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 mm300 mm150 mm72 mmØ50x̄ = ?

A 240 mm × 300 mm plate has a circular hole of diameter 50 mm whose centre is 72 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 240 mmh = 300 mmd = 50 mmhole centre: x = 72 mm
x̄ = mm
2.Easy
2202028012ȳ = ?dimensions in mm

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

bf = 220 mmtf = 20 mmtw = 12 mmhw = 280 mm
ȳ = mm
3.Medium
1402012012xdimensions 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 = 12 mmhw = 120 mm
Ix = × 10⁶ mm⁴
4.Medium
200 mm240 mm156 mmØ40xIx​ = ?

A 200 mm × 240 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 156 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 200 mmh = 240 mmd = 40 mmhole centre: y = 156 mm
Ix = × 10⁶ mm⁴
5.Hard
170300222801014xdimensions in mm

A welded I-section has a top flange 170 × 22 mm, a web 280 mm high and 14 mm thick, and a bottom flange 300 × 10 mm (width × thickness). Find its second moment of area Ix about the horizontal axis x through its centroid.

top flange: 170 × 22 mmweb: 14 × 280 mmbottom flange: 300 × 10 mm
Ix = × 10⁶ mm⁴
6.Hard
2202030020xM = 20 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 20 kN·m. Find the bending stress σbottom at the bottom edge.

bf = 220 mmtf = 20 mmtw = 20 mmhw = 300 mmM = 20 kN·m
σbottom = MPa

Answer key

  1. 1. x̄ = 121.3 mm
  2. 2. ȳ = 225.1 mm
  3. 3. Ix = 6.481 × 10⁶ mm⁴
  4. 4. Ix = 228.6 × 10⁶ mm⁴
  5. 5. Ix = 172.6 × 10⁶ mm⁴
  6. 6. σbottom = 39.53 MPa

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