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
1602528010ȳ = ?dimensions in mm

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

bf = 160 mmtf = 25 mmtw = 10 mmhw = 280 mm
ȳ = mm
2.Easy
xD = 100dimensions in mm

A solid circular bar has diameter D = 100 mm. Find its second moment of area Ix about a diameter.

D = 100 mm
Ix = × 10⁶ mm⁴
3.Medium
100 mm240 mm144 mmØ50xIx​ = ?

A 100 mm × 240 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 144 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmd = 50 mmhole centre: y = 144 mm
Ix = × 10⁶ mm⁴
4.Medium
100 mm200 mm60 mmØ40xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 60 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 200 mmd = 40 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
5.Hard
15021010170148xdimensions in mm

A welded I-section has a top flange 150 × 10 mm, a web 170 mm high and 8 mm thick, and a bottom flange 210 × 14 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 150 × 10 mmweb: 8 × 170 mmbottom flange: 210 × 14 mm
Ix = × 10⁶ mm⁴
6.Hard
1802028016xM = 50 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 50 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 180 mmtf = 20 mmtw = 16 mmhw = 280 mmM = 50 kN·m
σbottom = MPa

Answer key

  1. 1. ȳ = 229.7 mm
  2. 2. Ix = 4.909 × 10⁶ mm⁴
  3. 3. Ix = 113.7 × 10⁶ mm⁴
  4. 4. Ix = 64.4 × 10⁶ mm⁴
  5. 5. Ix = 37.21 × 10⁶ mm⁴
  6. 6. σbottom = 139.2 MPa

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