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
200 mm200 mm100 mm60 mmØ80x̄ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 80 mm whose centre is 60 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 200 mmh = 200 mmd = 80 mmhole centre: x = 60 mm
x̄ = mm
2.Easy
200 mm200 mm100 mm150 mmØ50x̄ = ?

A 200 mm × 200 mm plate has a circular hole of diameter 50 mm whose centre is 150 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 200 mmh = 200 mmd = 50 mmhole centre: x = 150 mm
x̄ = mm
3.Medium
B = 280H = 400t = 6xdimensions in mm

A hollow rectangular (box) section has outer width B = 280 mm, outer height H = 400 mm and a uniform wall thickness t = 6 mm. Find its radius of gyration r about the horizontal centroidal axis.

B = 280 mmH = 400 mmt = 6 mm
r = mm
4.Medium
100 mm200 mm140 mmØ30xIx​ = ?

A 100 mm × 200 mm plate has a circular hole of diameter 30 mm on its vertical centre line, with its centre 140 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 200 mmd = 30 mmhole centre: y = 140 mm
Ix = × 10⁶ mm⁴
5.Hard
1603001210xM = 100 kN·mdimensions in mm

A symmetric I-section has flanges 160 mm wide and 12 mm thick, an overall depth of 300 mm and a web 10 mm thick. It carries a bending moment of 100 kN·m about the axis x. Find the size of the bending stress σj at the junction of the web and the top flange.

B = 160 mmH = 300 mmtf = 12 mmtw = 10 mmM = 100 kN·m
σj = MPa
6.Hard
2402028016xM = 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 bending stress σbottom at the bottom edge.

bf = 240 mmtf = 20 mmtw = 16 mmhw = 280 mmM = 5 kN·m
σbottom = MPa

Answer key

  1. 1. x̄ = 105.7 mm
  2. 2. x̄ = 97.42 mm
  3. 3. r = 153.5 mm
  4. 4. Ix = 65.45 × 10⁶ mm⁴
  5. 5. σj = 142 MPa
  6. 6. σbottom = 13.34 MPa

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