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 mm180 mmØ60x̄ = ?

A 240 mm × 300 mm plate has a circular hole of diameter 60 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 = 300 mmd = 60 mmhole centre: x = 180 mm
x̄ = mm
2.Easy
b = 220h = 275dimensions in mm

A rectangular section has width b = 220 mm and height h = 275 mm. Find its second moment of area Ibase about the axis along its bottom edge.

b = 220 mmh = 275 mm
Ibase = × 10⁶ mm⁴
3.Medium
150 mm240 mm156 mmØ30xIx​ = ?

A 150 mm × 240 mm plate has a circular hole of diameter 30 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 = 150 mmh = 240 mmd = 30 mmhole centre: y = 156 mm
Ix = × 10⁶ mm⁴
4.Medium
120 mm200 mm60 mmØ60xIx​ = ?

A 120 mm × 200 mm plate has a circular hole of diameter 60 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 = 120 mmh = 200 mmd = 60 mmhole centre: y = 60 mm
Ix = × 10⁶ mm⁴
5.Hard
1801014012xM = 5 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 5 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 180 mmtf = 10 mmtw = 12 mmhw = 140 mmM = 5 kN·m
σtop = MPa
6.Hard
100 mm240 mm96 mm50 × 30xIx​ = ?

A 100 mm × 240 mm plate has a rectangular cut-out 50 mm wide and 30 mm high, centred on the vertical centre line with its centre 96 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmcut-out: 50 × 30 mmhole centre: y = 96 mm
Ix = × 10⁶ mm⁴

Answer key

  1. 1. x̄ = 117.5 mm
  2. 2. Ibase = 1525 × 10⁶ mm⁴
  3. 3. Ix = 171.8 × 10⁶ mm⁴
  4. 4. Ix = 74.24 × 10⁶ mm⁴
  5. 5. σtop = 26.94 MPa
  6. 6. Ix = 114.2 × 10⁶ mm⁴

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