm⁴
4.Medium
1201030010xdimensions 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 = 10 mmhw = 300 mm
Ix = × 10⁶ mm⁴
5.Hard
2603020014xM = 15 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 15 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 260 mmtf = 30 mmtw = 14 mmhw = 200 mmM = 15 kN·m
σbottom = MPa
6.Hard
130290184002410xdimensions in mm

A welded I-section has a top flange 130 × 18 mm, a web 400 mm high and 10 mm thick, and a bottom flange 290 × 24 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 130 × 18 mmweb: 10 × 400 mmbottom flange: 290 × 24 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. ȳ = 97.79 mm
  2. 2. x̄ = 113 mm
  3. 3. Ix = 112 × 10⁶ mm⁴
  4. 4. Ix = 43.1 × 10⁶ mm⁴
  5. 5. σbottom = 74.51 MPa
  6. 6. Ix = 395.6 × 10⁶ mm⁴

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